O Sean Pitman
Zachriel
"Sean Pitman" <seanpi...@naturalselection.0catch.com> wrote in message
news:80d0c26f.04012...@posting.google.com...
> "Zachriel" <an...@zachriel.com> wrote in message
news:<100j472...@corp.supernews.com>...
Updates and refinements to the rules:
* Point-mutations now include deletions.
* Snippets now include possible viability of both the snippet and the
remainder of the string.
* Generations defined.
* Examples provided.
> So, what you "start with" is quite important to determining what is
> and what is not beneficial. Then, beyond this, say you start with a short
> sequence, like a two or three-letter word that is defined or recognized as
> beneficial by a much larger system of function, such as a living cell or
> an English language system. Try evolving this short word, one letter at a
> time, into a longer and longer word or phrase. See how far you can go.
> Very quickly you will find yourself running into walls of non-beneficial
> function.
-----------------------
Please review these rules and definitions.
* STRING: a sequence of letters. To be valid and remain extant, it must form
an English word or phrase, e.g. "DOG".
* POPULATION: a collection of valid strings, e.g. "DOG", "CAT IN THE HAT".
* POINT-MUTATIONS: Change from any letter to any other letter, e.g. "BIND"
to "BAND"; or the addition of any letter to the beginning or ending of a
string, e.g. "LIMES" to "SLIMES", or "HONE" to "HONEY"; or the insertion of
any letter at any point in the string, e.g. "LAD" to "LAID"; or the deletion
of any letter at any point in the string, "LIKES" to "LIES". Every single
possible point-mutation must be considered, but if it forms a non-valid
string, it is automatically de-selected.
* SNIPPETS: Any contiguous section of a string, in whole or in part, e.g.
"PPE" from "SLIPPERY". If the snippet forms a valid string, it can become a
member of the population, e.g. "LIP" from "SLIPPERY". The remainder of the
string, minus the snipped portion, can also become a member of the
population if it forms a valid string, e.g. snipping "IPPER" from "SLIPPERY"
leaves "SLY". Every single possible snippet and remainder must be
considered, but if it forms a non-valid string, it is automatically
de-selected. All snippets, valid or not, must be considered for insertions.
* INSERTIONS: An insertion is made by taking any snippet of any string and
inserting it into any valid string at any place in that string, e.g. "RAV"
from "BRAVERY" can be inserted into "TELLING" to form "TRAVELLING". Every
single possible insertion must be considered, but if it forms a non-valid
string, it is automatically de-selected.
* SELECTION: Besides automatic selection, at the end of each generation, we
can de-select any strings we choose leaving a pool of "beneficial" strings.
We can cull the herd.
* CALCULATION: During each generation, we must calculate every possible
point-mutation, snippet and insertion. This number must be less than
"zillions" or the game is over. As I don't know what a zillion is, let us
use a typical number from biology. The number of prokaryotes on Earth is on
the order of 10^30. That's TOO big. Let's use a smaller number, just for a
little challenge. There are about 10^14 prokaryotes living in the typical
human gut. A hundred trillion. That's about right.
* GENERATION: Consider that a population of prokaryotes will reproduce about
every hour. Let's assume that they reproduce a thousand times a year. In a
billion years, that's 10^12 generations. But let's be conservative. Assume
the population only reproduces once a year for a million years, or 10^6
generations. This is certainly less than a "zillion". For the purposes of
our puzzle analogy, we will assume that a reproductive cycle is simultaneous
for the entire population.
Are these rules and definitions acceptable?
Zachriel
"Zachriel" <sp...@zachriel.com> wrote in message
news:105a4iv...@corp.supernews.com...
Has anyone heard from Dr. Pitman lately? I haven't seen a post from him in a
month. I hope I didn't scare him away. I have developed several good
arguments to refute his "zillions of years" assertion based on the preceding
rules, but want to make sure the goalposts don't get moved *before* I post.
Oh well. He probably just got busy.
Zachriel
>
<snip>
>
> Has anyone heard from Dr. Pitman lately? I haven't seen a post from him in
a
> month. I hope I didn't scare him away. I have developed several good
> arguments to refute his "zillions of years" assertion based on the
preceding
> rules, but want to make sure the goalposts don't get moved *before* I
post.
>
> Oh well. He probably just got busy.
>
Sigh. Still no sign of Dr. Pitman on talk.origins. I've decided to make my
response anyway. Please keep in mind that Dr. Pitman is not here to defend
his position or to affirm the ground-rules I laid out previously; however, I
have several interesting and pertinent arguments to make concerning his
"word-games" and will delay no longer.
If you remember, Dr. Pitman had made an analogy between biological evolution
and the possible "evolution" of words by mutation and selection. I had
responded with a poem, "O Sean Pitman", and a story, "Sea of Beneficence".
We know that a pathway exists, but he insisted that I must calculate every
possible mutation and recombination involved in evolving my bit of doggerel.
His own, ahem, calculations indicated it would take "zillions of years."
I have broken my response down into several pieces for the convenience of
the reader. Remember, I had warned Dr. Pitman to "beware a war of words,"
but to no avail.
"Statistically impossible"
The Limit of Cats and Dogs
Just a Dog
Cats and Dogs
The Menagerie
"You simply cannot"
A Pond of Doggerel
The Blind Pig and the Acorn
What can I say?
Zillions of Sean Pitman's
"Stepping stones"
Malthusian Catastrophe
Mass Extinction
Our P's and Q's
A Zillion Roads Diverged
"Start with a meaningful English word"
Serendipity
Elementary Arithmetic, My Dear Pitman
A Big Fish in a Little Pond
Meaning
"There are 8,031,810,176 potential 7-letter words"
The Proof is in the Pudding
The Pudding in the Pond
Zachriel's Special Pudding Recipe
Notes for the Cook
Ingredients
You can also read the latest version of this post on the web at
http://www.zachriel.com/mutagenation/
There is also a software package available on the website called the "Word
Mutagenator" that actually mutates and recombines words according to the
Extended Rules (requires VBA6, included in Office 2000 and Excel 2000).
Zachriel
"Sean Pitman" <seanpi...@naturalselection.0catch.com> wrote
> "Zachriel" <an...@zachriel.com>
> START with a MEANINGFUL ENGLISH WORD
> start with a meaningful English word and then add to or
> change that word so that it makes both meaningful and beneficial sense
> in a given situation/environment. At first such a game is fairly easy
> to do. But, very quickly you get to a point where any more additions
> or changes become very difficult without there being significant
> changes happening that are "just right". . . The same thing
> happens with genes and proteins.
Sean Pitman's "meaningful words".
http://tinyurl.com/ysfka
-----------------
SERENDIPITY
We have calculated every single possible mutation in every single
generation, but is this really necessary? Perhaps, we could just try half
the number, or 1% of the number, or 1% of 1% of the number.
Consider L=1000 such that M=10^9. If the rate of mutation in a population of
10^14 is just one in a million, we will see 10^8 mutations per generation.
Assuming we are looking for one very particular and fortuitous mutation, and
all others are to be discarded as useless, we can still expect to find that
one mutation occurring once every ten generations or so. We are bound to
have beneficial mutations after enough generations; indeed, in a population
of 10^14 we will see a myriad of interesting mutations in every generation.
And perhaps that one singular mutation isn't required. Perhaps, it may never
be considered as there are many synonyms and phrases which may have the same
meaning.
* Consequently, we have overstated the computational difficulty by many,
many orders of magnitude.
-------------
ELEMENTARY ARITHMETIC, MY DEAR PITMAN
> It all works much like the English language system or any other
> language system. . . . In the English language system
> there are around 23,109 meaningful 7-letter words. This seems like a
> lot until one realizes that there are 8,031,810,176 potential 7-letter
> words out there in 7-letter sequence space. This ratio of meaningful
> vs. potential 7-letter words gives us 1 meaningful 7-letter word for
> every 347,561 meaningless 7-letter words. What this means is that on
> average each meaningful 7-letter word is surrounded like an island by
> well over 300,000 meaningless words.
http://tinyurl.com/2p3hr
The root of Sean Pitman's argument is this:
x = number of letters.
N(x) = number of valid English words with x letters.
M(x) = number of arrangements of x letters whether valid or not.
From this he calculates the chance of 'evolving' a word with x letters is
N/M, which for seven-letter words is about 1 in 300,000. Of note, he hasn't
included seven-letter phrases, e.g. "the cat", but no matter.
Let's try a slightly different problem. Consider a dictionary of 100,000
words. How many possible thousand-word essays or poems or lists can we form
from this dictionary? Well, the answer is 100,000^1000 or 10^5000. This is a
number larger than all the particles in the universe.
* This is very excellent news for those in the language-arts, indeed!
But is this how evolution works? Of course not. Evolution works by tinkering
with what is already there. We only need to count the number of mutations
available at any one time, make a selection or a limited number of
selections, then repeat the procedure. This will not result in a complete
search of the available options. We may never be able to evolve from one
particular seven-letter word to another particular seven-letter word.
However, that does not mean that all available pathways are unavailable, as
we have shown repeatedly.
----------------------------------
A BIG FISH in a LITTLE POND
The Sea of Beneficence
http://tinyurl.com/39jz9
We have successfully shown that the number of possible mutations is very low
compared to the population of our little pond, so much so, that we can
expect virtually every single beneficial and non-valid mutation to be tried
in each and every generation.
We purposefully chose a very, very small pond, on the order of the number of
prokaryotes in the human gut (10^14). We didn't even count the number of
base-pairs for those prokaryotes (10^20), or count the base-pairs in the
bigger pond of the prokaryote oceans (10^36), or allow our computations to
extend over a billion years (10^12 generations), for a total computational
capacity on the order of 10^48; and considering all our simplifying
assumptions, this is counting way, way above the number of computations
actually required.
In any case, we can always have the Grim Reaper drop by with a huge
extinction event, a Malthusian Catastrophe, and wipe out huge numbers of
unneeded words and phrases. Then we can create a whole new poem or
essay--like the extinction of dinosaurs making room for mammals. In fact, we
can constantly evolve new ecosystems as long as they fit within our pond.
And, of course, there may be more than one pond in the world. Indeed, each
self-reproducing species is a genetic world unto itself. (And perhaps our
analogy illustrates why speciation, that is, the segregation of gene-pools,
is so prevalent in nature.)
------------
MEANING
We have shown that random mutation with selection allows the 'evolution' of
a bit of doggerel -- a verse in iambic pentameter, complete with allusions,
imagery and syntax, contributing to a unified whole, communicating a
specific message. This contradicts the claim made by Sean Pitman that there
exist "walls of non-beneficial function", that is, "significant gaps of
neutral or even detrimental meaning/function", and that it would take
"zillions of years" to sort through all the non-beneficial possibilities.
Sean Pitman's use of the word "zillions" had immediately indicated to me
that he had not bothered to calculate the number of permutations involved,
and that he probably had conceptual problems with very large numbers --
-- a classic argument from incredulity founded on ignorance.
Now, does any of this really mean anything to the study of biology? Heck no!
Are you kidding? Though both genetics and our word-game display features of
information networks, we must be careful about extrapolating between the
systems. But to those who would assert that complex order can't arise from
random mutation (with selection), let this be a warning.
"Beware a war of words, ere you err."
O Sean Pitman
http://tinyurl.com/yqhb3
Zachriel
I'm posting the core code from "The Mutator" and "The Mutagenator" for those
that don't have access to VBA6 (included in Office 2000 and Excel 2000).
Don't forget, you can also find this information on the web at
http://www.zachriel.com/mutagenation/Pudding.asp
'----------------------
'THE MUTATOR
'for each Word in population
'DELETE MUTATION
For i = 0 To lengthWord - 1
Mutation = Left(Word, i) & Right(Word, lengthWord - i - 1)
Call Validate(Mutation)
Next i
'POINT MUTATION
For i = 0 To lengthWord - 1
For j = 97 To 122 ' from a to z
Mutation = Left(Word, i) & Chr(j) & Right(Word, lengthWord - i - 1)
Call Validate(Mutation)
Next j
Next i
'INSERT MUTATION
For i = 0 To lengthWord
For j = 97 To 122
Mutation = Left(Word, i) & Chr(j) & Right(Word, lengthWord - i)
Call Validate(Mutation)
Next j
Next i
'SNIP MUTATIONS
'every snippet of every length
For i = 1 To lengthWord
For j = 1 To lengthWord - i + 1
'REMAINDERS (Snip deletes)
Mutation = Left(Word, i - 1) & Right(Word, lengthWord - i - j + 1)
Call Validate(Mutation)
'SNIPPETS
Snippet = Mid(Word, i, j)
Call Validate(Snippet)
'RECOMBINATIONS
'for every point in every word in population
For p = loPop To hiPop
Insert = Pop(p)
lengthInsert = Len(Insert)
For q = 0 To lengthInsert
Mutation = Left(Insert, q) & Snippet & Right(Insert,
lengthInsert - q
Call Validate(Mutation)
Next q
Next p
Next j
Next i
'------------------------
'MUTAGENATOR
'for a random Word in population
'Random for Mutation or Recombination
'(reCombine set by form slider)
If Rnd < reCombine / 100 Then
'MUTATIONS
'Random type of Mutation
c = Random(1, 5)
Select Case c
Case 1 'Delete Mutation
i = Random(0, lengthWord - 1)
Mutation = Left(Word, i) & Right(Word, lengthWord - i - 1)
Case 2 'Point Mutation
i = Random(0, lengthWord - 1)
j = Random(97, 122)
Mutation = Left(Word, i) & Chr(j) & Right(Word, lengthWord - i - 1)
Case 3 'Insert Mutation
i = Random(0, lengthWord)
j = Random(97, 122)
Mutation = Left(Word, i) & Chr(j) & Right(Word, lengthWord - i)
Case 4 'Remainders
i = Random(1, lengthWord)
j = Random(1, lengthWord - i + 1)
Mutation = Left(Word, i - 1) & Right(Word, lengthWord - i - j + 1)
Case 5 'Snippets
i = Random(1, lengthWord)
j = Random(1, lengthWord - i + 1)
Mutation = Mid(Word, i, j)
End Select
Else
'RECOMBINATIONS
i = Random(1, lengthWord)
j = Random(1, lengthWord - i + 1)
Snippet = Mid(Word, i, j) 'Take a snippet from Word
'Select another word from existing population
p = Random(loPop, hiPop) Insert = Pop(p)
lengthInsert = Len(Insert)
'Pick a random point in this subject word
q = Random(0, lengthInsert)
Mutation = Left(Insert, q) & Snippet & Right(Insert, lengthInsert - q)
End If
call Validate(Mutation)
'(Validate checks if Mutation is in Dictionary and not already in
population.)
Sean Pitman
Well Zach, I must have really gotten to you. It seems as you have
devoted an entire website to trying to counter my arguments. I am
truly flattered.
But, alas, you make several serious mistakes in your assumptions and
calculations. Now I might be wrong here, but it seems to me that one
of the biggest mistakes you make on your website is your inaccurate
calculation of sequence space for a given level of complexity or
sequence length. For example, you wrote:
"Now, our Creationist claims that anything over seven-letters has
millions of possible permutations. This is clearly incorrect. Our
upper-limit M for 20-letters (which might be a bunch of small words, a
few larger ones, or a mixture of phrases and words) is 8,000."
I have read your website a couple of times now and I fail to see how
you could possibly think that a 7-letter sequence has only 8,000
possible permutations. Clearly, the total number of permutations of a
7-letter sequence is 27^7 or 10,460,353,203 (calculation is based on
the 26 letters of the alphabet plus a space for 27 possible characters
per position). Now, 10 billion is way more than 8,000.
It seems that despite my previous explanation of this very point, you
continue to think you can join various words end-to-end without
considering the other possible ways that sequences may be joined or
mutated. You write:
" Now consider two words, "cat" and "dog". Create a new string for
consideration (not meant to be an actual mutation, just an aid in
computation), with a space at the beginning and end of each word, "
cat dog " (consistent with our new definition of L). We can count
each of the point-mutations on the combined string and use this to
calculate the sum of the number for each of the strings separately."
By doing this you actually think to assume that the potential sequence
space for 7-letter sequences is less than 8,000? Come on now man.
This simply makes no sense to me at all, nor do any other evolutionary
scenarios that even evolutionists have published in peer reviewed
journals work like this. Perhaps it would help you a great deal to
read up on a paper published in Nature by Lenski et. al., entitled
"The evolutionary origin of complex features." (Reference listed below
with a link to my discussion about of it). You will note that at
least Lenski's computer program assumed the correct size of sequence
space in their calculations, which you do not.
However, you did get one thing right. You are correct in noting that
a larger population of evolving sequences is much faster at finding a
rare beneficial sequence in sequence space as compared to a smaller
population. For example, if the ratio of beneficial vs.
non-beneficial were 1 in 1 million, a single evolving phrase would
have to take 1 million random walk steps on average to find a
"correct" sequence. However, a million individuals evolving at the
same time would find a "correct" sequence in just a few mutational
generations. Certainly then the problems for evolution could be
solved by simply increasing the population - right? The problem for
this little thought is the fact that a given environment can only
support a limited number of genomes. Very quickly this limit is
reached and higher levels of specified complexity (i.e. longer minimum
sequence lengths with high specificity for given types of functions)
create exponentially growing gaps that a fixed population size simply
cannot keep up with this side of "zillions" of years (i.e., trillions
upon trillions upon trillions of years. If you want the actual
numbers and don't like the word "zillions" you can see how my
calculations were done both in this forum by searching for my name and
on my own website).
Also, as an aside, have you ever thought that if your computer program
worked as you present it as working that it could basically evolve
extremely complex meaningful works of English language composition in
very short order? Certainly, if it can evolve very meaningful phrases
that are hundreds and even thousands of letters long in very short
order, you could basically get your little computer program to evolve
all kinds of very helpful computer software programs from scratch
without the help of human programmers. You could also get you
computer to write incredible works of poetry and literature all by
itself. You're rich my man, RICH! I can't wait to see your face on
the next cover of Fortune Magazine! ; )
Oh, and one last thing. Are you really confused by my use of the word
"zillions" for numbers greater than trillions upon trillions upon
trillions - say for numbers greater than 10^50? Please . . .
Sean
www.naturalselection.0catch.com
Lenski, Richard, Ofria, Charles, Pennock, Robert and Adami, Christoph.
"The evolutionary origin of complex features." Nature, 8 May 2003,
vol. 423, p.130.
http://naturalselection.0catch.com/Files/computerevolution.html
Zachriel
"Sean Pitman" <seanpi...@naturalselection.0catch.com> wrote in message
news:80d0c26f.0404...@posting.google.com...
> "Zachriel" <sp...@zachriel.com> wrote in message
news:<69udnb3Ae66...@adelphia.com>...
>
> Well Zach, I must have really gotten to you. It seems as you have
> devoted an entire website to trying to counter my arguments. I am
> truly flattered.
Actually, it is important to debunk these sorts of arguments.
> But, alas, you make several serious mistakes in your assumptions and
> calculations.
Let's see how specific you are about these so-called mistakes.
> Now I might be wrong here, but it seems to me that one
> of the biggest mistakes you make on your website is your inaccurate
> calculation of sequence space for a given level of complexity or
> sequence length. For example, you wrote:
>
> > Now, our Creationist claims that anything over seven-letters has
> > millions of possible permutations. This is clearly incorrect. Our
> > upper-limit M for 20-letters (which might be a bunch of small words,
> > a few larger ones, or a mixture of phrases and words) is 8,000."
>
> I have read your website a couple of times now and I fail to see how
> you could possibly think that a 7-letter sequence has only 8,000
> possible permutations. Clearly, the total number of permutations of a
> 7-letter sequence is 27^7 or 10,460,353,203 (calculation is based on
> the 26 letters of the alphabet plus a space for 27 possible characters
> per position). Now, 10 billion is way more than 8,000.
That's because you have violated the rules of the game. The question isn't
how many possible combinations of *any* seven letters can be made, but how
many mutants can be created under the rules *from* that string (including
point mutations, delete mutations, insert mutations, or recombinations).
Using a 7-letter word as an example, with 27 possible symbols:
You can mutate any of the 7 letters for 7*27 = 189 possible mutations; add a
symbol to either end for 2*27= 54; delete any of the symbols for 7; snip any
portion from the middle of the string for 7+6+5+4+3+2+1 = 7*(7+1)/2 = 28
snippets; any of the remainders from these snips for 28 more; or insert any
of these snippets back into the original word into any of 7+1 positions for
(7+1)*28 = 224. The total is 530 possible mutants.
And among these mutants will be strings which are longer than the original
word. And some of these strings will be valid words.
> It seems that despite my previous explanation of this very point, you
> continue to think you can join various words end-to-end without
> considering the other possible ways that sequences may be joined or
> mutated.
Not true. I considered every possible snippet. I even created a simple piece
of software, the Word Mutator, which actually tries each and every single
mutation, snippet and recombination. Anyone (with VBA6) can try the software
and verify the results. The code is open source.
> You write:
>
> > Now consider two words, "cat" and "dog". Create a new string for
> > consideration (not meant to be an actual mutation, just an aid in
> > computation), with a space at the beginning and end of each word, "
> > cat dog " (consistent with our new definition of L). We can count
> > each of the point-mutations on the combined string and use this to
> > calculate the sum of the number for each of the strings separately.
>
> By doing this you actually think to assume that the potential sequence
> space for 7-letter sequences is less than 8,000?
Assuming 27 symbols, there are 530 possible mutants that can be created from
a seven-letter sequence, including all point mutations, delete mutations,
point insertions, snippets, remainders and recombinations. For twenty-letter
strings the precise answer is 5444.
> Come on now man.
Argument from incredulity. I have provided specific calculations. In
addition, I have used a simple computer program to actually calculate every
mutant for multiple generations to test these calculations. The code is open
source for your inspection. If you can't run the software, you can see the
core code on the website:
http://www.zachriel.com/Mutagenation/Pudding.asp
> This simply makes no sense to me at all, nor do any other evolutionary
> scenarios that even evolutionists have published in peer reviewed
> journals work like this.
It's your game and your analogy. Not mine. I merely point out that your
analogy is faulty and misleading. You are in fact wrong, but not merely
wrong, but completely, absolutely and utterly wrong.
> Perhaps it would help you a great deal to
> read up on a paper published in Nature by Lenski et. al., entitled
> "The evolutionary origin of complex features." (Reference listed below
> with a link to my discussion about of it). You will note that at
> least Lenski's computer program assumed the correct size of sequence
> space in their calculations, which you do not.
I feel the goal-posts shifting. You had claimed that it was impossible to
use the basic rules of mutation and recombination to evolve words longer
than a few letters. In response, I stated specific rules, then created a
piece of software that uses simple mutation and recombination to create
longer and longer words, including such dandies as "denominationalists" at
18 letters in just seven generations.
> However, you did get one thing right. You are correct in noting that
> a larger population of evolving sequences is much faster at finding a
> rare beneficial sequence in sequence space as compared to a smaller
> population. For example, if the ratio of beneficial vs.
> non-beneficial were 1 in 1 million, a single evolving phrase would
> have to take 1 million random walk steps on average to find a
> "correct" sequence. However, a million individuals evolving at the
> same time would find a "correct" sequence in just a few mutational
> generations. Certainly then the problems for evolution could be
> solved by simply increasing the population - right? The problem for
> this little thought is the fact that a given environment can only
> support a limited number of genomes.
The human gut contains about 10^14 organisms, each containing hundreds of
genes. The oceans contain many orders of magnitude more.
> Very quickly this limit is
> reached and higher levels of specified complexity (i.e. longer minimum
> sequence lengths with high specificity for given types of functions)
> create exponentially growing gaps that a fixed population size simply
> cannot keep up with this side of "zillions" of years (i.e., trillions
> upon trillions upon trillions of years.
There are 26^18 number of possible combinations of 18 letters, or
~29,479,510,200,013,900,000,000,000. The dictionary I used for Word
Mutagenation only contains 3786 eighteen-letter words--and yet, within a few
generations, starting from just one-letter strings, using simple rules of
mutation and recombination, and selecting only for the objective quality of
length, the Word Mutator had discovered "denominationalists". What are the
odds? (Hint: It's not 1 in 7,786,452,773,379,270,000,000.)
> If you want the actual
> numbers and don't like the word "zillions" you can see how my
> calculations were done both in this forum by searching for my name and
> on my own website).
Please be specific. I have looked and looked. I have even put many such
links to your "calculations" on my website for the benefit of my visitors.
On the other hand, you have offered nothing in this post so far other than
your incredulity.
> Also, as an aside, have you ever thought that if your computer program
> worked as you present it as working that it could basically evolve
> extremely complex meaningful works of English language composition in
> very short order?
I felt it sufficient to just answer this simple challenge (from one of your
previous posts):
> Just try a little experiment yourself. Start with a short 2 or
> 3-letter word and see how many words you can evolve
> that require greater and greater minimum sequence
> requirements. No doubt you will quickly find
> yourself coming to walls of meaningless or
> non-beneficial potential options that separate you from
> every other meaningful and beneficial option."
I then warned you to "beware a war of words", but you kept insisting.
(The technical problem of building a Phrasenator is objectively determining
what constitutes a meaningful expression--though I have some interesting
ideas on how to accomplish that goal. But what would be the point? I would
be happy to develop a more elaborate program, but you would no doubt simply
move the goal-posts.)
> Certainly, if it can evolve very meaningful phrases
> that are hundreds and even thousands of letters long in very short
> order, you could basically get your little computer program to evolve
> all kinds of very helpful computer software programs from scratch
> without the help of human programmers.
More argument from incredulity. You have not actually presented an actual
argument in this post.
> You could also get you
> computer to write incredible works of poetry and literature all by
> itself. You're rich my man, RICH! I can't wait to see your face on
> the next cover of Fortune Magazine! ; )
Poets don't usually get on the cover of Fortune Magazine.
> Oh, and one last thing. Are you really confused by my use of the word
> "zillions" for numbers greater than trillions upon trillions upon
> trillions - say for numbers greater than 10^50? Please . . .
Please calculate the number of possible mutants that can be created from a
seven-letter word. And don't forget to show your work.
Zachriel
Oops. Miscounted. The "add a symbol to either end" should be "insert a
symbol at any point" for (7+1)*27 = 216. The total for seven-letters should
therefore be 692, and the total for 20-letters should be 5957.
A small error, but should still be corrected. Sorry for the inconvenience.
RobinGoodfellow
> "Zachriel" <sp...@zachriel.com> wrote in message news:<69udnb3Ae66...@adelphia.com>...
Hello again, Sean:
> Well Zach, I must have really gotten to you. It seems as you have
> devoted an entire website to trying to counter my arguments. I am
> truly flattered.
Don't be. Zachriel came across an interesting problem, and dived right
into it. He conducted a thorough empirical investigation of the
problem, came up with concrete results, and presented his conclusions in
a clear, verifiable format. All the while, you have been making
unfounded, mathematically unsound (as has been pointed out to you
repeatedly) proclamations about "mindless processes" and English
sentences, without bothering to look into the matter closer, or produce
any empirical evidence to back up your claim. Zachriel's approach
highlights the spirit of scientific investigation, while yours shows off
the deficiencies of creationism as a means of learning about the world.
I really wouldn't be flatterred if I were you.
> But, alas, you make several serious mistakes in your assumptions and
> calculations. Now I might be wrong here, but it seems to me that one
> of the biggest mistakes you make on your website is your inaccurate
> calculation of sequence space for a given level of complexity or
> sequence length. For example, you wrote:
>
> "Now, our Creationist claims that anything over seven-letters has
> millions of possible permutations. This is clearly incorrect. Our
> upper-limit M for 20-letters (which might be a bunch of small words, a
> few larger ones, or a mixture of phrases and words) is 8,000."
>
> I have read your website a couple of times now and I fail to see how
> you could possibly think that a 7-letter sequence has only 8,000
> possible permutations. Clearly, the total number of permutations of a
> 7-letter sequence is 27^7 or 10,460,353,203 (calculation is based on
> the 26 letters of the alphabet plus a space for 27 possible characters
> per position). Now, 10 billion is way more than 8,000.
Well, either you haven't read Zach's argument carefully enough, or you
haven't understood it. Zachriel was specifying that for a given
7-letter word, the number of possible distinct "neighbors" as the result
of any mutation (whether a random insertion, deletion, point mutation,
domain swap), can be upper bounded by 8,000. The total size of the
sequence space, at any point, is irrelevant: evolutionary processes can
only explore the portions of the sequence space in the local vicinity of
existing words. If, of these, at least one "mindless" mutation proves
to be beneficial, it'll become fixated in the population, opening up a
new area of sequence space to explore. This is how larger and larger
"beneficial" words can be discovered.
Your notions about sequence space size and ratios of beneficial
sequences only become relevant if the words in "word space" have a
(nearly) random uniform distribution. In other words, your notion of
linguistic "neutral gaps" would be applicable if in English, the
8-letter word "baseball" were as likely to appear as the 8-letter words
"allebsba", or "xyzwqrnt". Now, English is hard enough to learn as it
is - but if it were structured like your argument requires it to be, no
one in their right mind would ever attempt to speak it.
> It seems that despite my previous explanation of this very point, you
> continue to think you can join various words end-to-end without
> considering the other possible ways that sequences may be joined or
> mutated. You write:
>
> " Now consider two words, "cat" and "dog". Create a new string for
> consideration (not meant to be an actual mutation, just an aid in
> computation), with a space at the beginning and end of each word, "
> cat dog " (consistent with our new definition of L). We can count
> each of the point-mutations on the combined string and use this to
> calculate the sum of the number for each of the strings separately."
>
> By doing this you actually think to assume that the potential sequence
> space for 7-letter sequences is less than 8,000? Come on now man.
Come on yourself. I've already suggested that you should actually learn
something about stochastic processes if you're going to try to reveal
the statistical impossibility of evolution to the world. (Something
that countless mathematicians, statisticians, computer scientists,
physicists, etc, etc doing active research in the field somehow
consistently fail to notice.) Evolutionary algorithms never need to
explore the entirety of the sequence space - that is exactly why they
work as well as they do. So sequence space size, while trivially easy
to compute, is also almost completely irrelevant.
> This simply makes no sense to me at all, nor do any other evolutionary
> scenarios that even evolutionists have published in peer reviewed
> journals work like this. Perhaps it would help you a great deal to
> read up on a paper published in Nature by Lenski et. al., entitled
> "The evolutionary origin of complex features." (Reference listed below
> with a link to my discussion about of it). You will note that at
> least Lenski's computer program assumed the correct size of sequence
> space in their calculations, which you do not.
Lenski's computer program did not "assume" anything about the size of
the sequence space: Lenski et. al. computed it directly. (After all,
surprising as it may seem, you're not the only person in the world who
knows how to raise k to the n-th power). However, their program knew
nothing about the size or the topology of the sequence space it was
exploring - it proceeded via simple, "mindless" evolutionary processes.
And, strangely enough, it was able to locate every one of the five
beneficial functions (NOT, AND, OR, XOR, and EQ, starting with the
function NAND) of varying complexity in this vast sequence space, as
long as the beneficial aspects of the simpler as well as the more
complex functions were recognized. And if you think these functions
were "designed" specifically to pass this test, I suggest you open an
introductory computer architecture text. You'll find that NAND, NOT,
AND, OR, XOR, and EQ are all very standard boolean circuits, that have
been in extensive use for many decades. NAND is the simplest of these:
in fact, using only multiple combinations of NAND, you can construct any
of the other five circuits - or for that matter, any other boolean
circuit or arithmetic function. Boolean functions were no more designed
to be evolvable from NAND than English words were designed to be
evolvable from individual letters. And yet evolution seems to have no
problem with either one.
> However, you did get one thing right. You are correct in noting that
> a larger population of evolving sequences is much faster at finding a
> rare beneficial sequence in sequence space as compared to a smaller
> population. For example, if the ratio of beneficial vs.
> non-beneficial were 1 in 1 million, a single evolving phrase would
> have to take 1 million random walk steps on average to find a
> "correct" sequence. However, a million individuals evolving at the
> same time would find a "correct" sequence in just a few mutational
> generations. Certainly then the problems for evolution could be
> solved by simply increasing the population - right? The problem for
> this little thought is the fact that a given environment can only
> support a limited number of genomes. Very quickly this limit is
> reached and higher levels of specified complexity (i.e. longer minimum
> sequence lengths with high specificity for given types of functions)
> create exponentially growing gaps that a fixed population size simply
> cannot keep up with this side of "zillions" of years (i.e., trillions
> upon trillions upon trillions of years. If you want the actual
> numbers and don't like the word "zillions" you can see how my
> calculations were done both in this forum by searching for my name and
> on my own website).
Strangely, Zachriel's one computer was able to support the thriving
population of organisms required to evolve some of the very long words
in the English language (e.g. those inhabiting the 26^18 sized "word
space" - exhaustively searching which would have been far beyond the
resources of any modern desktop.) And yet, as Zach pointed out, the
number of micro-organisms inhabiting a single human body exceeds the
amount of RAM in today's best super-computers by several orders of
magnitude, and the number of genetic real-estate within any one of these
organisms will occupy several megabytes. In computational terms, nature
has far more resources than we can ever hope to obtain. And, yet, we've
seen evolutionary computation work successfully with our meager
resources in a variety of contexts. Now, why don't you raise one more
number to the power of some other number and tell us why what we are
observing is impossible?
> Also, as an aside, have you ever thought that if your computer program
> worked as you present it as working that it could basically evolve
> extremely complex meaningful works of English language composition in
> very short order? Certainly, if it can evolve very meaningful phrases
> that are hundreds and even thousands of letters long in very short
> order, you could basically get your little computer program to evolve
> all kinds of very helpful computer software programs from scratch
> without the help of human programmers. You could also get you
> computer to write incredible works of poetry and literature all by
> itself. You're rich my man, RICH! I can't wait to see your face on
> the next cover of Fortune Magazine! ; )
I sincerely hope that the entire last paragraph was a joke. Regardless,
I laughed. But, you've inadvertently hit the nail on the head - if
computers could tell what English phrases (or computer programs, etc.)
were beneficial, evolving them would be a piece of cake! Problem is,
it is notoriously difficult to get computers to understand natural
language - computers still can't recognize synctatically correct
sentences very well, much less make sense of these sentences.
(Consider, for instance, the sentences "Colorless green ideas sleep
furiously", or "Twas brillig, and slithy toves did gyre and gimble in
the wabe" ) Likewise for computer programs: a very famous theoretical
result in computer science establishes that it is impossible to
construct a program that can understand the workings of all other
possible programs: and in practice, the problem of automatically
determining if a program is working right even in a very limited context
is extraordinarily difficult. Thus, the hard part in evolving large
"beneficial" phrases (or programs) is not this "vast sea of neutral
gaps" of yours, but in determining what exactly is beneficial. Of
course, biological evolution does not need to concern itself with such
teleogical minutae, and can chug along merrily, constrained only by the
selecting environment and the underlying laws of physics and chemistry.
> Oh, and one last thing. Are you really confused by my use of the word
> "zillions" for numbers greater than trillions upon trillions upon
> trillions - say for numbers greater than 10^50? Please . . .
Well, honestly, I don't know about Zachriel, but to me, "zillions" is
just annoying. That word should not appear in any serious mathematical
discussion following third grade. But I guess that's a minor quibble,
given all the major ones.
Sean Pitman
>snip <
> > I have read your website a couple of times now and I fail to see how
> > you could possibly think that a 7-letter sequence has only 8,000
> > possible permutations. Clearly, the total number of permutations of a
> > 7-letter sequence is 27^7 or 10,460,353,203 (calculation is based on
> > the 26 letters of the alphabet plus a space for 27 possible characters
> > per position). Now, 10 billion is way more than 8,000.
>
> That's because you have violated the rules of the game. The question isn't
> how many possible combinations of *any* seven letters can be made, but how
> many mutants can be created under the rules *from* that string (including
> point mutations, delete mutations, insert mutations, or recombinations).
>
> Using a 7-letter word as an example, with 27 possible symbols:
>
> You can mutate any of the 7 letters for 7*27 = 189 possible mutations;
That is just for a single point mutation event. The question is
though, what are the odds that any one of these 189 possible mutations
will result in a new meaningful 7-character word or sequence? In
order to answer this question, you must know the density of defined
"words" or meaningful "sequences" in the sequence space of 7-letter
sequences. Only is this way can you determine the average number of
random mutational events (each with 189 new possibilities) it will
take to find a new 7-letter sequence.
Now for a little math: We know how large 7-character sequence space
is in this problem. It is 27^7 or 10,460,353,203. For arguments
sake, lets say that there are somewhere around 40,000 meaningfully
beneficial sequences distributed throughout the 7-letter sequence
space. If true, this would create a ratio of about 1 in 250,000
meaningful vs. meaningless sequences - right? So, what are the odds
that with the first spin of the 7 wheels on your lucky slot machine
that you would hit a winning sequence? Obviously the odds are
slightly less than 1 in 250,000 since you could end up on your
starting sequence 1/189th of the time. Given a population of 1
mutating sequence, the average number of mutational events it would
take to find any one of the 40,000 possible winning sequences is
250,000 random walk mutations.
Of course, if you increased your population size to 250,000 the
average random walk for the entire population already at equilibrium
in sequence space would be just one step/mutational event. The
problem with this, as previously described, is that with each doubling
of the minimum sequence length, the sequence space increases by a
factor of 2. In order for evolution to keep up, one of two things
must happen. Either the total number of beneficial sequences must
also increase by a factor of 2 or the population size must increase by
a factor of two. As one can easily show, it is very unlikely that the
total number of beneficial sequences increases by double, much less a
factor of 2. This means that the population must increase by a factor
of 2 for evolution to avoid stalling out. So, increasing the minimum
sequence size from 7 to 14 characters would require that the
population increase from 250,000 to 62,500,000,000. Now, 62 billion
individuals may be supported in some environments, depending on the
type of individual we are talking about as well as the type of
environment, but I think you may be starting to see my point. What
happens with a doubling from 14 to 28? The population must now go
from 62 billion to 3,906,250,000,000,000,000,000 - or about 4 billion
trillion. Very quickly, you see, we start working our way toward the
impossible "zillions" of individuals needed for evolution to avoid
stalling out this side of "zillions" of years. Or, if you like it
spelled out for you in longer phrasing, something as long as your "O
Sean" poem, would require trillions upon trillion upon trillions upon
trillion upon etc, etc, etc, years to evolve.
There simply is no way around these calculations that I can find, and
you certainly haven't done it by assuming that 189 possibilities for a
given mutational event limits the size of the sequence space that you
must search through. It doesn't. The "189" number is only the number
of possible sequences that you may end up on, on your first try. This
number says nothing about the odds of your finding one of the 40,000
winning sequences on your first try or any other subsequent try.
Unless . . . unless you want to do like Robin Goodfellow has suggested
and cluster all the possible winning sequences in sequence space
around your starting sequence (at least Robin recognizes the size of
sequence space in her calculations, and tries valiantly, though not
very convincingly, to explain how the deck is laterally stacked in
favor of evolutionary progression at higher and higher levels of
specified complexity). If you suggest stacking the deck like this,
then certainly evolution would be a very easy process. However, there
is absolutely nothing in nature that I know of, outside of deliberate
design, that could explain such clustering of all beneficial sequences
in one tiny corner of sequence space. It is much much more likely
that the beneficial sequences will be more evenly distributed in many
widely dispersed clusters or islands of sequences in a rather random
arrangement.
This same argument also seems to defeat the rest of your calculations,
which also calculate only the number of possibilities covered by the
first mutational event and say nothing concerning the average number
of mutational events needed to find one of the relatively rare
meaningful sequences in sequence space.
Sean Pitman
> > I have read your website a couple of times now and I fail to see how
> > you could possibly think that a 7-letter sequence has only 8,000
> > possible permutations. Clearly, the total number of permutations of a
> > 7-letter sequence is 27^7 or 10,460,353,203 (calculation is based on
> > the 26 letters of the alphabet plus a space for 27 possible characters
> > per position). Now, 10 billion is way more than 8,000.
>
> Well, either you haven't read Zach's argument carefully enough, or you
> haven't understood it. Zachriel was specifying that for a given
> 7-letter word, the number of possible distinct "neighbors" as the result
> of any mutation (whether a random insertion, deletion, point mutation,
> domain swap), can be upper bounded by 8,000. The total size of the
> sequence space, at any point, is irrelevant: evolutionary processes can
> only explore the portions of the sequence space in the local vicinity of
> existing words. If, of these, at least one "mindless" mutation proves
> to be beneficial, it'll become fixated in the population, opening up a
> new area of sequence space to explore. This is how larger and larger
> "beneficial" words can be discovered.
You make the extraordinary claim that "the total size of sequence
space, at any point, is irrelevant." This is only true if the deck is
stacked, as you have previously suggested, where there is an
extraordinary clustering of beneficial sequences around your starting
point. Such a stacking of the deck, if it were truly stacked in such
a fashion, as you have suggested, would in itself be evidence of
intelligent design. Outside of such an extremely unlikely stacking of
the deck, the total size of sequence space is indeed very relevant to
the problem. Only by knowing the total size of sequence space relative
to the total size of beneficial sequences will one be able to
determine the likelihood that any one of the "8,000" sequences within
the striking distance of the first mutational event will be
"beneficial."
Actually, knowing the initial striking distance is what is irrelevant
if you don't know the average distance to a new beneficial sequence.
The 8,000 number is really meaningless to knowing the time needed for
a new meaningful sequence to evolve at a given level. All that you
need to know in order to calculate the average time is the total
number of sequences in sequence space, the total number of beneficial
sequences in sequence space (assuming a more average distribution than
you assume for an average starting point), the total number of
evolving sequences in the population, the type of mutation(s), and the
mutation rate. If you know these things you can calculate the average
time needed to evolve a new meaningful sequence at a given level of
complexity (i.e., minimum sequence length).
None of the 8,000 striking distance possibilities have to be
beneficial in order for evolution to proceed - via purely random walk
or "neutral evolution." And, of course, that is what allows evolution
to proceed at lower levels of complexity, but, unfortunately, this is
also what rapidly kills evolutionary potential at higher and higher
levels of complexity. Evolution simply stalls out at higher levels of
functional complexity because every step up the ladder of functional
complexity increases the average neutral gap between meaningful
islands of function in sequence space in an exponential fashion.
Increasing population sizes can only keep up for so long. Just above
the lowest levels of functional complexity, the gaps are too big for
any environment to support the required population to maintain
evolution this side of trillions of years and evolution simply stalls
out.
This is exactly what the Lenski experiment and many other real life
experiments have demonstrated over and over again. The Lenski
experiment worked only because the 5 steppingstone functions between
starting sequence NAND and the EQU function were intelligently defined
as "beneficial" in a rather arbitrary manner, creating an average
neutral gap between each steppingstone of only 2.5 neutral steps
(average sequence space between each steppingstone of only 3,500
posibilities, which is easily covered by a population of 3,600
individuals in a very short period of time). In other words, Lenski et
al., clustered their "beneficial sequences" by intelligent design so
that they fell between the starting point and the predetermined ending
point goal in a sequence space of 5.6 x 10^70 sequences. If you keep
on reading however, you will note that Lenski and his team did
something very interesting. They removed the arbitrary definition of
"beneficial" from the intermediate steppingstones, leaving a neutral
gap of just 16 steps. And, you guest it, their population of evolving
sequences (180,000 individual sequences divided into 50 "populations"
of 3,600 individuals each) could not cross this gap to find the EQU
function that was just 16 neutral mutations away (translating into a
sequence space of 43,608,742,899,428,874,059,776 or about 43 billion
trillion).
So you see, the size of the sequence space and the relative density of
beneficial sequences in that sequence space is indeed very relevant to
understanding the process and problems of functional evolutionary
scenarios.
> Your notions about sequence space size and ratios of beneficial
> sequences only become relevant if the words in "word space" have a
> (nearly) random uniform distribution. In other words, your notion of
> linguistic "neutral gaps" would be applicable if in English, the
> 8-letter word "baseball" were as likely to appear as the 8-letter words
> "allebsba", or "xyzwqrnt". Now, English is hard enough to learn as it
> is - but if it were structured like your argument requires it to be, no
> one in their right mind would ever attempt to speak it.
Certainly there are clusters of words close by each other forming
islands of closely packed meaningful sequences. That is not the
question here. I'm talking about getting off your island. Certainly
not all or even more than a tiny fraction of English words or phrases
of a given length are clustered neatly together as you suggest here.
The question is, how do you get from the "baseball cluster" to the
"amazing cluster"? Starting on one island cluster, that island is
surrounded, on average, by a sizable gulf on non-defined sequences on
all sides. So, it may be easy to evolve from "amended" to "amender",
and a few other clustered words in this island, but how do you get to
a new island without having to pass through sequences like "allbsba"
or "xyzwqrmt"? And another thing, do you really think English words
are actually inherently sequentially different from sequences such as
"allbsba"? Consider the word "zyzzyva" (a tropical American weevil).
Is that word at all close to the word "baseball" in structure? And,
there are many many more widely spread out 7-letter words for you to
check out.
So, you see, the 7-letter words in the English language are actually
fairly "randomly" distributed. They certainly are not all that
clustered in a general fashion. Islands of them are scattered pretty
much randomly throughout the possible 7-letter sequence space. If you
still don't believe me, check out the following link listing all the
26,109 defined 7-letter words in the English language system (WORDOX
Dictionary):
http://aaron.doosh.net/lexicon/07LetterWords.html
Go back and read the Lenski paper again and you will see that
evolution did have a very big problem evolving the EQU function once
intelligent design and arbitrary definition of the gap steppingstone
sequences between NAND and EQU were removed.
Sean Pitman
http://www.zachriel.com/mutagenation/Doggerel.asp
Consider the following phrase "evolution" as illustrated on your above
listed website:
___________
Sean Pitman
pitman
pit, man
put, pan, wit
jut, plan, wig
just, plain, wing
just plain, wring
just plain, wrong
just plain wrong
Let L = total length of all extant string species
Let M = total possible mutations
Let G = number of generations
We have shown that the number of possible mutations under the extended
rules is M < L^3 per generation. Including spaces and commas, the
largest L is 17 in length, so M < 5000 for each generation (most of
which are not even valid words or phrases). The selection criterion is
obvious in this case; pit, put, jut, just. The total choices we must
make are not 5000^G as Sean Pitman would suggest, but on the order of
5000*G. It is the process of selecting that makes it a mathematical
product rather than an exponent. (And the choosing is obvious in this
case.)
__________
There are just a few obvious problems with this little "evolutionary
scenario". Certainly you did show that an evolutionary pathway exists
between many different 3- and 4- and 5-letter words. That is how you
got from pit to put to jut to just and from man to pan to plan to
plain etc. But, since it gets much much harder to evolve all that
much between longer and longer phrases by simply changing one
character at a time, you think that you can overcome this problem by
joining smaller sequences together once you evolve all the necessarily
smaller sequences - right?
What you don't seem to realize, despite my previous discussions of
concerning this very point, is that in this game words don't just
float around in neat little packages bumping into each other.
For example, say that we had all of the possible meaningful 3, 4, and
5 character sequences already evolved in various places within a
single genome. Say now that we want to evolve a meaningful
16-character sequence made up of joined 3, 4, and 5 character
sequences. What needs to happen is not as easy as getting two
particular words like "just" and "plain" to bump together. In fact,
the problem is rather difficult owing to several factors. First off,
you have to consider the odds of cutting or copying a meaningful
sequence, such as "just" fully intact. For example, the copied
sequence could have read "justa" or "ust" or "jus" or "fjust" etc.
But, say you just happen to copy "just" just right. Now, you have to
consider the odds that "just" will get inserted into just the right
spot in order for a newly combined "just plain" to make sense. What
are the odds that "just" will get inserted right next to a sequence,
such as "plain" so that the combination actually makes unified sense
in English, much less beneficial sense? I mean, the insertion could
have ended up in the middle of "plain" as read, "pljustain" or "pjust
lain" or "plaijust n" etc.
Then, just say that by some extraordinary twist of luck you just
happened to get "just plain" stuck together just right. What are the
odds that the seqeunce "wrong" would get snipped out from its other
location and get inserted in just the right position so that the
combination read, "just plain wrong"? I mean, even if "wrong"
happened to get copied intact, and even if it happened to get inserted
into the "just plain" area (out of millions of other possible
insertion spots) what are the odd that it will get inserted right at
the end of "just plain"? It could also get inserted in the middle
somewhere to read, "just wrong plain" or "juswrong t plain" or "wrong
just plain" or "just plwrongain" or etc.
Are you starting to see the problem? Given one mutation per
generation per individual genome or evolving sequence, the odds that
that mutation will result in a new meaningful sequence in a given
individual is indeed the ratio of all meaningful sequences of a given
length divided by the total number of possible sequences of that
length. For 7-letter sequences, this works out to be around 1 in
250,000 mutations.
On the other hand, you suggest that there are only about 8,000
possible choices per mutation, but this does not change the odds that
success will only be achieved once every 250,000 mutations. The odds
that a winning sequence will be within one of the first 8,000 options
can also be calculated and is 1 chance in 31. On average then, none
of the first 8,000 options will be meaningful.
Now certainly you can find many cases where one 7-letter word can get
mutated into another meaningful 7-letter word. That is not a problem
for my position. There are certainly islands of 7-letter words that
are separated from each other by no more than a single letter change.
However, most islands of 7-letter words are separated from every other
island by a little sea of some 250,000 meaningless sequences. The
question is, how do you get from one island to any other? If you
can't get from one island to another except by going through the
neutral sea, natural selection is not going to help you since
mutations in this sea are functionally neutral and therefore
completely random. You could just stay on your little island, but
then evolution would be severely limited now wouldn't it?
Again, your idea of linking smaller words, which are easier to evolve,
together to make bigger words and phrases doesn't work so well because
of the above mention problems of proper copying and pasting of these
words given all the millions of potentially non-meaningful
possibilities.
In short, you must take all of these possibilities into account in
your calculation of the average number of mutational events it would
take for mutating a new beneficial sequence of 16 characters starting
with a bunch of 3, 4, and 5 character sequences. As far as I have
been able to tell, you have failed to do this.
Also, in your explaination of how to evolve new meaningful 7-letter
sequences, you use a population of 10^14 or 100 trillion?! The total
sequence space for a 7-character sequence (give 27 possible
characters) is just over 10 billion. Within this sequence space the
ratio is only about 1 in 250,000 meaningful vs. meaningless. Now, if
you have a population of 100 trillion, you are going to cover the
distance between all meaningful possibilities in very short order at
even a fairly low mutation rate. The evolution of absolutely ANY
beneficial 7-letter sequence could and would be achieved by such a
population.
What you evidently fail to realize is that the population expansion
trick can only work so long because of limited ability of a given
environment to support an growing population beyond a certain point.
What happens when you double the sequence length to 14-characters?
Now you are at a ratio of 1 in about 62 billion. With a population of
100 trillion, evolution still does pretty well. Moving on to a
sequence length of 28-characters the ratio drops to 1 in
3,906,250,000,000,000,000,000 or almost 4 trillion. Still, with a
population of 100 trillion, this distance can be covered in a
reasonable amount of time. However, with a sequence of 56-characters
the ratio drops to 1 in 10^43. Now, each and every individual in our
population of 100 trillion is surrounded by a vast ocean of 10^29
meaningless sequences. With one generation per day, this works out to
be around 273 trillion years for just one member of our population to
find a new meaningful 56-character sequence on average.
See the problem?
RobinGoodfellow
> RobinGoodfellow <lmuc...@yahoo.com> wrote in message news:<c6l10q$4qt$1...@news01.cit.cornell.edu>...
>
Hello Sean:
First order of business - contrary to what you've written in your reply
to Zachriel, I'm not a "she", nor do I play one on Usenet. See:
http://www.boldoutlaw.com/puckrobin/puck.html
Or better yet, go read "Midsummer Night's Dream". It's a far more
productive use of your time than attempting to overturn the Theory of
Evolution using only high school algebra.
>>>I have read your website a couple of times now and I fail to see how
>>>you could possibly think that a 7-letter sequence has only 8,000
>>>possible permutations. Clearly, the total number of permutations of a
>>>7-letter sequence is 27^7 or 10,460,353,203 (calculation is based on
>>>the 26 letters of the alphabet plus a space for 27 possible characters
>>>per position). Now, 10 billion is way more than 8,000.
>>
>>Well, either you haven't read Zach's argument carefully enough, or you
>>haven't understood it. Zachriel was specifying that for a given
>>7-letter word, the number of possible distinct "neighbors" as the result
>>of any mutation (whether a random insertion, deletion, point mutation,
>>domain swap), can be upper bounded by 8,000. The total size of the
>>sequence space, at any point, is irrelevant: evolutionary processes can
>>only explore the portions of the sequence space in the local vicinity of
>>existing words. If, of these, at least one "mindless" mutation proves
>>to be beneficial, it'll become fixated in the population, opening up a
>>new area of sequence space to explore. This is how larger and larger
>>"beneficial" words can be discovered.
>
>
> You make the extraordinary claim that "the total size of sequence
> space, at any point, is irrelevant."
It's only extraordinary to you because you stubbornly refuse to accept
that evolutionary processes neither can nor have to search the entire
sequence space. All that matters for their success is the starting
point, the types of steps, and the distribution of beneficial states. I
have already given you both an example where an evolutionary process
would succeed in a sequence space virtually devoid of beneficial
sequences, and where it would fail in a space where almost every
sequence is beneficial, based simply on the above parameters. (It
appears that you didn't understand the second example - underscoring
your lack of knowledge of basic combinatorics. I'd be happy to explain
the math to you if you'd like, but I once again would like to encourage
you to study the subject if you seriously wish to argue it.) In case
you need to refresh your memory, the URL is here:
http://groups.google.com/groups?q=g:thl2571645201d&dq=&hl=en&lr=&ie=UTF-8&oe=UTF-8&c2coff=1&selm=bt8i6p%24r9h%241%40news01.cit.cornell.edu
and your response is at
http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&oe=UTF-8&c2coff=1&selm=80d0c26f.0401131529.1b1e9814%40posting.google.com&rnum=5
> This is only true if the deck is
> stacked, as you have previously suggested, where there is an
> extraordinary clustering of beneficial sequences around your starting
> point. Such a stacking of the deck, if it were truly stacked in such
> a fashion, as you have suggested, would in itself be evidence of
> intelligent design.
Even you agree that such "stacking" (or clustering) can occur naturally
to some degree. You don't seem to be invoking the ineffable Designer
every time a letter is added to a word to form a new word, or when one
protein domain gets tacked on to the C-terminus of another to form a
protein with a novel function - you seem content that mindless processes
can do such things (once they've been shoved under your nose). Yet your
mathematical analysis miserably fails to account for such instances:
according to your notions of sequence space, *any* such occurances
should be wildly improbable, even for relatively short words or
polypeptide chains. Your math (or rather the application thereof) is
just very, very, very wrong. You simply can't raise the size of the
alphabet to power of sequence length and say that's all there's to it.
> Outside of such an extremely unlikely stacking of
> the deck, the total size of sequence space is indeed very relevant to
> the problem. Only by knowing the total size of sequence space relative
> to the total size of beneficial sequences will one be able to
> determine the likelihood that any one of the "8,000" sequences within
> the striking distance of the first mutational event will be
> "beneficial."
Here's an exercise for you, Sean - in case you are actually interested
in putting your wits where your mouth is. Come up with a list of ten
English words or phrases in common usage that are not within the
"striking distance" of at most three mutations (point mutations,
insertions, deletions, domain re-combinations, e.t.c.) from some other
valid English word or phrase. They can be of arbitrary length: that is,
make your "word space" as big as you would like. You could then go on
to claim such words/phrases are unevolvable.
Remember, use only words in common usage (although you can combine them
in an arbitrary manner). Avoid words like "zyzzyva" - unless you agree
to amend the mutational model so that it supports direct "lateral
transfers" of words from foreign languages, and bastardizations thereof.
I would be most impressed if you could succeed in this task - though,
after giving it a little bit of thought, I think that success would be
very hard to come by.
> Actually, knowing the initial striking distance is what is irrelevant
> if you don't know the average distance to a new beneficial sequence.
> The 8,000 number is really meaningless to knowing the time needed for
> a new meaningful sequence to evolve at a given level. All that you
> need to know in order to calculate the average time is the total
> number of sequences in sequence space,
Utterly irrelevant. To reiterate, an evolutionary process can only take
local steps, and is neither capable nor in need of exploring the entire
sequence space.
> the total number of beneficial
> sequences in sequence space (assuming a more average distribution than
> you assume for an average starting point),
Your assumption is completely unjustified. We already know considerable
clustering occurs (whether in languages and in biological systems), and
that qualitatively different beneficial sequences may come about as the
result of a very small number of mutations. Further, the semantic,
phonetic, and synctatic contrstraints imposed on the development of
language, and the physical and biochemical constraints imposed on living
organisms, will guarantee that the distribution of sequences that is
anything but "average" - i.e. uniform random. Which means that your
math does apply.
> the total number of
> evolving sequences in the population,
Correct.
> the type of mutation(s), and the
Correct.
> mutation rate.
Correct, with one major omission - the starting point in the
evolutionary process. If Zachriel's program were to start at any random
point in word space - say "xsadfaseawerd" - it would not evolve much of
anything. However, starting with the very basic building blocks for
words (individual letters), the evolutionary algorithm was able to
easily climb up the "ladder of complexity", and produce words up to 18
letters long. (Word space size: 26^18 - which no modern desktop
computer would be able to explore exhaustively, as your math suggests
should be done.) Of course, this must mean that starting out with the
simplest buildings blocks and slowly building up more complex
functionality is brilliant insight requiring an ineffable Intelligent
Designer! Right, Sean?
> If you know these things you can calculate the average
> time needed to evolve a new meaningful sequence at a given level of
> complexity (i.e., minimum sequence length).
Technically, yes, but the calculation is not remotely as simple as you
suggest. I suspect - though I may be wrong - that, unless you use a
very simple mutational model with a well known distribution of
"beneficial sequences" in sequence space, computing the probability in
question would become P#-hard. (A class of counting problems in
computer science that are not known to have any computationally
tractable solutions.) It would certainly require you to compute a large
number of complex, time-dependent recurrance relations. And if you wish
to model actual biological evolution, you have to take a myriad of
additional intricacies into account - not the least of all, the
continual effect that living organisms have on their own selecting
environment. It is a computational nightmare - that's why all the
models of evolution you see today in the published literature (including
Lenski's) are very simplistic. But it seems you've already solved
everything via you mighty powers of exponentiation. I guess all the
research in the field can stop now.
> None of the 8,000 striking distance possibilities have to be
> beneficial in order for evolution to proceed - via purely random walk
> or "neutral evolution." And, of course, that is what allows evolution
> to proceed at lower levels of complexity, but, unfortunately, this is
> also what rapidly kills evolutionary potential at higher and higher
> levels of complexity. Evolution simply stalls out at higher levels of
> functional complexity because every step up the ladder of functional
> complexity increases the average neutral gap between meaningful
> islands of function in sequence space in an exponential fashion.
> Increasing population sizes can only keep up for so long. Just above
> the lowest levels of functional complexity, the gaps are too big for
> any environment to support the required population to maintain
> evolution this side of trillions of years and evolution simply stalls
> out.
And yet, Zach's program seems to encounter no such neutral gaps - nor is
there any evidence that they exist in real life, much less that they are
as ubiquitous as you claim. Certainly, neutral drift plays some role in
evolution (though the extent of that role is still being debated), but
then there is no shortage of simple mutations that produce qualitative,
selectable changes.
(Yes, I've read your lactose page. Let's not dig up that dead horse
again. Suffice it to say, I was not convinced.)
> This is exactly what the Lenski experiment and many other real life
> experiments have demonstrated over and over again. The Lenski
> experiment worked only because the 5 steppingstone functions between
> starting sequence NAND and the EQU function were intelligently defined
> as "beneficial" in a rather arbitrary manner,
You didn't actually read what I wrote in my previous post, did you?
Again, NAND, NOT, AND, OR, XOR, EQU are exteremely standard functions in
boolean logic, defined well over a century ago, and used in computers
for many decades. NAND is the simplest of these, and can be used to
build the more complex boolean circuits (NOT, AND, OR). These, in turn,
can be combined to form yet more complex boolean functions, and so on -
up to an arbitrary level of complexity. For instance, the simplest
(though far from only) way to express EQU for one-bit inputs A and B is:
A EQU B if and only if (A AND B) OR (NOT A AND NOT B)
Saying that AND, OR, and NOT are arbitrary with respect to EQU is like
saying that "base" and "ball" are arbitrary with respect to "baseball".
> creating an average
> neutral gap between each steppingstone of only 2.5 neutral steps
> (average sequence space between each steppingstone of only 3,500
> posibilities, which is easily covered by a population of 3,600
> individuals in a very short period of time). In other words, Lenski et
> al., clustered their "beneficial sequences" by intelligent design so
> that they fell between the starting point and the predetermined ending
> point goal in a sequence space of 5.6 x 10^70 sequences. If you keep
> on reading however, you will note that Lenski and his team did
> something very interesting. They removed the arbitrary definition of
> "beneficial" from the intermediate steppingstones, leaving a neutral
> gap of just 16 steps. And, you guest it, their population of evolving
> sequences (180,000 individual sequences divided into 50 "populations"
> of 3,600 individuals each) could not cross this gap to find the EQU
> function that was just 16 neutral mutations away (translating into a
> sequence space of 43,608,742,899,428,874,059,776 or about 43 billion
> trillion).
Honestly, Sean, I can appreciate large numbers without the "billion
trillion" bit. However, I can see that your sequence space size
suddenly has suddenly shifted from 26^50 (the total number of possible
sequences, assuming length stays constant) to 26^16 (the number of
sub-sequences at the sixteen sites necessary for the formation of the
shortest possible EQU circuit). So, which one is it? All your
"analysis" applies to the total sequence space, but now you're suddenly
interested in the much smaller (but still very large) subsequence! If
you're going to be wrong, at least try to be consistently wrong.
But I hope my explanation above makes it clear to you why you can't hope
to achieve EQU if without working AND, OR, or NOT. It's not the
"neutral gap" that's the problem - it is the absence of necessary steps
in the "ladder of complexity". Evolution cannot simply poof complex
features into thin air - it needs existing material to work with. That
is what Lenski et. al. have been trying to demonstrate.
> So you see, the size of the sequence space and the relative density of
> beneficial sequences in that sequence space is indeed very relevant to
> understanding the process and problems of functional evolutionary
> scenarios.
So, when the "density" of beneficial sequences is 2 in 26^50, evolution
is impossible, but when that density is 6 in 26^50, evolution works just
fine. Yeah, that makes sense.
>>Your notions about sequence space size and ratios of beneficial
>>sequences only become relevant if the words in "word space" have a
>>(nearly) random uniform distribution. In other words, your notion of
>>linguistic "neutral gaps" would be applicable if in English, the
>>8-letter word "baseball" were as likely to appear as the 8-letter words
>>"allebsba", or "xyzwqrnt". Now, English is hard enough to learn as it
>>is - but if it were structured like your argument requires it to be, no
>>one in their right mind would ever attempt to speak it.
>
>
> Certainly there are clusters of words close by each other forming
> islands of closely packed meaningful sequences. That is not the
> question here. I'm talking about getting off your island.
And I am saying that my island (while in the case of language, unable to
accomodate *every* word), is so large that it can easily accomodate
phrases of as high a complexity as the English language supports.
> Certainly
> not all or even more than a tiny fraction of English words or phrases
> of a given length are clustered neatly together as you suggest here.
> The question is, how do you get from the "baseball cluster" to the
> "amazing cluster"?
Exteremely easy. Start with " cluster" as a common ancestor. One
descendant splits off when the domain "baseball" is prepended to "
cluster". A similar subsequent event forms "amazing cluster". What
else you got?
Incidentally, here's a simple math problem for you. Suppose you have
"baseball" and " cluster" in your population, and a random domain swap
occurs between the two. (A domain can be any part of either word, up to
and including the whole word.) What's the probability that the phrase
"baseball cluster" forms?
> Starting on one island cluster, that island is
> surrounded, on average, by a sizable gulf on non-defined sequences on
> all sides. So, it may be easy to evolve from "amended" to "amender",
> and a few other clustered words in this island, but how do you get to
> a new island without having to pass through sequences like "allbsba"
> or "xyzwqrmt"? And another thing, do you really think English words
> are actually inherently sequentially different from sequences such as
> "allbsba"? Consider the word "zyzzyva" (a tropical American weevil).
> Is that word at all close to the word "baseball" in structure? And,
> there are many many more widely spread out 7-letter words for you to
> check out.
As I've said, I don't expect to be able to generate "every" English
word. "Zyzzyva" will probably be beyond my reach, unless we expand our
model of language evolution to allow lateral transfers from foreigh
languages. But you are shifting goalposts. Your argument is that a
"mindless" evolutionary process will stall at a certain level of
complexity, not that it will be able to explore the entire word space
quickly (that *would* be impossible). And as such, your argument is
simply incorrect. Unless, of course, you care to explain how Zachriel's
algorithm was able to evolve an 18-letter word. (There are at most a
few thousand 18-letter words in the Enlish languages, and word space
size is 26^18. By your math, it should have taken his computer many
ages of the Universe - the real ages, not the Creationist ones - to
stumble across a single such word. I assume, however, than no time
travel was involved.)
> So, you see, the 7-letter words in the English language are actually
> fairly "randomly" distributed. They certainly are not all that
> clustered in a general fashion. Islands of them are scattered pretty
> much randomly throughout the possible 7-letter sequence space. If you
> still don't believe me, check out the following link listing all the
> 26,109 defined 7-letter words in the English language system (WORDOX
> Dictionary):
>
> http://aaron.doosh.net/lexicon/07LetterWords.html
My challenge stands. Give me 10 words or phrases *in common usage*
you'd consider unreachable by individual mutations in the set-up of this
word problem.
Again, the stepping stones are no more arbitrary than "base" and "ball"
are arbitrary for "baseball". To say that they are "arbitrary" is to
admit that you have not understood even the basic point of the paper,
much less the actual methodology involved. And yet that does not
prevent you in the slightest from confidently expounding upon its
meaning. All I can say is: I wish I had your confidence!
Zachriel
I'm not in the least concerned with the length of the words, but only the
length of the entire string. A string of 17-letters has no more than 5000
possible mutations. I have shown a clear path exists and have only to decide
which of the 5000 mutant strings to keep at each generation.
> That is how you
> got from pit to put to jut to just and from man to pan to plan to
> plain etc. But, since it gets much much harder to evolve all that
> much between longer and longer phrases by simply changing one
> character at a time, you think that you can overcome this problem by
> joining smaller sequences together once you evolve all the necessarily
> smaller sequences - right?
Your basic claim is that we would have to consider zillions of permutations
is just wrong.
> What you don't seem to realize, despite my previous discussions of
> concerning this very point, is that in this game words don't just
> float around in neat little packages bumping into each other.
<snip exponential redux>
You can't even get past the fact that we can "evolve" long words. Until you
admit the obvious on this point, there is no reason to consider the more
complex problem of valid English phrases.
Zachriel
> "Zachriel" <sp...@zachriel.com> wrote in message
news:<ZbSdnWsQ-rc...@adelphia.com>...
>
> >snip <
>
> > > I have read your website a couple of times now and I fail to see how
> > > you could possibly think that a 7-letter sequence has only 8,000
> > > possible permutations. Clearly, the total number of permutations of a
> > > 7-letter sequence is 27^7 or 10,460,353,203 (calculation is based on
> > > the 26 letters of the alphabet plus a space for 27 possible characters
> > > per position). Now, 10 billion is way more than 8,000.
> >
> > That's because you have violated the rules of the game. The question
isn't
> > how many possible combinations of *any* seven letters can be made, but
how
> > many mutants can be created under the rules *from* that string
(including
> > point mutations, delete mutations, insert mutations, or recombinations).
> >
> > Using a 7-letter word as an example, with 27 possible symbols:
> >
> > You can mutate any of the 7 letters for 7*27 = 189 possible mutations;
>
> That is just for a single point mutation event.
> The question is
> though, what are the odds that any one of these 189 possible mutations
> will result in a new meaningful 7-character word or sequence?
It depends on the word, of course. Pick a word, or a few words, put them in
the Word Mutator, and it will try every possible mutation and every possible
recombination.
> In
> order to answer this question, you must know the density of defined
> "words" or meaningful "sequences" in the sequence space of 7-letter
> sequences.
No. That will give you the *wrong* answer. If you want to know the actual
answer, one obvious way would be to just try each of the possible mutants
and compare them to a dictionary--which is exactly what the Word Mutator
does.
For instance, let's put the seven-letter word "letters" into the Word
Mutator. In a split second, out of the 676 mutants considered, 13 are valid
words, the longest being nine-letters in length; "letterers", plus "fetters,
betters, getters, letters, litters, netters, setters, letter, leers, lets,
les, let". But the next generation is where it gets interesting as the
various species diverge into a variety of forms. Out of the 32618 additional
mutants, we now have 107 valid words, including "begetters, letterers,
flitters, fretters, glitters, letterer, settlers, slitters, festers,
fetters". Note that "letterers" was formed by recombination of "letters"
with itself.
Another example. Let's try "words" and "letters". Out of 1374 mutants, 27
are valid words. The longest words look much the same as the previous
example; "letterers, fetters, betters, getters, letters, litters, netters,
setters, swords, worlds". But in the next generation the population diverges
into a myriad of different forms. After an additional 92533 mutants
considered, 230 are valid words, including a word of length 10;
"forgetters", plus "woodworks, woodworms, wormwoods, begetters, letterers,
forwards, networks, warlords, wordless, cordless".
Consider the evolution of "forgetters"
words, letters
fords, getters
for-getters (recombining)
This process takes just seconds, which is somewhat less than "zillions of
years", and we have evolved from seven letters to ten letters.
> Only is this way can you determine the average number of
> random mutational events (each with 189 new possibilities) it will
> take to find a new 7-letter sequence.
You haven't found a meaningful result. Your number has no value unless you
assume words are spread evenly throughout the space of possible
permutations. Words are just not randomly distributed through
"letter-space".
> Now for a little math: We know how large 7-character sequence space
> is in this problem. It is 27^7 or 10,460,353,203. For arguments
> sake, lets say that there are somewhere around 40,000 meaningfully
> beneficial sequences distributed throughout the 7-letter sequence
> space. If true, this would create a ratio of about 1 in 250,000
> meaningful vs. meaningless sequences - right? So, what are the odds
> that with the first spin of the 7 wheels on your lucky slot machine
> that you would hit a winning sequence? Obviously the odds are
> slightly less than 1 in 250,000 since you could end up on your
> starting sequence 1/189th of the time. Given a population of 1
> mutating sequence, the average number of mutational events it would
> take to find any one of the 40,000 possible winning sequences is
> 250,000 random walk mutations.
But we already know your answer is wrong. Anyone can play with the Word
Mutator and know that you are not just wrong, but absolutely, completely,
utterly wrong. Why do you keep pretending otherwise?
> This same argument also seems to defeat the rest of your calculations,
The proof is in the pudding.
http://www.zachriel.com/mutagenation/Pudding.asp
Extra bonus spreadsheet! I made a small spreadsheet (only 28k) that
calculates the number of mutants available for any length string. There's a
wee bit of overlap, so the numbers are a bit high. By the way, the Word
Mutator counts a bit high for the same reason. Some mutants are counted more
than once--but every mutant is counted and considered.
http://www.zachriel.com/mutagenation/Calcs.xls
Sean Pitman
> > You make the extraordinary claim that "the total size of sequence
> > space, at any point, is irrelevant."
>
> It's only extraordinary to you because you stubbornly refuse to accept
> that evolutionary processes neither can nor have to search the entire
> sequence space. All that matters for their success is the starting
> point, the types of steps, and the distribution of beneficial states.
My main beef with your position here is your idea of the distribution
of beneficial states. You dismiss the notion that the ratio of
beneficial vs. non-beneficial is relevant to this problem by
suggesting that all you have to do is cluster the relatively tiny
number of beneficial sequences around your starting point and then
evolution would be no problem. Well, as I have said before, if such a
stacking of the deck did occur, then you would certainly be correct.
Evolution in such a situation would proceed without a hitch. The
problem is, where is your evidence that such a stacked deck occurs on
a regular basis in any language system without intelligent design?
All your "math" is based on the assumption of an extraordinary
clustering of beneficial sequences in sequence space around your
starting point. Your position, as far as I have been able to
ascertain, is no more sophisticated than that one highly unlikely
assumption.
> Even you agree that such "stacking" (or clustering) can occur naturally
> to some degree. You don't seem to be invoking the ineffable Designer
> every time a letter is added to a word to form a new word, or when one
> protein domain gets tacked on to the C-terminus of another to form a
> protein with a novel function - you seem content that mindless processes
> can do such things (once they've been shoved under your nose). Yet your
> mathematical analysis miserably fails to account for such instances:
> according to your notions of sequence space, *any* such occurances
> should be wildly improbable, even for relatively short words or
> polypeptide chains. Your math (or rather the application thereof) is
> just very, very, very wrong. You simply can't raise the size of the
> alphabet to power of sequence length and say that's all there's to it.
You evidently haven't been following my posts very closely. For
example, 3-letter words have a ratio of about 1 in 8 in 3-letter
sequence space. With this ratio, it is very likely to have very large
clusters of 3-letter words, with practically all clusters linked
together by bridges. This gets less and less so as you move up the
ladder however. Also, none of the examples "shoved under my nose"
have been mathematically unlikely at all. If you will check on the
matter you will find that I discussed such occurrences like the
BCR-ABL chimeric gene/protein in some detail showing that such a union
and the resulting up-regulation of the tyrosine kinase activity of ABL
was not statistically unlikely in the least.
To continue to beat a dead horse here, take, for example, 7-letter
sequences. Even though there may be only 40,000 of them in a sequence
space of around 8 billion, odds are that a few small clusters will
indeed form. However, it is very unlikely that a relatively large
cluster exists outside of intelligent design. And indeed, that is
exactly what you will find if you look at any list of 7-letter words,
be they "common" or not. This cluster isolation gets more and more
pronounced as you move up the ladder of minimum sequence length
requirement. Meaningful 28-letter sequences may also have a few
clusters, but these clusters will be smaller, on average, that the
7-letter clusters and the average distance between clusters will be
exponentially greater. Given a set steady state population size and
mutation rate the population would find it exponentially harder, on
average, to find a new 28-character cluster starting from an average
starting point.
That is, unless you are correct and the vast majority of the tiny
fraction of beneficial 28-character sequences in the English language
system are all clustered together around your fortuitous starting
point.
> Here's an exercise for you, Sean - in case you are actually interested
> in putting your wits where your mouth is. Come up with a list of ten
> English words or phrases in common usage that are not within the
> "striking distance" of at most three mutations (point mutations,
> insertions, deletions, domain re-combinations, e.t.c.) from some other
> valid English word or phrase. They can be of arbitrary length: that is,
> make your "word space" as big as you would like. You could then go on
> to claim such words/phrases are unevolvable.
This would be no problem for point mutations, point insertions and
point deletions, but it would be a problem for larger insertions,
deletions, and domain re-combinations. This is exactly what Zach is
trying to pull off. He thinks that if a needed word or part of a word
exists somewhere in the genome that he can just link it together with
any other word without considering the odds of proper cutting and
pasting, as previously described. For example, he thinks that if you
have the words "just" and "plain" and "wrong" somewhere that it would
be no problem to quickly and easily link them together to form the
united phrase, "just plain wrong." The fact of the matter is that it
is just plain wrong to think that this is an easy matter. In the real
rules of the game, copying does not necessarily work just right and
neither does pasting. The copying process could take just part of a
needed sequence or too much of a sequence. Then, even if just the
right sequence was copied so that it could be inserted somewhere else,
the insertion does not necessarily work just right. Zach fails to
account for all the meaningless possibilities of copying and insertion
in his illustrations and he didn't discuss this problem in his most
recent reply.
Consider, for example, the Shakespearean phrase, "Methinks it is like
a weasel". This is a relatively short phrase, but changing one letter
at a time, to include point insertions and deletions, the cluster of
meaningful phrases that surround "Methinks it is like a weasel" is
very small. In fact, it is for this very reason that Zach tries to
appeal to the idea of evolving each of the individual words separately
and then "concatenating" or joining them together in large chunks.
This is where he apparently fails to realize that in real life genetic
concatenation comes with its own statistical problems.
Then again, even if you set up the rules of mutation so that only
intact meaningful words can interact together only at the ends of
other intact words, as Zach does, this still doesn't help all that
much. It only raises the bar a bit, but even this evolutionary
program stalls out very quickly at higher and higher levels of
functional complexity. One may be better able to evolve short phrases
by using intact word changes instead of or in combination with
letter-only and non-particular copying and insertional changes, but,
like with the limits of "letter change only" evolution, "word change
included" evolution will only work with relatively short phrases. The
attempt to evolve longer and longer phrases, with a steady state
population and a constant mutation rate, will result in an exponential
decline in evolutionary potential.
> > Actually, knowing the initial striking distance is what is irrelevant
> > if you don't know the average distance to a new beneficial sequence.
> > The 8,000 number is really meaningless to knowing the time needed for
> > a new meaningful sequence to evolve at a given level. All that you
> > need to know in order to calculate the average time is the total
> > number of sequences in sequence space,
>
> Utterly irrelevant. To reiterate, an evolutionary process can only take
> local steps, and is neither capable nor in need of exploring the entire
> sequence space.
Random walk is indeed capable of exploring the entire sequence space
of a particular level of sequence length - given enough time. Again,
this idea of the average random walk is very relevant if your starting
point happens to be somewhere other than your fortuitous clustering of
the majority of beneficial sequences in one tiny corner of sequence
space.
> > the total number of beneficial
> > sequences in sequence space (assuming a more average distribution than
> > you assume for an average starting point),
>
> Your assumption is completely unjustified. We already know considerable
> clustering occurs (whether in languages and in biological systems), and
> that qualitatively different beneficial sequences may come about as the
> result of a very small number of mutations.
We know that clustering occurs, but we also know that this clustering
gets less and less "significant" at higher and higher sequence sizes
of fairly high functional specificity. This is true in both human
language systems, such as English, as well as genetically based
information systems, such as living organisms.
> Further, the semantic,
> phonetic, and synctatic contrstraints imposed on the development of
> language, and the physical and biochemical constraints imposed on living
> organisms, will guarantee that the distribution of sequences that is
> anything but "average" - i.e. uniform random. Which means that your
> math does apply.
You are simply wrong here. If you look at both word lists and short
phrase possibilities in any language system, you will no doubt note
that there are large numbers of clusters and that these clusters cover
a very wide range of the potential sequence space.
> > the total number of
> > evolving sequences in the population,
>
> Correct.
>
> > the type of mutation(s), and the
>
> Correct.
>
> > mutation rate.
>
> Correct, with one major omission - the starting point in the
> evolutionary process. If Zachriel's program were to start at any random
> point in word space - say "xsadfaseawerd" - it would not evolve much of
> anything.
You are wrong again here. What Zach would do is break down the
sequence "xsadfaseawerd" into smaller sequences that did have an
English meaning, like "sea", "sad", "awe", "as", "a", etc., and then
"concatenate" these smaller words into a new phrase. That is what I'm
sure he would try to do anyway.
> However, starting with the very basic building blocks for
> words (individual letters), the evolutionary algorithm was able to
> easily climb up the "ladder of complexity", and produce words up to 18
> letters long. (Word space size: 26^18 - which no modern desktop
> computer would be able to explore exhaustively, as your math suggests
> should be done.) Of course, this must mean that starting out with the
> simplest buildings blocks and slowly building up more complex
> functionality is brilliant insight requiring an ineffable Intelligent
> Designer! Right, Sean?
Again, if you write rules that limit errors in copying and insertion,
like Zach did, you can get 18-letter phrases even with a relatively
small population. Also, even with my rules, you could evolve
18-letter phrases in a reasonable amount of time with the population
that Zach said he used (10^14 individuals). But, even such a large
population would still stall out with phrases requiring just 50 or so
letters. Or, using Zach's rules, a pretty significant evolutionary
stall would occur with phrases requiring just 50 or so words.
> > If you know these things you can calculate the average
> > time needed to evolve a new meaningful sequence at a given level of
> > complexity (i.e., minimum sequence length).
> And yet, Zach's program seems to encounter no such neutral gaps
Zach's program did indeed encounter neutral gaps, it is just that his
population was so huge (10^14) that it could rapidly cover the entire
seqeunce space of 7-letters (26^7) or even a few more in very short
order.
> - nor is
> there any evidence that they exist in real life, much less that they are
> as ubiquitous as you claim.
There is plenty of evidence that they exist in real life, not the
least of which is the fact that there are no examples of evolution
evolving any function in real time that requires a minimum of over
1,000 fairly specified amino acids all working together at the same
time.
> Certainly, neutral drift plays some role in
> evolution (though the extent of that role is still being debated), but
> then there is no shortage of simple mutations that produce qualitative,
> selectable changes.
This is only true at the lowest levels of functional complexity
requiring no more than a few hundred fairly specified amino acids, at
minimum, working together at the same time.
> (Yes, I've read your lactose page. Let's not dig up that dead horse
> again. Suffice it to say, I was not convinced.)
It is easy to simply say that one is "not convince", but it is another
thing entirely to be able to clearly explain why.
> > This is exactly what the Lenski experiment and many other real life
> > experiments have demonstrated over and over again. The Lenski
> > experiment worked only because the 5 steppingstone functions between
> > starting sequence NAND and the EQU function were intelligently defined
> > as "beneficial" in a rather arbitrary manner,
>
> You didn't actually read what I wrote in my previous post, did you?
> Again, NAND, NOT, AND, OR, XOR, EQU are exteremely standard functions in
> boolean logic, defined well over a century ago, and used in computers
> for many decades. NAND is the simplest of these, and can be used to
> build the more complex boolean circuits (NOT, AND, OR). These, in turn,
> can be combined to form yet more complex boolean functions, and so on -
> up to an arbitrary level of complexity. For instance, the simplest
> (though far from only) way to express EQU for one-bit inputs A and B is:
>
> A EQU B if and only if (A AND B) OR (NOT A AND NOT B)
>
> Saying that AND, OR, and NOT are arbitrary with respect to EQU is like
> saying that "base" and "ball" are arbitrary with respect to "baseball".
Evidently you don't understand what I mean when I use the term
"arbitrary" in this situation. The fact of the matter is that it was
arbitrary for the computer scientists to define such sequences as AND,
OR, XOR and NOT (meaningful or not), as "beneficial". Clearly there
was nothing inherent about their environment, outside of the
scientist's will, that made them "beneficial".
> > creating an average
> > neutral gap between each steppingstone of only 2.5 neutral steps
> > (average sequence space between each steppingstone of only 3,500
> > posibilities, which is easily covered by a population of 3,600
> > individuals in a very short period of time). In other words, Lenski et
> > al., clustered their "beneficial sequences" by intelligent design so
> > that they fell between the starting point and the predetermined ending
> > point goal in a sequence space of 5.6 x 10^70 sequences. If you keep
> > on reading however, you will note that Lenski and his team did
> > something very interesting. They removed the arbitrary definition of
> > "beneficial" from the intermediate steppingstones, leaving a neutral
> > gap of just 16 steps. And, you guest it, their population of evolving
> > sequences (180,000 individual sequences divided into 50 "populations"
> > of 3,600 individuals each) could not cross this gap to find the EQU
> > function that was just 16 neutral mutations away (translating into a
> > sequence space of 43,608,742,899,428,874,059,776 or about 43 billion
> > trillion).
> I can see that your sequence space size
> suddenly has suddenly shifted from 26^50 (the total number of possible
> sequences, assuming length stays constant) to 26^16 (the number of
> sub-sequences at the sixteen sites necessary for the formation of the
> shortest possible EQU circuit). So, which one is it? All your
> "analysis" applies to the total sequence space, but now you're suddenly
> interested in the much smaller (but still very large) subsequence! If
> you're going to be wrong, at least try to be consistently wrong.
I don't really understand your confusion here. 26^50 was the total
possible sequence space for the experiment. It just happened that the
"goal" sequence was determined to only be 16 steps/mutations from the
starting seqeunce. This knowledge reduces the average number of
random walk mutations to find this particular sequence to 26^16.
However, the total sequence space is still 26^50.
> But I hope my explanation above makes it clear to you why you can't hope
> to achieve EQU if without working AND, OR, or NOT. It's not the
> "neutral gap" that's the problem - it is the absence of necessary steps
> in the "ladder of complexity". Evolution cannot simply poof complex
> features into thin air - it needs existing material to work with. That
> is what Lenski et. al. have been trying to demonstrate.
The AND, OR, and NOT sequences were "working", they just were not long
defined as "beneficial". This lack of a beneficial definition by the
scientists did indeed create a functionally "neutral" gap between the
NAND and the EQU. It is this gap that blocked the evolution of the
EQU function in this scenario (i.e., the lack of beneficial stepping
stones IS a neutral gap).
> > So you see, the size of the sequence space and the relative density of
> > beneficial sequences in that sequence space is indeed very relevant to
> > understanding the process and problems of functional evolutionary
> > scenarios.
>
> So, when the "density" of beneficial sequences is 2 in 26^50, evolution
> is impossible, but when that density is 6 in 26^50, evolution works just
> fine. Yeah, that makes sense.
Yeah, when the 6 sequences are clustered together just right and
defined as beneficial all via intelligent design - then evolution
isn't a problem at all. But, just try getting such a nice
steppingstone alignment in an equivalent sequence space via purely
mindless processes. It just doesn't happen.
This is all for now. The rest is pretty much repetitive anyway. Let
me know if I missed some key point of yours though.
Andrew Arensburger
> (The technical problem of building a Phrasenator is objectively determining
> what constitutes a meaningful expression--though I have some interesting
> ideas on how to accomplish that goal.
You could ask Google how many pages include the candidate
phrase; the more hits, the more likely the phrase is to be meaningful.
(Actually, I can think of a number of problems with this heuristic,
but it might still be useful.)
--
Andrew Arensburger, Systems guy University of Maryland
arensb.no-...@umd.edu Office of Information Technology
I'll have to put something into their food to make them forget about this.
Sean Pitman
> Let's try "words" and "letters". Out of 1374 mutants, 27
> are valid words. The longest words look much the same as the previous
> example; "letterers, fetters, betters, getters, letters, litters, netters,
> setters, swords, worlds". But in the next generation the population diverges
> into a myriad of different forms. After an additional 92533 mutants
> considered, 230 are valid words, including a word of length 10;
> "forgetters", plus "woodworks, woodworms, wormwoods, begetters, letterers,
> forwards, networks, warlords, wordless, cordless".
>
> Consider the evolution of "forgetters"
>
> words, letters
> fords, getters
> for-getters (recombining)
>
> This process takes just seconds, which is somewhat less than "zillions of
> years", and we have evolved from seven letters to ten letters.
What is your population size and what is your mutation rate compared
to the ratio of meaningful words in sequence space? In other words,
how many sequences are you able to cover with each generation? Why
is this important?
Consider, for example, a steady state population of 2 sequences
"words" and "letters". Certainly "words" can evolve easily to "for"
and letters can evolve easily to "getters". However, what are the
odds that both sequences will evolve in this manner at the same time
so that they can recombine with each other to form the unified word,
"forgetters"? Also, you must consider that even when you have both
"for" and "getters" at the same time and place that they may recombine
in many non-meaningful ways (as I previously described, but which you
snipped). For example, you could get "getforters" or "fogettersr" or
gforetters", etc.
Of course, if your population were much larger than just 2 sequences,
the odds of getting "for" and "getters" together at the same time in
the proper orientation would be much better. As I recall, you use a
population of 10^14. Now that is a rather large population size which
indeed allows your computer to evolve fairly easily at the 7-letter
and even higher levels in very short order, but still not as easily as
it could evolve at the 2- or 3-letter levels, which is my entire
point. You will note, even with your computer program, that it gets
more and more difficult to evolve with each step up the ladder,
requiring exponentially longer amounts of average time. Given a
population of 10^14, your computer would probably do ok up till the or
30- or 40 character level before it started requiring "zillions" of
years on average to come up with a new meaningful sequence at that
level given the limits of its population size and mutation rate.
That is why, even given trillions upon trillions upon trillions of
years (i.e., "zillions" of years), your computer would never produce
something like a simple Shakespearean sonnet without intelligent
input. It could select among all possible meaningful phrases of a
sonnet size or smaller, but the meaningless options are so great that
it would never come up with anything that actually made up a
meaningful English poem of just a few hundred characters - even with a
steady state population of 10^14 mutating and recombining sequences.
RobinGoodfellow
[snip]
Hey Sean,
Sorry, but I suspect I won't be able to reply for a few days. I expect
to be much busier than usual in the coming weeks, so posting time will
be hard to come by. And, it appears that your last post has elucidated
a few aspects of your approach that need to be addressed in detail. I
think that, with some effort on both our parts, it might actually be
possible for the two us to start speaking the same language - which is
all I am interested in at this point, as the chances of us actually
agreeing with one another are virtually nil.
At any rate, I'll get back to you as soon as I have the time.
Cheers,
Robin.
Bill Rogers
> "Zachriel" <sp...@zachriel.com> wrote in message news:<rdGdnUJgkfm...@adelphia.com>...
>
> > Let's try "words" and "letters". Out of 1374 mutants, 27
> > are valid words. The longest words look much the same as the previous
> > example; "letterers, fetters, betters, getters, letters, litters, netters,
> > setters, swords, worlds". But in the next generation the population diverges
> > into a myriad of different forms. After an additional 92533 mutants
> > considered, 230 are valid words, including a word of length 10;
> > "forgetters", plus "woodworks, woodworms, wormwoods, begetters, letterers,
> > forwards, networks, warlords, wordless, cordless".
> >
> > Consider the evolution of "forgetters"
> >
> > words, letters
> > fords, getters
> > for-getters (recombining)
> >
> > This process takes just seconds, which is somewhat less than "zillions of
> > years", and we have evolved from seven letters to ten letters.
>
> What is your population size and what is your mutation rate compared
> to the ratio of meaningful words in sequence space? In other words,
> how many sequences are you able to cover with each generation? Why
> is this important?
As Zach keeps pointing out to you, the ratio of meaningful words to
sequence space does not matter. At each generation in his program
selection eliminates all the strings that are not words, so his
starting population (prior to each round of selection) is vastly
enriched for meaningful words, and as a by-product of that, vastly
enriched for useful combinations of letters, "th" "chers" "ing" which
do not have meaning on their own but which are common components of
meaningful words. Sort of like protein domains.
It was probably a mistake to make this Shakespeare challenge so
explicit. Now all he need do is use a digital file of Shakespeare's
sonnets as the selection for whether a string is meaningful or not and
I suspect he will be able to evolve "That time of year thou mays't in
me behold...." and all the rest with no difficulty whatsoever.
Starting from a single letter. And his program will get there without
having covered more than a "zillionth" of the potential sequence space
of character strings long enough to be sonnets. The size of sequence
don't matter at all.
>
> Sean
> www.naturalselection.0catch.com
Bill Rogers
> years (i.e., "zillions" of years), your computer would never produce
> something like a simple Shakespearean sonnet without intelligent
> input. It could select among all possible meaningful phrases of a
> sonnet size or smaller, but the meaningless options are so great that
> it would never come up with anything that actually made up a
> meaningful English poem of just a few hundred characters - even with a
> steady state population of 10^14 mutating and recombining sequences.
Sorry to answer the same post twice. When Zach's computer evolves a
Shakespeare sonnet in much less than a zillion years you will
doubtless complain that using the criterion "this character string
exists in Shakespeare's sonnets" as a selection is "intelligent
input." But it isn't. Intelligent input might occur if Zach scanned
the population by eye, laid it out as scrabble tiles and played around
with it until he found "My lady's eyes are nothing like the sun." But
establishing the selection criterion, as he will, is not intelligent
input. In real biological evolution the selection criteria are a lot
looser than this; there is no goal, no specific struggle to evolve a
red crested woodpecker, just a struggle to evolve something that's
good enough to hang in there.
If you could define an objective approach to measuring poetic elegance
and use that as a selection criterion, I am sure Zach's program could
write a new sonnet. But the problem (in this model, not in biological
evolution) is defining an objective criterion for "poetic elegance"
that you could plug into the "mindless process."
>
> Sean
> www.naturalselection.0catch.com
Von Smith
> seanpi...@naturalselection.0catch.com (Sean Pitman) wrote in message news:<80d0c26f.04042...@posting.google.com>...
> > "Zachriel" <sp...@zachriel.com> wrote in message news:<rdGdnUJgkfm...@adelphia.com>...
<snip>
> >
> > That is why, even given trillions upon trillions upon trillions of
> > years (i.e., "zillions" of years), your computer would never produce
> > something like a simple Shakespearean sonnet without intelligent
> > input. It could select among all possible meaningful phrases of a
> > sonnet size or smaller, but the meaningless options are so great that
> > it would never come up with anything that actually made up a
> > meaningful English poem of just a few hundred characters - even with a
> > steady state population of 10^14 mutating and recombining sequences.
>
> It was probably a mistake to make this Shakespeare challenge so
> explicit. Now all he need do is use a digital file of Shakespeare's
> sonnets as the selection for whether a string is meaningful or not and
> I suspect he will be able to evolve "That time of year thou mays't in
> me behold...." and all the rest with no difficulty whatsoever.
> Starting from a single letter. And his program will get there without
> having covered more than a "zillionth" of the potential sequence space
> of character strings long enough to be sonnets. The size of sequence
> don't matter at all.
"Shall I compare thee to a target string?"
Von Smith
Fortuna nimis dat multis, satis nulli.
Sean Pitman
> > That is why, even given trillions upon trillions upon trillions of
> > years (i.e., "zillions" of years), your computer would never produce
> > something like a simple Shakespearean sonnet without intelligent
> > input. It could select among all possible meaningful phrases of a
> > sonnet size or smaller, but the meaningless options are so great that
> > it would never come up with anything that actually made up a
> > meaningful English poem of just a few hundred characters - even with a
> > steady state population of 10^14 mutating and recombining sequences.
>
> Sorry to answer the same post twice. When Zach's computer evolves a
> Shakespeare sonnet in much less than a zillion years you will
> doubtless complain that using the criterion "this character string
> exists in Shakespeare's sonnets" as a selection is "intelligent
> input." But it isn't. Intelligent input might occur if Zach scanned
> the population by eye, laid it out as scrabble tiles and played around
> with it until he found "My lady's eyes are nothing like the sun." But
> establishing the selection criterion, as he will, is not intelligent
> input. In real biological evolution the selection criteria are a lot
> looser than this; there is no goal, no specific struggle to evolve a
> red crested woodpecker, just a struggle to evolve something that's
> good enough to hang in there.
You don't seem to understand my challenge. What I am saying is that
NO English language work the SIZE of a Shakespearean sonnet (say 600
characters), be it an actual Shakespearean sonnet or not doesn't
matter, will evolve with the use of a limited population size of
evolving character strings (say 10^14) and a limited mutation rate
(say once per individual per generation) where each meaningful random
mutational change is positively selectable if meaningful according to
standard English grammar and usage.
Given these rules, the limited nature of the population size and
mutation rate will limit the ability for meaningful evolution to
create anything meaningful the size of a few hundred English
characters (made up of letters and punctuation).
> If you could define an objective approach to measuring poetic elegance
> and use that as a selection criterion, I am sure Zach's program could
> write a new sonnet. But the problem (in this model, not in biological
> evolution) is defining an objective criterion for "poetic elegance"
> that you could plug into the "mindless process."
This is not a problem at all since I do not demand poetry or elegance
in the evolved sequence. All that I demand is coherent meaning of a
string of characters provided by following the usual rules of English
word definition and grammar.
Zach thinks that he has really done something by evolving a number of
English words of 10-letters or less using random mutation and
English-based selection. However, given the huge population size and
rather rapid mutation rate that he used, this level of evolution is
not a problem, even in very short periods of time. What Zach doesn't
seem to realize though is that even the enormous population that he
used, if kept at a steady state, would rapidly stall out in its
attempts to evolve anything beyond a certain rather low level of
meaningful complexity (i.e., far less than the size of a Shakespearean
sonnet).
John Wilkins
> bro...@noguchi.mimcom.net (Bill Rogers) wrote:
> > seanpi...@naturalselection.0catch.com (Sean Pitman) wrote:
> > > "Zachriel" <sp...@zachriel.com> wrote:
>
> <snip>
>
> > >
> > > That is why, even given trillions upon trillions upon trillions of
> > > years (i.e., "zillions" of years), your computer would never produce
> > > something like a simple Shakespearean sonnet without intelligent
> > > input. It could select among all possible meaningful phrases of a
> > > sonnet size or smaller, but the meaningless options are so great that
> > > it would never come up with anything that actually made up a
> > > meaningful English poem of just a few hundred characters - even with a
> > > steady state population of 10^14 mutating and recombining sequences.
> >
> > It was probably a mistake to make this Shakespeare challenge so
> > explicit. Now all he need do is use a digital file of Shakespeare's
> > sonnets as the selection for whether a string is meaningful or not and
> > I suspect he will be able to evolve "That time of year thou mays't in
> > me behold...." and all the rest with no difficulty whatsoever.
> > Starting from a single letter. And his program will get there without
> > having covered more than a "zillionth" of the potential sequence space
> > of character strings long enough to be sonnets. The size of sequence
> > don't matter at all.
>
> "Shall I compare thee to a target string?"
>
To be encoded, or not to be encoded
That is compression
--
John Wilkins
john...@wilkins.id.au http://www.wilkins.id.au
"Men mark it when they hit, but do not mark it when they miss"
- Francis Bacon
Zachriel
"Sean Pitman" <seanpi...@naturalselection.0catch.com> wrote in message
news:80d0c26f.04042...@posting.google.com...
news:<rdGdnUJgkfm...@adelphia.com>...
>
> > Let's try "words" and "letters". Out of 1374 mutants, 27
> > are valid words. The longest words look much the same as the previous
> > example; "letterers, fetters, betters, getters, letters, litters,
netters,
> > setters, swords, worlds". But in the next generation the population
diverges
> > into a myriad of different forms. After an additional 92533 mutants
> > considered, 230 are valid words, including a word of length 10;
> > "forgetters", plus "woodworks, woodworms, wormwoods, begetters,
letterers,
> > forwards, networks, warlords, wordless, cordless".
> >
> > Consider the evolution of "forgetters"
> >
> > words, letters
> > fords, getters
> > for-getters (recombining)
> >
> > This process takes just seconds, which is somewhat less than "zillions
of
> > years", and we have evolved from seven letters to ten letters.
>
> What is your population size and what is your mutation rate compared
> to the ratio of meaningful words in sequence space? In other words,
> how many sequences are you able to cover with each generation? Why
> is this important?
The Word Mutator calculates every possible mutation and recombination. The
Word Mutator does this not just for a single word, but for dozens or even
hundreds of words, composed of thousands of letters. This was the task you
insisted upon. We know how many mutants have to be covered in each
generations--and it is much less than "zillions". Indeed, it is not even
half a "zillion". But to answer this new objection.
In the example given with "words" and "letters", the Word Mutator was set to
the default Pond size of 25. (More words may be shown at the end of each
generation, but are pruned before the next generation.) That means we can
only have at most 25 different words under consideration. It also means that
each and every generation we will look at
*every possible mutation and every possible recombination of every possible
snippet of each and every one of these words inserted into every possible
point in each and every word*.
Is that clear enough? These recombinations are in the thousands, not the
"zillions", and can still result in the discovery of novel words. In a sea
swimming with trillions of such words and snippets of words, with at most a
few tens-of-thousands of mutants, every possible combination will be tried
simultaneously many times over. You must have missed the story, Sea of
Beneficence.
http://www.zachriel.com/mutagenation/Sea.asp
Try it and see. Put "talk" and "origins" into the Word Mutator, press
Generate, and out pops every possible mutation, snippet, or recombination.
"originals, origins, origin, stalk, talks, walk, balk, calk, tack, talk,
tank, task, talc, gins, tale, tall, gin, rig, ins, ors, in, or, a, i, o".
In particular take note of "originals" which is a recombination of "al" from
the middle of "talk" inserted into the middle of "origins".
> Consider, for example, a steady state population of 2 sequences
> "words" and "letters". Certainly "words" can evolve easily to "for"
> and letters can evolve easily to "getters". However, what are the
> odds that both sequences will evolve in this manner at the same time
> so that they can recombine with each other to form the unified word,
> "forgetters"?
We already know the answer. It's a virtual certainty. In any reasonably
sized population, every combination will be tried many, many times. There
just aren't that many combinations possible.
----------
Rather than calculate every single mutation as you originally required.
let's try random mutation. This random process is seen in the Word
Mutagenator, which not only mutates randomly, but
*inserts (recombines) random snippets from random words into random points
in random words*.
Is that clear? The results of the Word Mutagenator can't ever be exactly
replicated--due to the nature of random mutation--but the Word Mutagenator
(Pond = 150) just evolved "warhorses", "foresters" and "twittered" in 30
generations (generations in this case being simply screen updates every few
seconds). In 76 generations, the Word Mutagenator had discovered
"brassieres" and "betrotheds" at 10 letters. At generation 127, Word
Mutagenator had discovered "caseworkers" length 11.
It took about 5 minutes, which is considerably less than "zillions of
years." (And keep in mind that VBA is a slow interpreted language.) If you
run the Word Mutagenator, I can't say for sure that you will evolve
"betrotheds", but I can say with great confidence that with a reasonable
Pond Size and a few minutes of cpu-time, you will evolve novel words, some
of which will be longer than "letters".
(By the way, the limiting factors appear to be Pond Size and Time. Too small
a Pond Size and the words tend to be small. Too large a Pond Size and the
calculations can take a long time, but nowhere near as long as "zillions of
years". Program note: there is a courtesy time-out function after 10
seconds. You can find the setting on the Dictionary worksheet at "R30", but
you have to tools/protection/unprotect the worksheet to change it.)
I set Pond Size to 1000 and started again with "words" and "letters". After
728 generations, and about 800,000 randomly generated mutants, Word
Mutagenator had discovered "sandblasters" at length 12. After 1382
generations and 20 million mutations, we were up to "peppershakers" at
length 13. That's a long way from "words" and "letters" and took much less
than the square-root of zillions of seconds, er years.
> Also, you must consider that even when you have both
> "for" and "getters" at the same time and place that they may recombine
> in many non-meaningful ways (as I previously described, but which you
> snipped). For example, you could get "getforters" or "fogettersr" or
> gforetters", etc.
Every single one of those combinations is considered by the Word Mutator
(which tries every single combination), and every one of those combinations
are equally likely to be considered in the Word Mutagenator (which tries
random combinations) as any other combination.
The Word Mutagenator shows how random recombination of random snips between
random words results in new words, some long, some short, some with high
scrabble score, some with low scrabble score. From there it is a matter of
selection and Pond Size. Here is a typical Word Mutagenator example (Pond =
10, Select by Scrabble score):
Let's start with this simple string with a Scrabble score of 14: "sean,
pitman"
In a few seconds, we have a longer string with a Scrabble score of 72:
"flash, flips, pitman, flip, blip, limp, maim, pipe, bring, vanes"
A minute later, after about 19000 mutants considered, this is what a score
137 string looks like: "faxed, jaws, washy, flashed, primped, jaw, pshaw,
hashed, pimped, flashes"
> Of course, if your population were much larger than just 2 sequences,
As I pointed out, the population is longer than two sequences. That number
is set with the Size of Pond option.
> the odds of getting "for" and "getters" together at the same time in
> the proper orientation would be much better. As I recall, you use a
> population of 10^14. Now that is a rather large population size
That's the approximate number of microbes in the human gut. Not a very big
number biologically speaking. When you consider that these microbes can
reproduce every few hours (10^3 per year), and that each microbe has
hundreds or thousands of genetic bases (10^3), and that there are billions
of human guts (10^9)--that represents a number of gut-bug-bases tried each
year more on the order of 10^29. Over a few millions years, that adds up.
Sorry, my PC just can't do those sorts of calculations. Fortunately, it
isn't necessary.
> which
> indeed allows your computer to evolve fairly easily at the 7-letter
> and even higher levels in very short order, but still not as easily as
> it could evolve at the 2- or 3-letter levels, which is my entire
> point. You will note, even with your computer program, that it gets
> more and more difficult to evolve with each step up the ladder,
> requiring exponentially longer amounts of average time.
Granted, and calculated. There is an upper-bound on the order of L^3 where L
is the length of the string. So if we are evolving a string of combined
length 10, then our thumbnail number is 1000 mutants per generation; if our
string is of length 1000, then we can set an upper-limit of about a billion
mutants per generation. The vast majority of such mutants are not valid and
can be immediately discarded.
Gee whiz, "Beware a war of words ere you err" really can be discovered in
just a few generations and requires a working space of much less than
"zillions" letters. So, it is apparent that great complexity can be evolved
from simple beginnings "step-by-step".
> Given a
> population of 10^14, your computer would probably do ok up
Fortunately, it doesn't take "zillions" or even 10^14 calculations to
demonstrate the power of mutation and selection. It turns out we can evolve
long words and even longer strings of words after considering just a few
tens-of-thousands randomly generated mutants.
> till the or
> 30- or 40 character level before it started requiring "zillions" of
> years on average
No. It's on the order of L^3. By the way, what is the cube-root of "zillions
of years"?
(I note that you no longer claim that words longer than 7-letters can't be
evolved. Apparently your incredulity has been pushed back to 30 or 40
letters. Is this an admission, or a simple moving of the goal-posts?)
Zachriel
"Sean Pitman" <seanpi...@naturalselection.0catch.com> wrote in message
news:80d0c26f.04042...@posting.google.com...
Actually, Word Mutagenator can find new words by mutation and selection with
a population on the order of 10^3 to 10^5 letters.
> and a limited mutation rate
> (say once per individual per generation) where each meaningful random
> mutational change is positively selectable if meaningful according to
> standard English grammar and usage.
>
> Given these rules, the limited nature of the population size and
> mutation rate will limit the ability for meaningful evolution to
> create anything meaningful the size of a few hundred English
> characters (made up of letters and punctuation).
Now it's a few hundred characters. You started with more than only seven.
Dr. Pitman discusses 7-letter words:
http://tinyurl.com/yuuzm
> > If you could define an objective approach to measuring poetic elegance
> > and use that as a selection criterion, I am sure Zach's program could
> > write a new sonnet. But the problem (in this model, not in biological
> > evolution) is defining an objective criterion for "poetic elegance"
> > that you could plug into the "mindless process."
>
> This is not a problem at all since I do not demand poetry or elegance
> in the evolved sequence. All that I demand is coherent meaning of a
> string of characters provided by following the usual rules of English
> word definition and grammar.
>
> Zach thinks that he has really done something by evolving a number of
> English words of 10-letters or less using random mutation and
> English-based selection.
Actually quite a bit more than 10-letters--and it doesn't take "zillions of
years!" What I accomplished is pushing your incredulity back a few notches.
.. . .
Psst. Sean. Your "Gap" is showing.
Bill Rogers
>
> >
> > Sorry to answer the same post twice. When Zach's computer evolves a
> > Shakespeare sonnet in much less than a zillion years you will
> > doubtless complain that using the criterion "this character string
> > exists in Shakespeare's sonnets" as a selection is "intelligent
> > input." But it isn't. Intelligent input might occur if Zach scanned
> > the population by eye, laid it out as scrabble tiles and played around
> > with it until he found "My lady's eyes are nothing like the sun." But
> > establishing the selection criterion, as he will, is not intelligent
> > input. In real biological evolution the selection criteria are a lot
> > looser than this; there is no goal, no specific struggle to evolve a
> > red crested woodpecker, just a struggle to evolve something that's
> > good enough to hang in there.
>
> You don't seem to understand my challenge. What I am saying is that
> NO English language work the SIZE of a Shakespearean sonnet (say 600
> characters), be it an actual Shakespearean sonnet or not doesn't
> matter, will evolve with the use of a limited population size of
> evolving character strings (say 10^14) and a limited mutation rate
> (say once per individual per generation) where each meaningful random
> mutational change is positively selectable if meaningful according to
> standard English grammar and usage.
Well, here's a question then. What about my (misunderstood) version of
your challenge. Will Zach's program be able to evolve a specific
Shakespearean sonnet in a period of time less than zillions of years,
or not? I think this challenge is a bit easier than the other, but
only because the selection to apply at each step is simpler to define.
What's your prediction, though? Will it take more or less than
zillions of years? (Feel free to make them virtual years by defining
the length of time in each generation).
>
> Given these rules, the limited nature of the population size and
> mutation rate will limit the ability for meaningful evolution to
> create anything meaningful the size of a few hundred English
> characters (made up of letters and punctuation).
You should be very, very careful here. You are making a specific,
testable prediction. If you do that too often your goal posts will
have to start moving at relativistic speeds. The only problem for Zach
at this point is do define an appropriate selection for
"meaningfulness" to be applied at each generation. And I doubt that it
is that serious a problem. To the extent that it is a problem, is a
linguistic one, not an evolutionary one; but I do not think you will
be able to leave those goalposts in place for more than a week.
>
> > If you could define an objective approach to measuring poetic elegance
> > and use that as a selection criterion, I am sure Zach's program could
> > write a new sonnet. But the problem (in this model, not in biological
> > evolution) is defining an objective criterion for "poetic elegance"
> > that you could plug into the "mindless process."
>
> This is not a problem at all since I do not demand poetry or elegance
> in the evolved sequence. All that I demand is coherent meaning of a
> string of characters provided by following the usual rules of English
> word definition and grammar.
>
> Zach thinks that he has really done something by evolving a number of
> English words of 10-letters or less using random mutation and
> English-based selection. However, given the huge population size and
> rather rapid mutation rate that he used, this level of evolution is
> not a problem, even in very short periods of time. What Zach doesn't
> seem to realize though is that even the enormous population that he
> used, if kept at a steady state, would rapidly stall out in its
> attempts to evolve anything beyond a certain rather low level of
> meaningful complexity (i.e., far less than the size of a Shakespearean
> sonnet).
You keep saying this, but Zach is actually testing it, and finding,
repeatedly, that your goalposts are not far enough back. I would
suggest you make the following claim. Zach's computer program will not
be able to generate an original article that will be published by the
New Yorker (except maybe as a curiousity). I really think that that
goalpost is safe for you. The only problem is that the limiting factor
there will not be the size of sequence space (a modest number raised
to a very big power), but the inability to define an appropriate
selection. But nature has no problem whatsoever defining the selection
required in biological evolution.
I appreciate your keeping up the fight, because it is stimulating Zach
to do interesting things, but you're getting creamed.
>
> Sean
> www.naturalselection.0catch.com
Sean Pitman
> (I note that you no longer claim that words longer than 7-letters can't be
> evolved. Apparently your incredulity has been pushed back to 30 or 40
> letters. Is this an admission, or a simple moving of the goal-posts?)
Uh - excuse me?! Where did I ever say that 7-letter sequences or even
10 or 20 letter sequences would take "zillions" of years to evolve? -
Especially with populations of hundreds of trillions of individuals
and high mutation rates? You claim over and over again on your
website that I made this claim, but I never did. Go back and read
what I actually wrote in both talk.orgins discussions as well as on my
own website.
For example, here is a portion of one discussion I had on talk.origins
a good while back:
"So if, on average, it took a colony of malaria parasites 10 years to
cross a gap of 5 neutral steps, then 6 neutral steps would take over
200 years, 7 steps would take 4,000 years, 8 steps would take 80,000
years, etc., on average. Increasing the population will help, but
after a point the population simply cannot keep up with the
statistical averages and evolutionary processes simply stall out
searching through all the search space required to find the
exponentially rarer and rarer functions at increasing levels of
complexity this side of trillions upon trillions of years." (1)
Or consider the following discussion:
"A population of 10,000 such sequences (blind men) would find most if
not all the beneficial 3-letter words (ice-cream cones) in 3-letter
sequence space in less than 30 generations (given that there was one
step each, on average, per generation).
This looks good so far now doesn't it? However, the problems come as
you move up the ladder of specified complexity. Using language as an
illustration again, it is not so easy to evolve new beneficial
sequences that require say, 20 fairly specified letters, to transmit
an idea/function. Now, each member of our 10,000 blind men is going
to have to take over a trillion steps before success (the finding of a
new type of beneficial state/ice cream cone) is realized for just one
of them at this level of complexity." (2)
It seems then that you have quoted me entirely out of context in an
attempt to discredit my position far beyond what you have actually
been able to demonstrate. You have in fact done nothing beyond what I
myself have already predicted.
Don't give up though. Keep trying. It has been most interesting.
Sean Pitman
> > You don't seem to understand my challenge. What I am saying is that
> > NO English language work the SIZE of a Shakespearean sonnet (say 600
> > characters), be it an actual Shakespearean sonnet or not doesn't
> > matter, will evolve with the use of a limited population size of
> > evolving character strings (say 10^14)
>
> Actually, Word Mutagenator can find new words by mutation and selection with
> a population on the order of 10^3 to 10^5 letters.
Again, random walk does pretty good at low levels, even levels
requiring a dozen or so letters with such a population size and
mutation rate. However, even with your 100 trillion individuals, you
can't evolve anything meaningful in English the size of a relatively
short Sonnet of, say, just 500 characters.
> > and a limited mutation rate
> > (say once per individual per generation) where each meaningful random
> > mutational change is positively selectable if meaningful according to
> > standard English grammar and usage.
> >
> > Given these rules, the limited nature of the population size and
> > mutation rate will limit the ability for meaningful evolution to
> > create anything meaningful the size of a few hundred English
> > characters (made up of letters and punctuation).
>
> Now it's a few hundred characters. You started with more than only seven.
>
> Dr. Pitman discusses 7-letter words:
> http://tinyurl.com/yuuzm
Why don't you reference a specific thread or statement that I made
where I actually said that evolution at the level of 7-letters would
take "zillions of years"? Again, I never said this even though you
keep claiming that I did like a mantra.
> > > If you could define an objective approach to measuring poetic elegance
> > > and use that as a selection criterion, I am sure Zach's program could
> > > write a new sonnet. But the problem (in this model, not in biological
> > > evolution) is defining an objective criterion for "poetic elegance"
> > > that you could plug into the "mindless process."
> >
> > This is not a problem at all since I do not demand poetry or elegance
> > in the evolved sequence. All that I demand is coherent meaning of a
> > string of characters provided by following the usual rules of English
> > word definition and grammar.
> >
> > Zach thinks that he has really done something by evolving a number of
> > English words of 10-letters or less using random mutation and
> > English-based selection.
>
> Actually quite a bit more than 10-letters--and it doesn't take "zillions of
> years!" What I accomplished is pushing your incredulity back a few notches.
How much more Zach? Pretty soon it really does require "zillions of
years". Try evolving just 100 uniquely meaningful characters
sequences just 100 characters in minimum size with your huge
population and high mutation rate and see how many generations it
takes.
> Psst. Sean. Your "Gap" is showing.
Why thank you! I'm glad that you are finally starting to see it. My
"Gap" is rather impressive, if I do say so myself! ; )
But really Zach, it is your misquoting and distortion of my position
that is really glaring.
Sean Pitman
> > You don't seem to understand my challenge. What I am saying is that
> > NO English language work the SIZE of a Shakespearean sonnet (say 600
> > characters), be it an actual Shakespearean sonnet or not doesn't
> > matter, will evolve with the use of a limited population size of
> > evolving character strings (say 10^14) and a limited mutation rate
> > (say once per individual per generation) where each meaningful random
> > mutational change is positively selectable if meaningful according to
> > standard English grammar and usage.
>
> Well, here's a question then. What about my (misunderstood) version of
> your challenge. Will Zach's program be able to evolve a specific
> Shakespearean sonnet in a period of time less than zillions of years,
> or not? I think this challenge is a bit easier than the other, but
> only because the selection to apply at each step is simpler to define.
> What's your prediction, though? Will it take more or less than
> zillions of years? (Feel free to make them virtual years by defining
> the length of time in each generation).
If you already have the specific pattern of comparison beforehand,
then selection based on comparison to a pre-established pattern isn't
a problem at all and will happen rapidly. This is exactly what
Dawkins did with his "Methinks it is like a weasel" evolution
scenario. This is not how evolution works (at least not the type of
evolution that I am interested in) or even can work since there is no
pre-established pattern. You can only select for function changes,
not spelling or pattern changes.
> > Given these rules, the limited nature of the population size and
> > mutation rate will limit the ability for meaningful evolution to
> > create anything meaningful the size of a few hundred English
> > characters (made up of letters and punctuation).
>
> You should be very, very careful here. You are making a specific,
> testable prediction.
Exactly. My position is in fact a scientific position since it is in
fact testable in a falsifiable manner. Why then should I be careful
to avoid making my position testable?
> If you do that too often your goal posts will
> have to start moving at relativistic speeds.
Not if they are pretty much correct as currently stated, which they
still seem to be despite Zach's repetitive misrepresentations of my
position . . .
> The only problem for Zach
> at this point is do define an appropriate selection for
> "meaningfulness" to be applied at each generation.
This has already been taken care of. "Meaningfulness", in terms of
this particular experiment, is defined as anything that makes
meaningful sense in English, be it a word or phrase of meaningfully
arranged words.
> And I doubt that it
> is that serious a problem. To the extent that it is a problem, is a
> linguistic one, not an evolutionary one; but I do not think you will
> be able to leave those goalposts in place for more than a week.
Well then, we will just have to see about that since they have been in
place for well over a year now already.
> > > If you could define an objective approach to measuring poetic elegance
> > > and use that as a selection criterion, I am sure Zach's program could
> > > write a new sonnet. But the problem (in this model, not in biological
> > > evolution) is defining an objective criterion for "poetic elegance"
> > > that you could plug into the "mindless process."
> >
> > This is not a problem at all since I do not demand poetry or elegance
> > in the evolved sequence. All that I demand is coherent meaning of a
> > string of characters provided by following the usual rules of English
> > word definition and grammar.
> >
> > Zach thinks that he has really done something by evolving a number of
> > English words of 10-letters or less using random mutation and
> > English-based selection. However, given the huge population size and
> > rather rapid mutation rate that he used, this level of evolution is
> > not a problem, even in very short periods of time. What Zach doesn't
> > seem to realize though is that even the enormous population that he
> > used, if kept at a steady state, would rapidly stall out in its
> > attempts to evolve anything beyond a certain rather low level of
> > meaningful complexity (i.e., far less than the size of a Shakespearean
> > sonnet).
>
> You keep saying this, but Zach is actually testing it, and finding,
> repeatedly, that your goalposts are not far enough back.
Zach has _claimed_ that I have moved my goalposts. But, if you look
carefully and don't just take Zach's bravado for reality, you will
notice that my goalposts are right were they were before Zach came
along and made his website about me.
> I would
> suggest you make the following claim. Zach's computer program will not
> be able to generate an original article that will be published by the
> New Yorker (except maybe as a curiousity). I really think that that
> goalpost is safe for you.
Yes, that would be a very safe bet, but not really significantly more
safe than my current position as previously stated.
> The only problem is that the limiting factor
> there will not be the size of sequence space (a modest number raised
> to a very big power), but the inability to define an appropriate
> selection.
Again, there is no inability to define appropriate selection. The
selection criteria is anything and everything that actually makes
sense in the English language system. This limiting factor then is in
fact the ratio of beneficial vs. non-beneficial sequences existing
within the sequence space.
> But nature has no problem whatsoever defining the selection
> required in biological evolution.
No, it doesn't. Nature just has a problem evolving new beneficial
functions beyond the lowest levels of functional complexity and
completely stalls out this side of any function requiring more than a
couple thousand fairly specified amino acids working together at the
same time.
> I appreciate your keeping up the fight, because it is stimulating Zach
> to do interesting things, but you're getting creamed.
I'm only getting creamed if you actually believe what Zach says about
my position without actually checking up to see if Zach's claims are
actually valid.
Sean
www.naturalselection.0catch.com
Zachriel
> "Zachriel" <sp...@zachriel.com> wrote in message
news:<C-Kdnc_H6oD...@adelphia.com>...
>
> > > You don't seem to understand my challenge. What I am saying is that
> > > NO English language work the SIZE of a Shakespearean sonnet (say 600
> > > characters), be it an actual Shakespearean sonnet or not doesn't
> > > matter, will evolve with the use of a limited population size of
> > > evolving character strings (say 10^14)
> >
> > Actually, Word Mutagenator can find new words by mutation and selection
with
> > a population on the order of 10^3 to 10^5 letters.
>
> Again, random walk does pretty good at low levels, even levels
> requiring a dozen or so letters with such a population size and
> mutation rate. However, even with your 100 trillion individuals, you
> can't evolve anything meaningful in English the size of a relatively
> short Sonnet of, say, just 500 characters.
Moving the goal-posts, eh Sean? This was your challenge:
"Just try a little experiment yourself. Start with a short 2 or
3-letter word and see how many words you can evolve that require greater and
greater minimum sequence requirements. No doubt you will quickly find
yourself coming to walls of meaningless or non-beneficial potential options
that separate you from every other meaningful and beneficial option. . . .
(Genetic evolution works the very same way)."
You said to evolve "words", Sean, "words". I warned you to "beware a war of
words", then you could have continued on with your fallacious arguments
about genetics--*but you kept insisting*. I warned you repeatedly. Now you
have been shown to be wrong, and are currently attempting to move the
goal-posts.
Your challenge has been met. Quit moving the goal-posts.
Zachriel
> "Zachriel" <sp...@zachriel.com> wrote in message
news:<DLOdncSo6bz...@adelphia.com>...
>
> > (I note that you no longer claim that words longer than 7-letters can't
be
> > evolved. Apparently your incredulity has been pushed back to 30 or 40
> > letters. Is this an admission, or a simple moving of the goal-posts?)
>
> Uh - excuse me?! Where did I ever say that 7-letter sequences
That was a little bit of the Patented Pitman Hand-Waving. Note that I said
"longer than". I didn't specify when "zillions" take over for merely big
numbers--and neither did you! However you did say this explicitly, and this
is your challenge:
"Just try a little experiment yourself. Start with a short 2 or
3-letter word and see how many words you can evolve that require greater and
greater minimum sequence requirements. No doubt you will quickly find
yourself coming to walls of meaningless or non-beneficial potential options
that separate you from every other meaningful and beneficial option. . . .
(Genetic evolution works the very same way).
"Without some sort of outside pre-established guidance, such a random
walk quickly works itself into the trillions upon trillions of years
of average time at fairly low levels of specified complexity."
http://tinyurl.com/33otq
Is "trillions upon trillions" a "zillion"? Your use of the word "walls"
indicates an impassable barrier. After our calculations and experimentations
we have determined that this assertion is FALSE and MISLEADING. You have
gone from a few letters, and a few exponents, to falsely claim that you have
"disproven" evolution.
> or even
> 10 or 20 letter sequences would take "zillions" of years to evolve? -
> Especially with populations of hundreds of trillions of individuals
> and high mutation rates?
> You claim over and over again on your
> website that I made this claim, but I never did. Go back and read
> what I actually wrote in both talk.origins discussions as well as on my
> own website.
Um, my simulation dealt with only a population of one member per species
(plus mutants) and no more than one mutation per mutant per generation.
Let's check the numbers. Here is another Sean Pitman claim:
"In the English language system there are around 23,109 meaningful
7-letter words. This seems like a lot until one realizes that there are
8,031,810,176 potential 7-letter words out there in 7-letter sequence space.
.. . . With a population of 1, this random walk will take, on average, over
300,000 mutations to arrive at a new meaningful word at the level of
7-letters."
http://tinyurl.com/2c4fk
This also is FALSE. There are two problems with the statement. First, it
implies that any 7-letter word can be evolved (under our rules). This is not
true. For instance (assuming "qqqqqq" is added to our Dictionary), "pitman"
will never evolve into "qqqqqq" no matter how long our simulation runs.
There is no simply path from "pitman" to "qqqqqq". And even though
"Zachriel" is in our Dictionary, I have never seen "Zachriel" naturally
occur.
Second, you seriously miscalculate the number of mutants. There are (no more
than) 646 mutants with seven-letters. (Word Mutator double-counts some
mutants for technical reasons, but counts every mutant at least once.) That
means there are at most 646 mutants per generation. So let's look for a path
from "pitman" to "beware".
pitman
pit man
pi mar
bi mare
be ware
beware
So we know a path exists. Counting seven-letters for each generation, there
are 646*7 possible mutants along our path due to our careful selection at
each generation. If we can't find an appropriate path, then the number of
mutations required might be a bit higher as we experiment with a few winding
paths. Without selection, it could take much more, perhaps even more than a
Pitman Zillion!
This is important: There is no way to know if particular words are evolvable
by simply using exponents. The words might be lined up nice and pretty, or
they might be separated by impassable evolutionary barriers. There is no way
to know without actually testing and with some sort of selection criterion.
It turns out that most words are indeed lined up nice and pretty. They
weren't designed that way, but they accreted that way through the historical
evolution of the language. Consider "denominationalists" at 18-letters. How
many different Latin conjugations are required to make up that word? "de",
"nom", "in", "nate", "tion", "al", "ist", "s". Hopefully, this example helps
everyone understand why so many words are evolvable--because our process of
word discovery emulates, in a fashion, the historical evolution of words.
Now, let's look at another Pitman Number:
"the potential space of a 14-letter word or phrase is over
109,418,989,131,512,359,209 (over 100 million trillion). . . . Very quickly
the exponential expansion of the meaningless ocean outpaces the ability of
any population on this earth to keep up - and the evolution of new functions
at this level of complexity simply stalls out."
http://tinyurl.com/2zlue
Is 10^20 a "zillion"? It would take Word Mutator thousands of years to try
that many mutants. (Ok, ok. I wrote it in VBA. It would run perhaps 10^2
times faster in a dialect of C or machine language.) Yet, Word Mutator
evolves 14-letter words quite regularly. Even the slower Word Mutagenator,
working randomly one mutant at a time, evolves 14-letter words in just a few
minutes (though there is a problem with it timing out, which I will try to
correct in the next revision).
In brief, your formula is, letting L = number of letters and N = number of
valid words of length N, N / (26^L). You are correct that you do not pin
yourself down as to exactly when "zillions" takes over from merely huge
numbers. However, this calculation is FALSE and MISLEADING for the reasons
given above. Specifically, the number of mutants for 14-letters is actually
no more than 2552 per generation, and for 26-letters it's no more than
11582. More interesting is multiple words. "Sean" and "Pitman" as two words
has 1014 mutants, while "SeanPitman" as one word has 1270 mutants. That's
because snippets like "nP" are considered in the latter example.
And here is a typical example of a Patented Pitman Handwaving:
"The problem here is that there simply is not enough time this side of
zillions of years to get the limited number of phrases to "bump together"
enough times to make anything beyond the lowest levels of functional
complexity without the input of a higher intelligence or pre-established
information system. It just won't happen. Try it and see."
<snip more Exponential Pitman>
Sean, it was ok to start a new thread on this, but try not to post it in two
*different* threads, or I have to respond in both places, especially since
one post was xposted to a second newsgroup, and the other wasn't.
Sean Pitman
> > > (I note that you no longer claim that words longer than 7-letters can't be
> > > evolved. Apparently your incredulity has been pushed back to 30 or 40
> > > letters. Is this an admission, or a simple moving of the goal-posts?)
> >
> > Uh - excuse me?! Where did I ever say that 7-letter sequences
>
> That was a little bit of the Patented Pitman Hand-Waving. Note that I said
> "longer than". I didn't specify when "zillions" take over for merely big
> numbers--and neither did you! However you did say this explicitly, and this
> is your challenge:
Come on now Zach. You know that in claiming that I said that words,
"longer than 7-letters can't be evolved" you are grossly
misrepresenting what I actually said since your statement seems to
indicate that I believe that sequences just a little bit longer than
7-letters could not be evolved.
On top of this, I did specify many times were I thought "zillions"
(i.e., trillions upon trillions upon trillions) of years would take
over. For example, in my discussions of genetic evolution I predicted
that the level of impossibility would occur for the evolution of
functions at just a couple thousand fairly specified amino acids
working together at the same time. You, however, strongly
misrepresent my position in your posts and on my website by making it
seem like I said that evolution of meaningful 7-letter sequences or
something at least close to that would require "zillions" of years.
Of course, I never said anything of the sort.
> "Just try a little experiment yourself. Start with a short 2 or
> 3-letter word and see how many words you can evolve that require greater and
> greater minimum sequence requirements. No doubt you will quickly find
> yourself coming to walls of meaningless or non-beneficial potential options
> that separate you from every other meaningful and beneficial option. . . .
> (Genetic evolution works the very same way).
And this is still my position. You certainly haven't come close to
showing how this statement is wrong . . .
> "Without some sort of outside pre-established guidance, such a random
> walk quickly works itself into the trillions upon trillions of years
> of average time at fairly low levels of specified complexity."
> http://tinyurl.com/33otq
Again, where have you shown this statement to be wrong?
> Is "trillions upon trillions" a "zillion"?
Sure, why not . . . I just can't believe that you're so hung up over
this word "zillion." I give plenty of very specific numbers on my
posts as well and yet you pick one word out and start harping away on
it when you know full well what I meant when I used it.
> Your use of the word "walls"
> indicates an impassable barrier. After our calculations and experimentations
> we have determined that this assertion is FALSE and MISLEADING. You have
> gone from a few letters, and a few exponents, to falsely claim that you have
> "disproven" evolution.
Your calculations have done nothing more than my own calculations and
statements have already predicted. I didn't not predict an
"impassable barrier" at the level of 7-fairly specified characters or
even 20 or 30 even though you misstate that I did over and over again.
As I have detailed to you before, even with a population of 100
trillion (or even a trillion trillion) and a high mutation rate per
generation, the impassable wall becomes insurmountable this side of
trillions upon trillions upon trillions of years (i.e., zillions) when
the minimum fairly specified sequence requirement reaches several
hundred to a few thousand for a given type of function.
I have made this same sort of predictive statement many times in this
forum and on my website if you care to look. Evidently though, you
prefer to ignore such statements so that you can build your own straw
man representation of my position.
> > or even
> > 10 or 20 letter sequences would take "zillions" of years to evolve? -
> > Especially with populations of hundreds of trillions of individuals
> > and high mutation rates?
> > You claim over and over again on your
> > website that I made this claim, but I never did. Go back and read
> > what I actually wrote in both talk.origins discussions as well as on my
> > own website.
>
> Um, my simulation dealt with only a population of one member per species
> (plus mutants) and no more than one mutation per mutant per generation.
Yes, and your point is . . . ?
My point is that on your website you specifically use the number 10^14
as a population that could evolve very complex meaningful sequences in
a very short amount of time. My argument is that EVEN if you could
monitor such a huge population in computer simulation (which you can't
owing to a lack of memory as well as speed), you would never evolve a
meaningful English text the size of a small Shakespearean sonnet.
Certainly the use of a significantly smaller population size, even
with a very high mutation rate, would do significantly worse in the
same challenge.
What I am saying here is that your "O Sean" poem and anything else of
equivalent size would not evolve using truly random rules of mutation
combined with meaning/function based selection as I have previously
detailed.
> Let's check the numbers. Here is another Sean Pitman claim:
>
> "In the English language system there are around 23,109 meaningful
> 7-letter words. This seems like a lot until one realizes that there are
> 8,031,810,176 potential 7-letter words out there in 7-letter sequence space.
> .. . . With a population of 1, this random walk will take, on average, over
> 300,000 mutations to arrive at a new meaningful word at the level of
> 7-letters."
> http://tinyurl.com/2c4fk
>
> This also is FALSE. There are two problems with the statement. First, it
> implies that any 7-letter word can be evolved (under our rules). This is not
> true. For instance (assuming "qqqqqq" is added to our Dictionary), "pitman"
> will never evolve into "qqqqqq" no matter how long our simulation runs.
> There is no simply path from "pitman" to "qqqqqq". And even though
> "Zachriel" is in our Dictionary, I have never seen "Zachriel" naturally
> occur.
Even according to your rules, if you extrapolate them, evolving
"qqqqqq" should be no problem since a path does actually exist - as
you envision paths existing that is. For example, consider a
population of six sequences in a population of 6 reading, "queen,
quiet, quite, quick, quilt, and quiz". Lets say that in a single
generation they all recombined in the following fashion before the
selection process took place:
"Quiet" recombined with "queen" to read, "qquieteen" and then "quite"
recombined with "qquieteen" to read "qqquiteuieteen", and etc., until
you ended up with "qqqqqquizuiltuickuiteuieteen." Aha! Successful
pathway established!
Of course, you will argue by saying, "what are the odds of all size
sequences recombining in one generation like this?!" And, I will
answer by saying, "Not very good at all, but still _possible_." Of
course, although possible, the average number of generations required
would no doubt be quite high indeed.
> Second, you seriously miscalculate the number of mutants. There are (no more
> than) 646 mutants with seven-letters. (Word Mutator double-counts some
> mutants for technical reasons, but counts every mutant at least once.) That
> means there are at most 646 mutants per generation.
As I see it, this is one of your problems. You calculate the number
646 based on the perspective of a single individual 7-letter sequence
over the course of just one generation. What you need to do to
calculate the total number of possible mutants that could be realized,
even in one generation, is to consider _all_ members of your
population. For example, say you had a population of 10 different
7-letter sequences. With each of these 10 sequences in the population
being able to go to any one of 646 sequences, the population as a
whole would be able to cover 6,460 sequences in one generation -
right? Now, this isn't what really happens of course since there are
only 10 individuals. At most they can only reach 10 different
sequences per generation with a mutation rate of one mutation per
sequence per generation.
The fact of the matter is that no matter how you look at it, the
sequence space for 7-letter sequences remains the same at just over 8
billion. Given say, 40,000 meaningful 7-letter sequences total, each
meaningful 7-letter sequence is surrounded, on AVERAGE, by about
200,000 meaningless sequences.
Of course, you think to disprove this by showing that many
interconnected islands of 7-letter sequences exist in 7-letter
sequence space. But, I never argued that this was not the case. I
even argued that it was the case, though I disagree with how you
connect some of your islands as I will discuss after your next point .
. .
> So let's look for a path
> from "pitman" to "beware".
>
> pitman
> pit man
> pi mar
> bi mare
> be ware
> beware
Consider for a moment what you have just done here - though I have
explained this to you time and again and you will most likely snip
this explanation as you have snipped the others. What you have done
is divide your starting sequence into two populations of smaller and
more easily evolved meaningful sequences. You then join these two
populations together at some point in time when their combination
would again be meaningful as a larger sequence. For example, "pi" and
"mar" cannot combine because the combination would be the meaningless
sequence "pimar" - right? However, "be" and "ware" can combine
because the sequence "be ware" makes meaningful sense in English -
right? What you seem to not take into account is the average number
of generations in a given population that would be required to
successfully achieve this sort of division and recombination.
Say, for example, that you had a population limit of two sequences
(owing to environmental factors which limit your population from
further growth) with a mutation rate of one mutation per generation.
You start out with a population of 1 that reads, "pitman". In each
generation "pitman" produces two offspring. If both offspring are
meaningless/non-functional, the original "pitman" survives. If only
one offspring is meaningful, the original "pitman" also survives, for
a total of 2 members in our population. If both offspring are
meaningful, the original "pitman" dies and each of the two offspring
each produce two more offspring in the next generation, but the 2
"weakest" must die in that generation to maintain the population at
the max of 2.
Considering that you have all kinds of possible mutations, to include
point, deletion, insertion, split and recombination mutations
available, how many generations, on average, would it take to get the
meaningful split in "pitman" to form two smaller populations, such as
"pit" and "man"? Not all splits will be meaningful - right? In fact,
the ratio of meaningful "pitman" splits is 1 in 5 and the ratio of
split to non-split mutations is also 1 in 5 for a total odds of a
meaningful split of 1 in 25 mutations, or one in about 12 generations
in our steady state population of 2.
Now, say we get or "pit" and "man", each of these will mutate
separately down different paths - right? How many generations will it
take, on average, before both of these paths come to new sequences
that are not only meaningful independently, but would also be
meaningful IF they happened to be united by a recombination mutation?
I'm not sure what the answer is, but it wouldn't be too hard to find
out I'm sure. But, for now, let's just say that the odds of this
happening are around 1 in 20. The problem here is that it is not
enough to get two populations at the same time that COULD recombine to
form a meaningful sequence. What needs to happen is that a CORRECT
recombination mutation DOES happen exactly when it is beneficial.
Now, what are the odds of that?
Well, there are several ways that "be" and "ware" could recombine, but
few of these possibilities are "meaningful" in the English language
system. You could get "wbeare" or "wabere" or "warbee" or "bwaree" or
"warebe" or "beware". So, the odds of getting a meaningful
recombination is 1 in 6. Then, you must also consider the odds that a
recombination event will occur right at this time instead of another
possible type of mutation for an additional odds ratio of 1 in 5.
So, the total odds of successful recombination would be 1/6 * 1/5 *
1/20 = 1 in 600 generations. And, this is only for very short
sequences with very high ratios of non-recombined meaning vs.
non-meaning. This problem gets exponentially worse with each step of
the ladder of complexity.
Do you see the problem? Just because it CAN happen does not mean that
it WILL happen all that often. Does your computer program take this
little problem into account? You certainly don't in your written out
evolutionary scenarios. You simply assume that the path will be
easily found if it exists, but this is a fallacy.
> So we know a path exists. Counting seven-letters for each generation, there
> are 646*7 possible mutants along our path due to our careful selection at
> each generation. If we can't find an appropriate path, then the number of
> mutations required might be a bit higher as we experiment with a few winding
> paths. Without selection, it could take much more, perhaps even more than a
> Pitman Zillion!
See above descriptions of the problem with this "a path exists and
therefore evolution will be rapid" assumption.
> This is important: There is no way to know if particular words are evolvable
> by simply using exponents. The words might be lined up nice and pretty, or
> they might be separated by impassable evolutionary barriers. There is no way
> to know without actually testing and with some sort of selection criterion.
Actually, there is a very good way of knowing, beyond a reasonable
doubt that is, seeing as how no known language/information system, is
lined up as nicely as would be required for Darwinian-style evolution
to get beyond the lowest levels of existing complexity found in such
language systems. Why then should the genetic language/information
system found in living things be any different? And, in fact it is
not. Real life experiments have proved as much. In real life
evolution stalls at the lowest levels of functional complexity so that
there simply are no examples of a cellular function evolving that
requires more than a few hundred fairly specified amino acids working
together at the same time. There are examples of less complex
cellular functions evolving all the time, but evolution stalls out as
one looks higher than the few hundred fairly specified amino acid
level.
> It turns out that most words are indeed lined up nice and pretty.
This is true at the lower end of the spectrum of sequence lengths, but
you will notice that this becomes less and less true, in an
exponential fashion, with increasing minimum sequence length until the
remaining islands are relatively tiny and non-connected to the other
tiny islands in a truly vast ocean of non-meaningful sequences.
> They
> weren't designed that way, but they accreted that way through the historical
> evolution of the language. Consider "denominationalists" at 18-letters. How
> many different Latin conjugations are required to make up that word? "de",
> "nom", "in", "nate", "tion", "al", "ist", "s". Hopefully, this example helps
> everyone understand why so many words are evolvable--because our process of
> word discovery emulates, in a fashion, the historical evolution of words.
Consider also that this historical human language evolution had the
benefit of directing intelligence, which was able to cross gaps that
could not be so easily crossed by mindless evolutionary processes.
Human learning and language evolution are _not_ the same thing as
Darwinian-style evolution of mindless genetic information systems and
should not be compared as if they were the same or even very similar
processes.
> In brief, your formula is, letting L = number of letters and N = number of
> valid words of length N, N / (26^L). You are correct that you do not pin
> yourself down as to exactly when "zillions" takes over from merely huge
> numbers. However, this calculation is FALSE and MISLEADING for the reasons
> given above.
I'm glad that you actually admit that I never said the word "zillions"
outside of a relationship to truly enormous numbers, such as 10^100 or
10^1000 or some other such number. Also, it is not false or
misleading at all to roughly estimate the average time to evolve novel
meaningful sequences by dividing the total number of meaningful
sequences by the total size of sequence space. It works pretty good
at narrowing down the rough limits of evolutionary potential.
Certainly you have done nothing to counter my predictions in any sort
of significant way thus far. Neither your above reasons nor your
computer program simulation have done much of anything that I can
tell. You haven't even come close to showing that you can evolve
anything significantly beyond where I said you could (given a _true_
evolutionary scenario of truly random mutations and function-based
selection in a limited steady state population).
> Specifically, the number of mutants for 14-letters is actually
> no more than 2552 per generation, and for 26-letters it's no more than
> 11582.
Again, as pointed out above, this is not true for anything more than a
population of 1 evolving at the same time and it meanings nothing as
far as the average time a population needs to evolve a new meaningful
sequence of a given length.
> More interesting is multiple words. "Sean" and "Pitman" as two words
> has 1014 mutants, while "SeanPitman" as one word has 1270 mutants. That's
> because snippets like "nP" are considered in the latter example.
>
> And here is a typical example of a Patented Pitman Handwaving:
>
> "The problem here is that there simply is not enough time this side of
> zillions of years to get the limited number of phrases to "bump together"
> enough times to make anything beyond the lowest levels of functional
> complexity without the input of a higher intelligence or pre-established
> information system. It just won't happen. Try it and see."
Yes, try it and see. Only this time, try to actually prove that my
_true_ position is incorrect instead of attacking some strawman
version of my position.
> Sean, it was ok to start a new thread on this, but try not to post it in two
> *different* threads, or I have to respond in both places, especially since
> one post was xposted to a second newsgroup, and the other wasn't.
Sorry about that. I'll stick with this thread from now on then.
Zachriel
> "Zachriel" <sp...@zachriel.com> wrote in message
news:<NPadnbOGK9N...@adelphia.com>...
>
> > > > (I note that you no longer claim that words longer than 7-letters
can't be
> > > > evolved. Apparently your incredulity has been pushed back to 30 or
40
> > > > letters. Is this an admission, or a simple moving of the
goal-posts?)
> > >
> > > Uh - excuse me?! Where did I ever say that 7-letter sequences
> >
> > That was a little bit of the Patented Pitman Hand-Waving. Note that I
said
> > "longer than". I didn't specify when "zillions" take over for merely big
> > numbers--and neither did you! However you did say this explicitly, and
this
> > is your challenge:
>
> Come on now Zach. You know that in claiming that I said that words,
> "longer than 7-letters can't be evolved" you are grossly
> misrepresenting what I actually said since your statement seems to
> indicate that I believe that sequences just a little bit longer than
> 7-letters could not be evolved.
I quoted you extensively and pointed people to your original posts. They are
more than capable of making up their own minds as to how you use vagueness
and goal-post moving to avoid being pinned down.
Your challenge, "start a short 2 or 3-letter word and see how many words you
can evolve that require greater and greater minimum sequence requirements.
No doubt you will quickly find yourself coming to walls of meaningless or
non-beneficial potential options . . . "
You said "words". How long of words did you have in mind? The Word Mutator
has evolved 18-letter words, and overnight evolved a third of the available
Dictionary of 78,000 words. The Word Mutagenator has evolved 14-letter words
and thousands of words of varying length.
You gave the clear impression that we couldn't evolve long words by mutation
and selection. You were wrong. The Word Mutator not only evolves long words,
but evolves words with high scrabble score, short words, middle-sized words,
anything you want.
Admit it and move on.
> On top of this, I did specify many times were I thought "zillions"
> (i.e., trillions upon trillions upon trillions) of years would take
> over. For example, in my discussions of genetic evolution I predicted
> that the level of impossibility would occur for the evolution of
> functions at just a couple thousand fairly specified amino acids
> working together at the same time. You, however, strongly
> misrepresent my position in your posts and on my website by making it
> seem like I said that evolution of meaningful 7-letter sequences or
> something at least close to that would require "zillions" of years.
> Of course, I never said anything of the sort.
>
> > "Just try a little experiment yourself. Start with a short 2 or
> > 3-letter word and see how many words you can evolve that require greater
and
> > greater minimum sequence requirements. No doubt you will quickly find
> > yourself coming to walls of meaningless or non-beneficial potential
options
> > that separate you from every other meaningful and beneficial option. . .
..
> > (Genetic evolution works the very same way).
>
> And this is still my position. You certainly haven't come close to
> showing how this statement is wrong . . .
Hold it now. You say to start with 2- and 3-letter words, try to evolve
longer words, and you will "quickly find yourself coming to walls". I have
extensively tested this assertion and found it FALSE.
> > "Without some sort of outside pre-established guidance, such a
random
> > walk quickly works itself into the trillions upon trillions of years
> > of average time at fairly low levels of specified complexity."
> > http://tinyurl.com/33otq
>
> Again, where have you shown this statement to be wrong?
>
> > Is "trillions upon trillions" a "zillion"?
>
> Sure, why not . . . I just can't believe that you're so hung up over
> this word "zillion."
Because it doesn't take "zillions", or even millions. It takes on the order
of 10^3 to 10^6 mutations to evolve dozens of long words. It takes on the
order of 10^9 per generation to evolve strings of length 1000.
> I give plenty of very specific numbers on my
> posts as well and yet you pick one word out and start harping away on
> it when you know full well what I meant when I used it.
Yes, we all know exactly what you meant. You just didnt think anybody would
or could call you on it.
> > Your use of the word "walls"
> > indicates an impassable barrier. After our calculations and
experimentations
> > we have determined that this assertion is FALSE and MISLEADING. You have
> > gone from a few letters, and a few exponents, to falsely claim that you
have
> > "disproven" evolution.
>
> Your calculations have done nothing more than my own calculations and
> statements have already predicted. I didn't not predict an
> "impassable barrier" at the level of 7-fairly specified characters or
You stated these walls are approached "quickly" after starting at 2- or
3-letter words. What exactly did you mean then? When do we reach these
walls?
> even 20 or 30 even though you misstate that I did over and over again.
> As I have detailed to you before, even with a population of 100
> trillion (or even a trillion trillion) and a high mutation rate per
> generation, the impassable wall becomes insurmountable this side of
> trillions upon trillions upon trillions of years (i.e., zillions) when
> the minimum fairly specified sequence requirement reaches several
> hundred to a few thousand for a given type of function.
This is FALSE. The number of possble mutants for a letter-string of length
1000 is upper-bounded by 1000^3 or about a billion per generation.
> I have made this same sort of predictive statement many times in this
> forum and on my website if you care to look. Evidently though, you
> prefer to ignore such statements so that you can build your own straw
> man representation of my position.
Absolutely not. Your position is clearly represented on Google-Groups. You
made an analogy to words. I pointed out that your analogy was faulty. You
insisted you were right. I created a poem to give you some indication that
it was quite easy to evolve between words. You kept insisting your were
right. You could have abandoned the analogy--it's just an analogy--but you
insisted. You reap what you sow.
> > > or even
> > > 10 or 20 letter sequences would take "zillions" of years to evolve? -
> > > Especially with populations of hundreds of trillions of individuals
> > > and high mutation rates?
> > > You claim over and over again on your
> > > website that I made this claim, but I never did. Go back and read
> > > what I actually wrote in both talk.origins discussions as well as on
my
> > > own website.
> >
> > Um, my simulation dealt with only a population of one member per species
> > (plus mutants) and no more than one mutation per mutant per generation.
>
> Yes, and your point is . . . ?
>
> My point is that on your website you specifically use the number 10^14
> as a population that could evolve very complex meaningful sequences in
> a very short amount of time.
Again, I demonstrated with the Word Mutator that long words can be evolved
with populations of just a few, on the order of 10^2 or 10^3 species. The
10^14 population was for generating much much longer strings, not words.
They were two completely different treatments, one a simulation of short
strings with a clear rule for selection (word length), the other a
mathematical treatment for long strings selected by a "breeder" for a
specific meaning.
> My argument is that EVEN if you could
> monitor such a huge population in computer simulation (which you can't
> owing to a lack of memory as well as speed), you would never evolve a
> meaningful English text the size of a small Shakespearean sonnet.
No. You made a specific challenge. Now you have changed your requirements to
some impossible simulation. "Start with a short 2 or 3-letter word and see
how many words you can evolve that require greater and greater minimum
sequence requirements . . . " You are now claiming that your challenge was
specifically designed to be impossible.
Either you have moved the goal-posts, or have repeatedly put up a false
challenge. Or both.
> Certainly the use of a significantly smaller population size, even
> with a very high mutation rate, would do significantly worse in the
> same challenge.
Um. A population of one per species, with a number of species equal to about
10^2 or 10^3.
> What I am saying here is that your "O Sean" poem and anything else of
> equivalent size would not evolve using truly random rules of mutation
> combined with meaning/function based selection as I have previously
> detailed.
You keep saying that. But you have refused to admit that this challenge has
been met. "Start with a short 2 or 3-letter word and see how many words you
can evolve that require greater and greater minimum sequence requirements .
.. . "
Well, I did. I do it all the time. I put words into the Word Mutator and out
pops all sorts of novel words, some long, some short, some with high
Scrabble score, some words I didn't even know existed.
You are very confused. None of those recombinations are allowed. Don't you
remember the derivation of "O Sean Pitman"?
O
a
an
can
scan
sean
Every word must be valid to be available to the next generation (just as in
life, a mutant must be able to grow to maturity and then breed before its
genes can be carried forward to the next generation). Only one mutation or
recombination is allowed and then the mutants must be subject to validation.
So, "qquietten" would immediately die and not be available for
recombination, just as a mutant that doesn't survive and breed won't be
available to pass its genes on to the next generation.
The Word Mutator simulates this by testing each mutant and deselecting it if
it is invalid before going to the next mutant. Indeed, every possible mutant
is validated one at a time before *any* of the mutants are made available to
the next generation--and even then only the "best" are carried forward
depending on the allowable size of the Pond (which limits the number of
different words).
> Of course, you will argue by saying, "what are the odds of all size
> sequences recombining in one generation like this?!" And, I will
> answer by saying, "Not very good at all, but still _possible_." Of
> course, although possible, the average number of generations required
> would no doubt be quite high indeed.
It must be a valid word to enter the population. That's the rule, and it
must be the rule if the analogy is to have any meaning whatsoever.
> > Second, you seriously miscalculate the number of mutants. There are (no
more
> > than) 646 mutants with seven-letters. (Word Mutator double-counts some
> > mutants for technical reasons, but counts every mutant at least once.)
That
> > means there are at most 646 mutants per generation.
>
> As I see it, this is one of your problems. You calculate the number
> 646 based on the perspective of a single individual 7-letter sequence
> over the course of just one generation. What you need to do to
> calculate the total number of possible mutants that could be realized,
> even in one generation, is to consider _all_ members of your
> population.
>
> For example, say you had a population of 10 different
> 7-letter sequences. With each of these 10 sequences in the population
> being able to go to any one of 646 sequences, the population as a
> whole would be able to cover 6,460 sequences in one generation -
> right?
No, your calcuation is incorrect. You have not accounted for recombinations
between different strings. There are 26920 possible mutants. The Word
Mutator tries each and everyone of these mutants--one at a time. If they
are not valid words, they are immediately deselected. If they are valid
words, then the Word Mutator selects the "best" of the available population,
which is set to the longest words by default, but could be Scrabble score,
or any other well-defined rule for that matter.
> Now, this isn't what really happens of course since there are
> only 10 individuals. At most they can only reach 10 different
> sequences per generation with a mutation rate of one mutation per
> sequence per generation.
You really need to understand the computer simulation work. Each word in the
Word Mutator represents a population. It doesn't matter how many are in that
population. Somewhere sometime in that population a mutation occurs. That
mutation may occur today or in a thousand years. It doesn't matter. In Word
Mutator, we try just one mutation on one word. If it is a valid word, it is
potentially added to the population. If it is invalid, it is immediately
deselected. Word Mutator tries every possible mutation and every possible
recombination--one at a time.
If you prefer, you can use the Word Mutagenator, which randomizes the
mutations rather than trying every single one. In fact, both methods "take
into account all the other possible arrangements and potentially
non-beneficial connections and insertions of these words," as you had
required.
We know exactly how many mutations are available for each generation of a
seven-letter string. It's 646. Ain't combinatorics fine.
> Say, for example, that you had a population limit of two sequences
> (owing to environmental factors which limit your population from
> further growth) with a mutation rate of one mutation per generation.
> You start out with a population of 1 that reads, "pitman". In each
> generation "pitman" produces two offspring. If both offspring are
> meaningless/non-functional, the original "pitman" survives. If only
> one offspring is meaningful, the original "pitman" also survives, for
> a total of 2 members in our population. If both offspring are
> meaningful, the original "pitman" dies and each of the two offspring
> each produce two more offspring in the next generation, but the 2
> "weakest" must die in that generation to maintain the population at
> the max of 2.
>
> Considering that you have all kinds of possible mutations, to include
> point, deletion, insertion, split and recombination mutations
> available, how many generations, on average, would it take to get the
> meaningful split in "pitman" to form two smaller populations, such as
> "pit" and "man"?
There are 532 possible mutants of "pitman". Of these, eleven are valid words
found in our Dictionary of ~79000 words. "pitman", "man", "pan", "pin",
"pit", "ma", "pi", "an", "it", "a" and "i". From these the breeder will
eliminate all mutants except "pit" and "man".
> Not all splits will be meaningful - right? In fact,
> the ratio of meaningful "pitman" splits is 1 in 5 and the ratio of
> split to non-split mutations is also 1 in 5 for a total odds of a
> meaningful split of 1 in 25 mutations, or one in about 12 generations
> in our steady state population of 2.
I put "pitman" into the Word Mutator. The Word Mutator tried every possible
mutation and recombination, a total of 532 mutants. Then I eliminated
everything except "pit" and "man". After an additional 488 mutants, we find
"pi" and "mar" (from a total of 13 words including the self-recombination
"pipit"). Again, we cull everything but "pi" and "mar". Another 396 mutants
later, we have "bi" and "mare" (from a total of 7 valid words including
"pima"). Eliminating the unwanted words, and after another 498 mutants, we
have "be" and "ware" (from a total of 10 valid words including "aware"). We
cull the excess words, and so finally after another 498 mutants, a total of
2412 mutants considered (the vast majority of them junk, but a few
interesting in their own right), we have "beware".
Of course, I was selecting for a specific meaning, like a breeder selecting
a dog for the length of its nose, or selecting a horse for the strength of
its legs. Let's suppose we set the Pond Size to 25 (default). Let's put in
"pitman" and see what we get. In 10 generations we have "pinpricking"
"pinpointing" "cracklings" "implanting" . . . "chocking". Let's try it
without mutation, but only snippets enabled. We get "maintain", "attaint",
"pippin" . . . "mint".
So "natural" evolution allows many long words to evolve, but perhaps not the
ones this breeder was looking for.
> Now, say we get or "pit" and "man", each of these will mutate
> separately down different paths - right? How many generations will it
> take, on average, before both of these paths come to new sequences
> that are not only meaningful independently, but would also be
> meaningful IF they happened to be united by a recombination mutation?
> I'm not sure what the answer is, but it wouldn't be too hard to find
> out I'm sure.
That's right. It isn't hard to figure. We have to figure every point
mutation, every snippet, every remainder, and every possible insertion of
every possible snippet at every point in the string. The Word Mutator does
this quite well (with a little bit of overlapping for technical reasons).
> But, for now, let's just say that the odds of this
> happening are around 1 in 20. The problem here is that it is not
> enough to get two populations at the same time that COULD recombine to
> form a meaningful sequence. What needs to happen is that a CORRECT
> recombination mutation DOES happen exactly when it is beneficial.
> Now, what are the odds of that?
Well, without a breeder making the selection, then we wouldn't necessarily
expect "beware" to pop out. I think that's your point, and you would be
right. (We wouldn't necessarily expect Poodles to occur without a breeder's
eye either!) However, without a breeder, we can still expect some mutants
will be valid, and this is exactly what happens. "Pitman" evolves into
"pinpricking", a longer word, without the intervention of a breeder.
> Well, there are several ways that "be" and "ware" could recombine, but
> few of these possibilities are "meaningful" in the English language
> system. You could get "wbeare" or "wabere" or "warbee" or "bwaree" or
> "warebe" or "beware". So, the odds of getting a meaningful
> recombination is 1 in 6. Then, you must also consider the odds that a
> recombination event will occur right at this time instead of another
> possible type of mutation for an additional odds ratio of 1 in 5.
Sean, Sean, that's all been considered.
> So, the total odds of successful recombination would be 1/6 * 1/5 *
> 1/20 = 1 in 600 generations. And, this is only for very short
> sequences with very high ratios of non-recombined meaning vs.
> non-meaning. This problem gets exponentially worse with each step of
> the ladder of complexity.
>
> Do you see the problem? Just because it CAN happen does not mean that
> it WILL happen all that often.
It does happen. It did happen. It happens everytime someone runs the Word
Mutator.
And if you prefer using random mutation and random recombination. I just put
"pitman" into the Word Mutagenator, Pond = 25. I let it run about 15
seconds. It considered 13558 random mutations and recombinations. Out popped
"mammals", "mammal", "mammas", "parkas", "sparks", "magmas", and "pitman".
These are new words to our population. Some are longer than the word we
started with, and all aspects of the mutation process were done randomly.
The only thing that was not random is the culling for length when the
population exceeded 25.
Try it. It's actually quite interesting. There are limits, but they have
nothing to do with your "exponential" arguments; rather Pond Size appears to
be the major limiting factor.
> Does your computer program take this
> little problem into account?
Certainly. It's all there. Perhaps you should study the documentation a bit
more carefully, and with an open mind. The source code can be found here:
Zachriel's Special Pudding Recipe
http://www.zachriel.com/mutagenation/Pudding.asp
> You certainly don't in your written out
> evolutionary scenarios. You simply assume that the path will be
> easily found if it exists, but this is a fallacy.
In the long-string examples, I calculated the number of mutants available in
each generation. The selection is for meaning and is done by a "breeder".
> > So we know a path exists. Counting seven-letters for each generation,
there
> > are 646*7 possible mutants along our path due to our careful selection
at
> > each generation. If we can't find an appropriate path, then the number
of
> > mutations required might be a bit higher as we experiment with a few
winding
> > paths. Without selection, it could take much more, perhaps even more
than a
> > Pitman Zillion!
>
> See above descriptions of the problem with this "a path exists and
> therefore evolution will be rapid" assumption.
That's not an assumption. The number of available mutants is on the order of
L^3, where L is the length of the string. With L=100, the number of possible
mutants per generation will be about a million. And we can have some very
meaningful expression in a hundred letters.
> > This is important: There is no way to know if particular words are
evolvable
> > by simply using exponents. The words might be lined up nice and pretty,
or
> > they might be separated by impassable evolutionary barriers. There is no
way
> > to know without actually testing and with some sort of selection
criterion.
>
> Actually, there is a very good way of knowing, beyond a reasonable
> doubt that is, seeing as how no known language/information system, is
> lined up as nicely as would be required for Darwinian-style evolution
> to get beyond the lowest levels of existing complexity found in such
> language systems.
You have failed to provide any such argument. Your only argument has been
that there are 26^100 possible arrangements of a hundred letters. You have
absolutely no idea how many of those form valid English expressions, nor how
those expressions are connected in the space of possible permutations.
> Why then should the genetic language/information
> system found in living things be any different?
You are reaching a conclusion from a faulty premise.
> And, in fact it is
> not. Real life experiments have proved as much. In real life
> evolution stalls at the lowest levels of functional complexity so that
> there simply are no examples of a cellular function evolving that
> requires more than a few hundred fairly specified amino acids working
> together at the same time. There are examples of less complex
> cellular functions evolving all the time, but evolution stalls out as
> one looks higher than the few hundred fairly specified amino acid
> level.
>
Evolution of new traits has been directly observed. Large-scale adaptation
only occurs on geological time-scales, but is apparent from the fossil
record.
Sean Pitman
> > Again, random walk does pretty good at low levels, even levels
> > requiring a dozen or so letters with such a population size and
> > mutation rate. However, even with your 100 trillion individuals, you
> > can't evolve anything meaningful in English the size of a relatively
> > short Sonnet of, say, just 500 characters.
> <snip>
>
>
> Moving the goal-posts, eh Sean? This was your challenge:
>
> "Just try a little experiment yourself. Start with a short 2 or
> 3-letter word and see how many words you can evolve that require greater and
> greater minimum sequence requirements. No doubt you will quickly find
> yourself coming to walls of meaningless or non-beneficial potential options
> that separate you from every other meaningful and beneficial option. . . .
> (Genetic evolution works the very same way)."
>
> You said to evolve "words", Sean, "words". I warned you to "beware a war of
> words", then you could have continued on with your fallacious arguments
> about genetics--*but you kept insisting*. I warned you repeatedly. Now you
> have been shown to be wrong, and are currently attempting to move the
> goal-posts.
>
> Your challenge has been met. Quit moving the goal-posts.
Notice, Zach, that I used the pleural form "words" to indicate
multiple words in what you call a "war of words." Obviously, it is
very easy to see, from all that I have written on this topic, to
include the papers on my own website, that I'm talking about
meaningful sequences made up of one or many words as long as the
sequence has beneficial meaning. It doesn't matter at all whether the
sequence is one word or divided up into many words of the same length
- and I never said or indicated otherwise.
In fact, you seemed to fully recognize this fact _initially_ since you
wrote out long multi-word "poems" in your attempt to challenge my
position. You even have many multi-word poem on your website. Even
the title of this thread is the multi-word title to your poem, "O Sean
Pitman". Yet, you haven't evolved anything even close to the size of
one of these many hundred-character poems now have you? The very best
that you have evolved, even with extraordinary reproduction and
mutation rates, is no longer than a couple dozen characters in size
(truly tiny in comparison to your grandiose claims for the powers of
evolution).
Come on now Zach, in your war of words are you can't be seriously
accusing me of ever thinking to draw the line at short one-word-only
sequences? - Can you?! You are really reaching for straws Zach. It
really does seem very desperate of you, really it does, to accuse me
of "moving goal posts" here when I clearly said over and over again
that my limits were dependent upon population and genome size as well
as mutation rate and nowhere did I ever say that sequence lengths as
short as one or two dozen where "the limit". In fact, over and over
again I clearly drew the limit for genetic evolution at a couple of
thousand amino acids working together at the same time. I am truly at
a loss to see how you could have read what I actually wrote and assume
that my "goalposts" were at the level of 7- to 14-characters in size -
especially considering the enormous reproduction rates and mutation
rates that you used in your computer simulation!
You yourself recognized the fact that I never drew the line at such
low levels, so how can you possibly say that I've moved my goalposts?
They have only been moved relative to your misstatements about my
position. The real goalposts have not been moved at all. They are
right where I put them well over a year ago now and have remained
there, not even remotely challenged by anyone to include you, to this
day.
And, if you are really honest about this whole thing, you will reflect
my real position on your website - but I am not holding my breath on
that one. You see too attached to your strawman version of reality.
Zachriel
> "Zachriel" <sp...@zachriel.com> wrote in message
news:<s-OdnS_Mj8Q...@adelphia.com>...
>
> > > Again, random walk does pretty good at low levels, even levels
> > > requiring a dozen or so letters with such a population size and
> > > mutation rate. However, even with your 100 trillion individuals, you
> > > can't evolve anything meaningful in English the size of a relatively
> > > short Sonnet of, say, just 500 characters.
> > <snip>
> >
> >
> > Moving the goal-posts, eh Sean? This was your challenge:
> >
> > "Just try a little experiment yourself. Start with a short 2 or
> > 3-letter word and see how many words you can evolve that require greater
and
> > greater minimum sequence requirements. No doubt you will quickly find
> > yourself coming to walls of meaningless or non-beneficial potential
options
> > that separate you from every other meaningful and beneficial option. . .
> > (Genetic evolution works the very same way)."
> >
> > You said to evolve "words", Sean, "words". I warned you to "beware a war
of
> > words", then you could have continued on with your fallacious arguments
> > about genetics--*but you kept insisting*. I warned you repeatedly. Now
you
> > have been shown to be wrong, and are currently attempting to move the
> > goal-posts.
> >
> > Your challenge has been met. Quit moving the goal-posts.
>
> Notice, Zach, that I used the pleural form "words" to indicate
> multiple words in what you call a "war of words."
Sigh. I've generated multiple words. The Word Mutator deals in populations
of dozens or hundreds of word species.
It is also obvious you once believed that 14-letter words were out of reach
of evolution. Let's look again at what you wrote.
You claimed that "the potential space of a 14-letter word or phrase is over
109,418,989,131,512,359,209 (over 100 million trillion)." This is very close
to the Pitman Zillion and certainly beyond the capability of any computer to
explore in a reasonable time. My Dictionary contains exactly 1643 (~10^3)
14-letter words. According to your "calculations", my program would have to
explore 10^19 / 10^3 or 10^16 mutants before having a decent chance of
finding such a word. I invite everyone to read your "analysis" of the
problem for themselves.
http://tinyurl.com/2rx8g
And yet, the Word Mutator can solve this problem in minutes. How is it
possible? Can Sean Pitman please explain how the Word Mutator is capable of
doing this.
> Obviously, it is
> very easy to see, from all that I have written on this topic, to
> include the papers on my own website, that I'm talking about
> meaningful sequences made up of one or many words as long as the
> sequence has beneficial meaning. It doesn't matter at all whether the
> sequence is one word or divided up into many words of the same length
> - and I never said or indicated otherwise.
>
> In fact, you seemed to fully recognize this fact _initially_ since you
> wrote out long multi-word "poems" in your attempt to challenge my
> position. You even have many multi-word poem on your website. Even
> the title of this thread is the multi-word title to your poem, "O Sean
> Pitman". Yet, you haven't evolved anything even close to the size of
> one of these many hundred-character poems now have you? The very best
> that you have evolved, even with extraordinary reproduction and
> mutation rates, is no longer than a couple dozen characters in size
> (truly tiny in comparison to your grandiose claims for the powers of
> evolution).
As has been explained many times, the number of mutants for 1000 characters
is on the order of a billion per generation, too large to easily simulate on
a desktop computer, but much, much less than the "zillions" you claim.
> Come on now Zach, in your war of words are you can't be seriously
> accusing me of ever thinking to draw the line at short one-word-only
> sequences? - Can you?!
Yes. You did. "the potential space of a 14-letter word or phrase is over
109,418,989,131,512,359,209 (over 100 million trillion)." What did you mean
by that?
> You are really reaching for straws Zach. It
> really does seem very desperate of you, really it does, to accuse me
> of "moving goal posts" here when I clearly said over and over again
> that my limits were dependent upon population and genome size as well
> as mutation rate and nowhere did I ever say that sequence lengths as
> short as one or two dozen where "the limit". In fact, over and over
> again I clearly drew the limit for genetic evolution at a couple of
> thousand amino acids working together at the same time. I am truly at
> a loss to see how you could have read what I actually wrote and assume
> that my "goalposts" were at the level of 7- to 14-characters in size -
> especially considering the enormous reproduction rates and mutation
> rates that you used in your computer simulation!
On my 250MHz P4, Word Mutator only does about 40,000 mutants per second,
while the latest (just uploaded!) version of Word Mutagenator does about
25,000 mutants per second, hardly a huge number when we have to supposedly
explore a space of 100 million trillion. Yet, we have explored that space
sufficiently to find 14-letter and longer words.
With a reasonable algorithm for recognizing valid phrases, a Phrasenator
could easily handle dozens of phrases of reasonable length.
> You yourself recognized the fact that I never drew the line at such
> low levels, so how can you possibly say that I've moved my goalposts?
> They have only been moved relative to your misstatements about my
> position. The real goalposts have not been moved at all. They are
> right where I put them well over a year ago now and have remained
> there, not even remotely challenged by anyone to include you, to this
> day.
>
> And, if you are really honest about this whole thing, you will reflect
> my real position on your website - but I am not holding my breath on
> that one. You see too attached to your strawman version of reality.
I have linked to your website, and to many of your posts, including this
thread. You have ample opportunity for rebuttal.
Sean Pitman
> > Come on now Zach. You know that in claiming that I said that words,
> > "longer than 7-letters can't be evolved" you are grossly
> > misrepresenting what I actually said since your statement seems to
> > indicate that I believe that sequences just a little bit longer than
> > 7-letters could not be evolved.
>
> I quoted you extensively and pointed people to your original posts. They are
> more than capable of making up their own minds as to how you use vagueness
> and goal-post moving to avoid being pinned down.
You quoted me extensively out of context giving a light to my
statements that is nowhere near to what I truly intended. You also
give general links to searches for stuff that I said, but you do not
give specific links to the specific lines that you quote so people can
actually read what I said in context. You also avoid listing any
links to those places where I detail very specifically those boundary
lines that I considered truly "impossible" to cross, though they are
everywhere and easily found if you had wanted to find them, especially
on my own website.
No Zach, it is your desperate attempt to color all creationists as
crazy that has caused you to build a strawman version of my position
which is nothing like my real position at all.
> Your challenge, "start a short 2 or 3-letter word and see how many words you
> can evolve that require greater and greater minimum sequence requirements.
> No doubt you will quickly find yourself coming to walls of meaningless or
> non-beneficial potential options . . . "
>
> You said "words".
Yes - words Zach - to include multiword sequences. If you actually
read just a little bit more from what I wrote in this forum and on my
own website, you will notice that I am talking about both single and
multi-word phrases that are longer than a couple dozen characters -
especially when you are using extraordinarily high reproduction and
mutation rates.
Come on now Zach, what are you trying to prove here? I've already
talked about this sort of thing many times to include the average time
I think that such populations could and would evolve such extremely
short sequences.
Just for kicks though, why don't you check out my actually website?
Especially look at what I say about this topic at:
http://naturalselection.0catch.com/Files/galactosidaseevolution.html
> How long of words did you have in mind?
Again, a more accurate description of what I had in mind and what I
have said over and over again, would be sequences made up of one or
more words. I have detailed very specifically the limits of evolution
for various sequence lengths depending upon population size and
mutation rate. I have even put myself specifically on the line many
times saying that for no population of any creature that could be
supported by any environment on earth would evolution ever produce a
type of function that required at minimum more than a couple thousands
fairly specified amino acids working together at the same time. In
real life no function has ever evolved that required more than a few
hundred fairly specified amino acids working together at the same
time.
If we are talking hypothetical evolution using the English language or
computer code, I would and I have many times drawn the line at several
hundred and definitely the 1,000-character level. However, I don't
really think that even a 100-character sequence could evolve with even
a huge population (such as a trillion trillion) and a very high
mutation rate this side of a practical eternity of time (i.e.,
"zillions" or "gazillions" or "trillions upon trillions upon trillions
of years"). The reason for my drawing the line at a lower level here
in comparison to genetic evolution is that the English language system
and computer language systems are generally more specified as far as
meaning is concerned for a given sequence length.
> The Word Mutator
> has evolved 18-letter words, and overnight evolved a third of the available
> Dictionary of 78,000 words. The Word Mutagenator has evolved 14-letter words
> and thousands of words of varying length.
>
> You gave the clear impression that we couldn't evolve long words by mutation
> and selection. You were wrong. The Word Mutator not only evolves long words,
> but evolves words with high scrabble score, short words, middle-sized words,
> anything you want.
>
> Admit it and move on.
I gave the clear impression that you couldn't evolve long sequences
with a given steady-state population and average mutation rate. Give
the enormous reproduction rate and mutation rate of your computer
program, I certainly wouldn't classify even 14-letter sequences as
"long" at all. Relatively speaking, 14-letter sequences are tiny.
What you need to do is admit what I really said and indicated very
clearly many times in many locations even before you came on the scene
. . . and move on.
> > On top of this, I did specify many times were I thought "zillions"
> > (i.e., trillions upon trillions upon trillions) of years would take
> > over. For example, in my discussions of genetic evolution I predicted
> > that the level of impossibility would occur for the evolution of
> > functions at just a couple thousand fairly specified amino acids
> > working together at the same time. You, however, strongly
> > misrepresent my position in your posts and on my website by making it
> > seem like I said that evolution of meaningful 7-letter sequences or
> > something at least close to that would require "zillions" of years.
> > Of course, I never said anything of the sort.
No comment here? What do you have to say about this? Did you just
ignor these statement of mine on purpose?
> > > "Just try a little experiment yourself. Start with a short 2 or
> > > 3-letter word and see how many words you can evolve that require greater
> > > and greater minimum sequence requirements. No doubt you will quickly
> > > find yourself coming to walls of meaningless or non-beneficial potential
> > > options that separate you from every other meaningful and beneficial
> > > option. . .
>
> > > (Genetic evolution works the very same way).
> >
> > And this is still my position. You certainly haven't come close to
> > showing how this statement is wrong . . .
>
> Hold it now. You say to start with 2- and 3-letter words, try to evolve
> longer words, and you will "quickly find yourself coming to walls". I have
> extensively tested this assertion and found it FALSE.
It is not false at all simply because you assumed something that I
clearly did not indicate if you had read much of anything that I had
already written about this topic. This assertion, as stated in
context of my many other posts on this topic, is not false at all.
Interestingly enough, you yourself noted that you were able to evolve
short sequences composed of 2- and 3- letter words in "seconds". You
were even able to evolve longer meaningful sequences of 7-letters in
"seconds". However, it took you "minutes" to find your longer
sequences of up to 14-letters. This is exactly in line with my
predictions. Keep going Zach. You used multiple words in your "poem
evolution", so you clearly understood my meaning of sequence evolution
to include multiple words. Keep going then Zach. See how far you can
go. You will certainly find yourself "quickly" coming to walls that
block all further progress at very low levels of relative complexity.
> > > Is "trillions upon trillions" a "zillion"?
> >
> > Sure, why not . . . I just can't believe that you're so hung up over
> > this word "zillion."
>
> Because it doesn't take "zillions", or even millions. It takes on the order
> of 10^3 to 10^6 mutations to evolve dozens of long words. It takes on the
> order of 10^9 per generation to evolve strings of length 1000.
You've never evolved _meaningful_ strings of characters even close to
1,000 characters in length, and you never will. Also, it would take
far more than 10^9 mutations per generation, in a steady state
population that always maintains meaning in the population, to evolve
a meaningful English language string that is 1,000 characters in
length this side of "zillions" of generations.
> > I give plenty of very specific numbers on my
> > posts as well and yet you pick one word out and start harping away on
> > it when you know full well what I meant when I used it.
>
> Yes, we all know exactly what you meant. You just didnt think anybody would
> or could call you on it.
"Zillions"? You thought no one would call me on my use of the word
"zillions"? LOL - you are too funny Zach. I am still amazed on how
you could get so hung up on that word.
> > Your calculations have done nothing more than my own calculations and
> > statements have already predicted. I didn't not predict an
> > "impassable barrier" at the level of 7-fairly specified characters or
>
> You stated these walls are approached "quickly" after starting at 2- or
> 3-letter words. What exactly did you mean then? When do we reach these
> walls?
The word quickly is very appropriate to use if the walls are reached
on the very low end of the relative spectrum of complexity that exists
in a given common usage language system. If the impenetrable wall
occurred at the level of 100 characters, that would be by anyone's
definition a very quick end to the abilities of evolution to do very
much - relatively speaking. 100-character strings are nothing
compared to even a short children's story, much less a Shakespearean
play.
There was no need for confusion on your part Zach. I clearly spelled
out many many times what I meant by "quickly" if you had only done a
little more reading first.
> > even 20 or 30 even though you misstate that I did over and over again.
> > As I have detailed to you before, even with a population of 100
> > trillion (or even a trillion trillion) and a high mutation rate per
> > generation, the impassable wall becomes insurmountable this side of
> > trillions upon trillions upon trillions of years (i.e., zillions) when
> > the minimum fairly specified sequence requirement reaches several
> > hundred to a few thousand for a given type of function.
>
> This is FALSE. The number of possble mutants for a letter-string of length
> 1000 is upper-bounded by 1000^3 or about a billion per generation.
Again, this is only from the perspective of a single individual in
just one generation. This is not from the perspective of population
numbering 100 trillion or a trillion trillion where each individual
can cover a different sequence. With an average mutation rate of one
per individual, population of 100 trillion can cover up to 100
trillion new sequences in just one generation and population of a
trillion trillion can cover up to a trillion trillion new sequences in
just one generation.
You are wrong Zach. You must think from the perspective of the
population, not the individual. From this perspective your "about a
billion per generation" calculation is way way off given the size of
the population.
> > I have made this same sort of predictive statement many times in this
> > forum and on my website if you care to look. Evidently though, you
> > prefer to ignore such statements so that you can build your own straw
> > man representation of my position.
>
> Absolutely not. Your position is clearly represented on Google-Groups. You
> made an analogy to words. I pointed out that your analogy was faulty. You
> insisted you were right. I created a poem to give you some indication that
> it was quite easy to evolve between words.
You haven't shown this to be true beyond the lowest levels of English
language system complexity - as I have predicted.
> You kept insisting your were
> right. You could have abandoned the analogy--it's just an analogy--but you
> insisted. You reap what you sow.
I haven't abandoned the analogy at all. And, you haven't sown
anything that I haven't already predicted.
> > My argument is that EVEN if you could
> > monitor such a huge population in computer simulation (which you can't
> > owing to a lack of memory as well as speed), you would never evolve a
> > meaningful English text the size of a small Shakespearean sonnet.
>
> No. You made a specific challenge. Now you have changed your requirements to
> some impossible simulation. "Start with a short 2 or 3-letter word and see
> how many words you can evolve that require greater and greater minimum
> sequence requirements . . . " You are now claiming that your challenge was
> specifically designed to be impossible.
Exactly. My challenge is impossible and that is the whole point.
Evolution is impossible beyond the lowest levels of language system
complexity. You think that because I said to start with a 2- or
3-letter words and see how far you can go that you would win by simply
getting to the level of just a dozen or so letters?! How insane is
that especially given the enormous reproductive rate and mutation rate
of your simulation?!
You need to read what I my specific challenge really was again Zach.
I know you are disappointed that your strawman just isn't holding up
very well since you really did put a lot of work into making this
strawman. But, in the end, it really is and always was just a
strawman version of my position and nothing more.
> Either you have moved the goal-posts, or have repeatedly put up a false
> challenge. Or both.
I have done neither. You have just assumed a non-reality, which
anyone who is interested can easily validate.
> > What I am saying here is that your "O Sean" poem and anything else of
> > equivalent size would not evolve using truly random rules of mutation
> > combined with meaning/function based selection as I have previously
> > detailed.
>
> You keep saying that. But you have refused to admit that this challenge has
> been met. "Start with a short 2 or 3-letter word and see how many words you
> can evolve that require greater and greater minimum sequence requirements .
> .. . "
Where has anything the size of your complete "O Sean Pitman" poem been
evolved? Hmmmmm . . . That is and was my challenge and you have not
met it in even the most remote sense.
> Well, I did. I do it all the time. I put words into the Word Mutator and out
> pops all sorts of novel words, some long, some short, some with high
> Scrabble score, some words I didn't even know existed.
They are all "short" relatively speaking. You have no "long"
sequences at all.
> > Even according to your rules, if you extrapolate them, evolving
> > "qqqqqq" should be no problem since a path does actually exist - as
> > you envision paths existing that is. For example, consider a
> > population of six sequences in a population of 6 reading, "queen,
> > quiet, quite, quick, quilt, and quiz". Lets say that in a single
> > generation they all recombined in the following fashion before the
> > selection process took place:
> >
> > "Quiet" recombined with "queen" to read, "qquieteen" and then "quite"
> > recombined with "qquieteen" to read "qqquiteuieteen", and etc., until
> > you ended up with "qqqqqquizuiltuickuiteuieteen." Aha! Successful
> > pathway established!
>
> You are very confused. None of those recombinations are allowed.
But they are allowed in my version since they are allowed in real
life.
> Don't you
> remember the derivation of "O Sean Pitman"?
>
> O
> a
> an
> can
> scan
> sean
>
> Every word must be valid to be available to the next generation (just as in
> life, a mutant must be able to grow to maturity and then breed before its
> genes can be carried forward to the next generation). Only one mutation or
> recombination is allowed and then the mutants must be subject to validation.
This is quite wrong. The mutation rate can be higher than one per
individual genome. In fact, consider humans, for example. In every
generation each human genome (offspring) experiences well over 200
mutations. And, this is all BEFORE selection takes place for that
individual. See:
http://naturalselection.0catch.com/Files/dnamutationrates.html
> > As I see it, this is one of your problems. You calculate the number
> > 646 based on the perspective of a single individual 7-letter sequence
> > over the course of just one generation. What you need to do to
> > calculate the total number of possible mutants that could be realized,
> > even in one generation, is to consider _all_ members of your
> > population.
> >
> > For example, say you had a population of 10 different
> > 7-letter sequences. With each of these 10 sequences in the population
> > being able to go to any one of 646 sequences, the population as a
> > whole would be able to cover 6,460 sequences in one generation -
> > right?
>
> No, your calcuation is incorrect. You have not accounted for recombinations
> between different strings. There are 26920 possible mutants.
Fine. The actual numbers don't really matter as much as the concept
here. The concept is that the population can cover much more ground
that a single individual per generation.
> > Now, this isn't what really happens of course since there are
> > only 10 individuals. At most they can only reach 10 different
> > sequences per generation with a mutation rate of one mutation per
> > sequence per generation.
>
> You really need to understand the computer simulation work. Each word in the
> Word Mutator represents a population.
This is not exactly true as I currently understand your program. You
have a steady state population of 25. Those 25 different sequences
are your "population". In each of your "generations" each of these 25
sequences produces thousands of offspring to put into a "next
generation pool". Those thousands of offspring are then "selected"
for "fitness" and another 25 of the most "fit" sequences are chosen.
Those 25 are now your new "population" in a steady state population
situation of 25 in your particular computer environment.
> It doesn't matter how many are in that
> population.
Oh yes, it very much matters how many individuals are in your
"population".
> Somewhere sometime in that population a mutation occurs. That
> mutation may occur today or in a thousand years. It doesn't matter. In Word
> Mutator, we try just one mutation on one word. If it is a valid word, it is
> potentially added to the population.
This is called your "reproduction rate", but these offspring are not
"added to the population" yet. They are put into a "next generation
bin" for future selection - correct? This is like a bunch of
fertilized eggs that have mutations but have not been subject to
"natural selection" yet.
> If it is invalid, it is immediately
> deselected.
That is not what you said before. You said that selection takes place
in "batches" to save time in each generation.
Again, you have forgotten about your population as a whole. How many
mutations are available to your population per generation? That is
the real question.
You eliminated or your computer eliminated? Do you see the problem
here? If you did the elimination, then it was you who DIRECTED the
evolutionary process via intelligent design. If you let the computer
do it by it self with random chance alone, you must calculate the odds
that two words will be chosen that can actually join together in a
meaningful way, and these odds translate into average time.
> After an additional 488 mutants, we find
> "pi" and "mar" (from a total of 13 words including the self-recombination
> "pipit"). Again, we cull everything but "pi" and "mar". Another 396 mutants
> later, we have "bi" and "mare" (from a total of 7 valid words including
> "pima"). Eliminating the unwanted words, and after another 498 mutants, we
> have "be" and "ware" (from a total of 10 valid words including "aware"). We
> cull the excess words, and so finally after another 498 mutants, a total of
> 2412 mutants considered (the vast majority of them junk, but a few
> interesting in their own right), we have "beware".
>
> Of course, I was selecting for a specific meaning, like a breeder selecting
> a dog for the length of its nose, or selecting a horse for the strength of
> its legs. Let's suppose we set the Pond Size to 25 (default). Let's put in
> "pitman" and see what we get. In 10 generations we have "pinpricking"
> "pinpointing" "cracklings" "implanting" . . . "chocking". Let's try it
> without mutation, but only snippets enabled. We get "maintain", "attaint",
> "pippin" . . . "mint".
>
> So "natural" evolution allows many long words to evolve, but perhaps not the
> ones this breeder was looking for.
What you have done is to select for various short words that you know
can link together to form a meaningful longer word. You know this
because of your pre-established intelligence and insight and you
select for these particular short words via intelligent design. The
computer on the other hand, without your "intelligent" help, cannot do
what you have done. The computer, left to itself, would take a whole
lot longer to come up with the united meaningful combination that you
helped it come up with in a much shorter period of time.
In our experiment, the computer IS supposed to be the breeder who
selects based on the "meaning" of character sequences. In our
computer scenario no one type of meaning is given preference over any
other type of meaning. You therefore cannot step in and interfere
with your intelligent mind and select based on your personal
preference. That is called "cheating" or "intelligent evolution".
Which, is basically my whole point. Evolution just won't work without
intelligent direction.
> > Now, say we get or "pit" and "man", each of these will mutate
> > separately down different paths - right? How many generations will it
> > take, on average, before both of these paths come to new sequences
> > that are not only meaningful independently, but would also be
> > meaningful IF they happened to be united by a recombination mutation?
> > I'm not sure what the answer is, but it wouldn't be too hard to find
> > out I'm sure.
>
> That's right. It isn't hard to figure. We have to figure every point
> mutation, every snippet, every remainder, and every possible insertion of
> every possible snippet at every point in the string. The Word Mutator does
> this quite well (with a little bit of overlapping for technical reasons).
>
> > But, for now, let's just say that the odds of this
> > happening are around 1 in 20. The problem here is that it is not
> > enough to get two populations at the same time that COULD recombine to
> > form a meaningful sequence. What needs to happen is that a CORRECT
> > recombination mutation DOES happen exactly when it is beneficial.
> > Now, what are the odds of that?
>
> Well, without a breeder making the selection, then we wouldn't necessarily
> expect "beware" to pop out.
Exactly my point . . .
> I think that's your point, and you would be
> right. (We wouldn't necessarily expect Poodles to occur without a breeder's
> eye either!)
So you admit that without intelligent design that significant
meaningful evolution is impossible? Your computer just can do much
without your input? Is that what you really want to say here?
> However, without a breeder, we can still expect some mutants
> will be valid, and this is exactly what happens. "Pitman" evolves into
> "pinpricking", a longer word, without the intervention of a breeder.
Yes, your computer can do some things very well all by itself just by
random mutation and meaning-based selection. But, without your help,
it is much more limited now isn't it?! Certainly then, without your
help, the computer would never come up with your whole "O Sean Pitman"
poem in a gazillion years or generations . . . whichever one you
prefer.
> > Well, there are several ways that "be" and "ware" could recombine, but
> > few of these possibilities are "meaningful" in the English language
> > system. You could get "wbeare" or "wabere" or "warbee" or "bwaree" or
> > "warebe" or "beware". So, the odds of getting a meaningful
> > recombination is 1 in 6. Then, you must also consider the odds that a
> > recombination event will occur right at this time instead of another
> > possible type of mutation for an additional odds ratio of 1 in 5.
>
> Sean, Sean, that's all been considered.
By intelligent design - right?
> > So, the total odds of successful recombination would be 1/6 * 1/5 *
> > 1/20 = 1 in 600 generations. And, this is only for very short
> > sequences with very high ratios of non-recombined meaning vs.
> > non-meaning. This problem gets exponentially worse with each step of
> > the ladder of complexity.
> >
> > Do you see the problem? Just because it CAN happen does not mean that
> > it WILL happen all that often.
>
> It does happen. It did happen. It happens everytime someone runs the Word
> Mutator.
Every time you are there to direct your mutator on just what words to
select for "recombination". You are just getting more and more
hilarious Zach. Don't you realize that this only proves my point?
Your little mutator, if left to itself, wouldn't come up with much of
anything beyond the lowest levels of English language system
complexity (i.e., probably no more than a meaningful 50-character
phrase and certainly no more than a 500 character phrase). Poor
little mentally challenged mutator . . .
> > Does your computer program take this
> > little problem into account?
>
> Certainly. It's all there. Perhaps you should study the documentation a bit
> more carefully, and with an open mind. The source code can be found here:
>
> Zachriel's Special Pudding Recipe
> http://www.zachriel.com/mutagenation/Pudding.asp
Oh, I have studies your document pretty carefully and I have found
your admissions that you yourself do quite a bit of selecting, helping
your little mutator along, quite enlightening to this whole
discussion.
> > You certainly don't in your written out
> > evolutionary scenarios. You simply assume that the path will be
> > easily found if it exists, but this is a fallacy.
>
> In the long-string examples, I calculated the number of mutants available in
> each generation. The selection is for meaning and is done by a "breeder".
By the _breeder_?! Don't you see my point here?! Your computer
program couldn't do it by itself because it is not intelligent. You
are the breeder here when the breeder in our scenario is supposed to
be limited to the computer in the computer's selection for meaning,
not yours. When you do the selection you bypass a great many possible
non-ideal paths that could have been taken and therefore you
dramatically shorten the required time involved for evolution to take
place via your insertion of intelligence into the equation. You
basically cheated and by doing so only demonstrated more convincingly
that intelligence is required for evolution to do much of anything.
> > See above descriptions of the problem with this "a path exists and
> > therefore evolution will be rapid" assumption.
>
> That's not an assumption. The number of available mutants is on the order of
> L^3, where L is the length of the string. With L=100, the number of possible
> mutants per generation will be about a million. And we can have some very
> meaningful expression in a hundred letters.
If you yourself do the selecting . . . I'm truly blown away.
> > Actually, there is a very good way of knowing, beyond a reasonable
> > doubt that is, seeing as how no known language/information system, is
> > lined up as nicely as would be required for Darwinian-style evolution
> > to get beyond the lowest levels of existing complexity found in such
> > language systems.
>
> You have failed to provide any such argument. Your only argument has been
> that there are 26^100 possible arrangements of a hundred letters. You have
> absolutely no idea how many of those form valid English expressions, nor how
> those expressions are connected in the space of possible permutations.
I do have a very good idea of how many there are and how they are
arranged in sequence space, at least to the degree necessary for the
purposes of my argument. You have only supported my argument all the
more by your demonstration of the limits of evolutionary processes to
the lowest levels of English language complexity without the input of
intelligent help.
> > Why then should the genetic language/information
> > system found in living things be any different?
>
> You are reaching a conclusion from a faulty premise.
Not at all. It is you who can't seem to understand that intelligence
is not allowed in this equation if you are arguing for evolution. A
breeder who selects based on phenotypic expression is not selecting
based on the idea that a combination of traits may yield a brand new
type of combined function with an entirely new phenotype. That is
impossible, even for human breeders to do, without actually looking at
the genetic sequences involved with the phenotypic expression - which
is what you are doing when you help your mutator out.
> > And, in fact it is
> > not. Real life experiments have proved as much. In real life
> > evolution stalls at the lowest levels of functional complexity so that
> > there simply are no examples of a cellular function evolving that
> > requires more than a few hundred fairly specified amino acids working
> > together at the same time. There are examples of less complex
> > cellular functions evolving all the time, but evolution stalls out as
> > one looks higher than the few hundred fairly specified amino acid
> > level.
>
> Evolution of new traits has been directly observed. Large-scale adaptation
> only occurs on geological time-scales, but is apparent from the fossil
> record.
Not at all. Nothing beyond systems requiring more than a few hundred
specified amino acids has ever been shown to evolve despite direct
observation for over a million generations. Relatively speaking, this
is not "large-scale" evolution here. Systems requiring a few or even
a few thousand fairly specified amino acids are rather low-level
systems, relatively speaking.
In short Zach, I find it very interesting and even amusing that you
actually admit to directing the evolutionary process of your computer
program. What it can do, it does only to very low levels of English
language complexity and rapidly stalls out as it tries to progress
upwards. Then, in cases where it seems to need a little help by human
directed intelligence, you freely step in and provide the needed help.
Please. This is getting ridiculous.
It would be much more ingenious if you would simply admit the obvious
limits of evolutionary processes instead of trying to help it along
via intelligent design. Actually, I'm starting to wonder if you
aren't really a creationist in disguise who is not so secretly trying
to help me prove my case.
Zachriel
3/14/04
http://tinyurl.com/2mjy9
"Sean Pitman" <seanpi...@naturalselection.0catch.com> wrote in message
news:80d0c26f.04050...@posting.google.com...
> "Zachriel" <sp...@zachriel.com> wrote in message
news:<-7mdnbFLHZw...@adelphia.com>...
>
> > > Come on now Zach. You know that in claiming that I said that words,
> > > "longer than 7-letters can't be evolved" you are grossly
> > > misrepresenting what I actually said since your statement seems to
> > > indicate that I believe that sequences just a little bit longer than
> > > 7-letters could not be evolved.
> >
> > I quoted you extensively and pointed people to your original posts. They
are
> > more than capable of making up their own minds as to how you use
vagueness
> > and goal-post moving to avoid being pinned down.
>
> You quoted me extensively out of context giving a light to my
> statements that is nowhere near to what I truly intended. You also
> give general links to searches for stuff that I said, but you do not
> give specific links to the specific lines that you quote so people can
> actually read what I said in context.
Sure I do. The Google links highlight the search terms at issue. I want
people to read as much of your post as required to understand your position.
Are you seriously complaining because I provide links to your entire
argument? That's ironic.
> You also avoid listing any
> links to those places where I detail very specifically those boundary
> lines that I considered truly "impossible" to cross, though they are
> everywhere and easily found if you had wanted to find them, especially
> on my own website.
>
> No Zach, it is your desperate attempt to color all creationists as
> crazy that has caused you to build a strawman version of my position
> which is nothing like my real position at all.
I will continue to quote you until you quit trying to twist the record. This
is what you stated,
" the potential space of 7-letter words is over 8 billion, but the potential
space of a 14-letter word or phrase is over 109,418,989,131,512,359,209
(over 100 million trillion). "
I call this number the Pitman Number of 14. Here is your post with the
number highlighted:
http://tinyurl.com/2rx8g
You have clearly trying to convince people that to find such words, you must
explore a space equal to 100 million trillion. And yet, Word Mutator finds
such words after just a few thousand mutations.
In other words, this number of yours is meaningless and worse, misleading.
Yet, you won't disown this idea, this fallacy. Instead, you pretend you said
something different.
> > Your challenge, "start a short 2 or 3-letter word and see how many words
you
> > can evolve that require greater and greater minimum sequence
requirements.
> > No doubt you will quickly find yourself coming to walls of meaningless
or
> > non-beneficial potential options . . . "
> >
> > You said "words".
>
> Yes - words Zach - to include multiword sequences. If you actually
> read just a little bit more from what I wrote in this forum and on my
> own website, you will notice that I am talking about both single and
> multi-word phrases that are longer than a couple dozen characters -
> especially when you are using extraordinarily high reproduction and
> mutation rates.
Sorry. I don't have the computational capacity of a genome. My machine is
limited to a few thousand mutants per second. To explore a 100 million
trillion permutations would take about 20 billion years. Yet, I found those
rare 14-letter words in just minutes.
>
> Come on now Zach, what are you trying to prove here? I've already
> talked about this sort of thing many times to include the average time
> I think that such populations could and would evolve such extremely
> short sequences.
Please calculate how long it would take to evolve 14-letter words starting
from 2- and 3-letter words, and tell us how you arrived at that figure.
Thanks.
We've already seen your math concerning shorter strings. Why should we
believe that you have a reasonable analysis of longer ones?
>
> > The Word Mutator
> > has evolved 18-letter words, and overnight evolved a third of the
available
> > Dictionary of 78,000 words. The Word Mutagenator has evolved 14-letter
words
> > and thousands of words of varying length.
> >
> > You gave the clear impression that we couldn't evolve long words by
mutation
> > and selection. You were wrong. The Word Mutator not only evolves long
words,
> > but evolves words with high scrabble score, short words, middle-sized
words,
> > anything you want.
> >
> > Admit it and move on.
>
> I gave the clear impression that you couldn't evolve long sequences
> with a given steady-state population and average mutation rate. Give
> the enormous reproduction rate and mutation rate of your computer
> program,
Enormous? What are you talking about? It only explores on the order of 10^5
per second. Yet it crossed a boundary you claimed was on the order of 100
million trillion.
> I certainly wouldn't classify even 14-letter sequences as
> "long" at all. Relatively speaking, 14-letter sequences are tiny.
I really can't let you get away with this Sean. You made specific assertion,
which you are now attempting to run away from. I will quote you once again.
" the potential space of 7-letter words is over 8 billion, but the potential
space of a 14-letter word or phrase is over 109,418,989,131,512,359,209
(over 100 million trillion). "
Here is your post with the Pitman Number(14) highlighted:
http://tinyurl.com/2rx8g
It is clear that you were convinced at that time that to evolve a 14-letter
word would require enormous numbers of calculations. This was FALSE. You
stated this argument more than once, in somewhat different words each time.
Please retract. We do NOT have to explore all 100 million trillion
permutations to explore that space. There are tendrils connecting words
together through that space, and an evolutionary algorithm can and does
navigate through that space.
> What you need to do is admit what I really said and indicated very
> clearly many times in many locations even before you came on the scene
> . . . and move on.
Let's get even more specific. Here you explain the entire calculation and
derive what I call the Pitman Number. From the same post:
"What this means is that on average each meaningful 7-letter word is
surrounded like an island by well over 300,000 meaningless words. If I want
to evolve a new 7-letter word starting with meaningful 7-letter word, I will
have to swim through this ocean of meaningless words. . . . There is no
selectable difference between any of the meaningless words in the ocean that
surrounds the scattered islands of meaningful 7-letter words. Therefore any
change or "evolution" between these meaningless words will be purely random.
So, all that I am left with to get across this ocean of meaningless words is
a blind "random walk". With a population of 1, this random walk will take,
on average, over 300,000 mutations to arrive at a new meaningful word at the
level of 7-letters."
THIS IS FALSE, and demonstrably so. You made a specific prediction. Let's
plug it in. Anyone with the Word Mutator can follow along, or if you prefer,
you can try every single permutation by hand, trying every single mutation
and recombination (which anyone can calculate with a spreadsheet, but here
are the calcs for those who want to take a look at them
http://www.zachriel.com/mutagenation/Calcs.xls )
There are only (no more than) 676 mutants available from any 7-letter word.
Let's start with the seven-letter words in your quote above. Starting with
"average", among the 646 mutants, there are 10 valid words, including these
of length 7 or longer "averages, averaged, overage". Please note that it
didn't take 300,000 mutations, but only 676.
Try another? Be sure to "Sterilize" the Word Mutator (and set Pond Size to
25). Don't want any little buggers to screw up the results!
"through" gives us "thorough", length +1
"between" gives us "betweens", length +1
"islands" gives us "inlands", same length
Do you think perhaps that words really are connected somehow with one
another? Let's try some longer ones from Pitman's prose. The Pitman Number
for length 9 = 26^9 divided by the number of length 9 words in our
dictionary (11588), or about 468 million.
"scattered", length 9
1 generation
1042 mutations
"shattered, smattered, spattered", length 9
"evolution", length 9
1 generation
1042 mutations
"evolutions, revolution, devolution", length 10
"mutations", length 9
3 generations
61617 mutations
"conations, donations", length 9
The Pitman Number(10) is about 14 billion. Let's see what happens.
"meaningful", length 10
3 generations
93303 mutations
"meaningfully", length 12
"selectable", length 10
1 generation
1270 mutations
"delectable", length 10
"surrounded", length 10
3 generations
161759 mutations
"underground", length 11
"ungrounded", length 10
Let's try length 11. The Pitman Number(11) is about 516 billion. Better set
Pond Size to 50. You can't grow horses in a dog kennel.
"meaningless", length 11
4 generations
1179835 mutations
"meaninglessness", length 15
Wow! That's a big horse, I mean word. You know, I'm beginning to think that
words aren't randomly distributed through sequence space as Dr. Pitman
originally conjectured. Indeed, I believe we have more than enough
information to conclude that the Pitman Conjecture is falsified.
> > > On top of this, I did specify many times were I thought "zillions"
> > > (i.e., trillions upon trillions upon trillions) of years would take
> > > over. For example, in my discussions of genetic evolution I predicted
> > > that the level of impossibility would occur for the evolution of
> > > functions at just a couple thousand fairly specified amino acids
> > > working together at the same time. You, however, strongly
> > > misrepresent my position in your posts and on my website by making it
> > > seem like I said that evolution of meaningful 7-letter sequences or
> > > something at least close to that would require "zillions" of years.
> > > Of course, I never said anything of the sort.
>
> No comment here? What do you have to say about this? Did you just
> ignor these statement of mine on purpose?
But Dr. Pitman, you did make those assertions. "If I want to evolve a new
7-letter word starting with meaningful 7-letter word, I will have to swim
through this ocean of meaningless words" and you derived what I have named
the Pitman Number. And you further stated, "So, all that I am left with to
get across this ocean of meaningless words is a blind 'random walk'."
You were talking about words--words, Dr. Pitman, though now you deny it. You
claimed we would have to cross oceans of meaningless words to get from one
word to another, but that ocean has archipelagos of words, and like ancient
Polynesians, we can cross that ocean.
You should have bewared a war of words.
Your predictions were wrong. According to your numbers it should take
millions and millions of years at 10000 mutations per second (that's a
Pitman Zillion divided by Time).
> Keep going Zach. You used multiple words in your "poem
> evolution", so you clearly understood my meaning of sequence evolution
> to include multiple words. Keep going then Zach. See how far you can
> go. You will certainly find yourself "quickly" coming to walls that
> block all further progress at very low levels of relative complexity.
When I built the Word Mutator I designed it to falsify your notion of oceans
of disconnected words per your quoted material above. Please don't deny what
is plain for everyone to see.
You are not capable of admitting error, but you have more-or-less pulled
away from that position. That is probably all we can hope for today.
>
> > > > Is "trillions upon trillions" a "zillion"?
> > >
> > > Sure, why not . . . I just can't believe that you're so hung up over
> > > this word "zillion."
> >
> > Because it doesn't take "zillions", or even millions. It takes on the
order
> > of 10^3 to 10^6 mutations to evolve dozens of long words. It takes on
the
> > order of 10^9 per generation to evolve strings of length 1000.
>
> You've never evolved _meaningful_ strings of characters even close to
> 1,000 characters in length, and you never will. Also, it would take
> far more than 10^9 mutations per generation, in a steady state
> population that always maintains meaning in the population, to evolve
> a meaningful English language string that is 1,000 characters in
> length this side of "zillions" of generations.
Oh boy. I'll see your zillions and raise you a gazillion.
> > > I give plenty of very specific numbers on my
> > > posts as well and yet you pick one word out and start harping away on
> > > it when you know full well what I meant when I used it.
> >
> > Yes, we all know exactly what you meant. You just didnt think anybody
would
> > or could call you on it.
>
> "Zillions"? You thought no one would call me on my use of the word
> "zillions"? LOL - you are too funny Zach. I am still amazed on how
> you could get so hung up on that word.
It was a clue that strongly indicated you had not applied proper methods to
your "calculations".
> > > Your calculations have done nothing more than my own calculations and
> > > statements have already predicted. I didn't not predict an
> > > "impassable barrier" at the level of 7-fairly specified characters or
> >
> > You stated these walls are approached "quickly" after starting at 2- or
> > 3-letter words. What exactly did you mean then? When do we reach these
> > walls?
>
> The word quickly is very appropriate to use if the walls are reached
> on the very low end of the relative spectrum of complexity that exists
> in a given common usage language system. If the impenetrable wall
> occurred at the level of 100 characters, that would be by anyone's
> definition a very quick end to the abilities of evolution to do very
> much - relatively speaking. 100-character strings are nothing
> compared to even a short children's story, much less a Shakespearean
> play.
Um, more denial. Here is Pitman's Conjecture, "If I want to evolve a new
7-letter word starting with meaningful 7-letter word, I will have to swim
through this ocean of meaningless words".
And Pitman's number: the Pitman Number(7) is defined as the "average each
meaningful 7-letter word is surrounded like an island by well over 300,000
meaningless words"
that is 26^7 divided by the number of valid 7-letter words, or more
generally, P(L) = 26^L / N, where N is the number of valid words of length
L.
> There was no need for confusion on your part Zach. I clearly spelled
> out many many times what I meant by "quickly" if you had only done a
> little more reading first.
Yes, you did. It's called the Pitman Number(L), which increases very
dramatically with L. The only problem is that it doesn't tell us anything
about the distribution of words. You claimed they were randomly distributed.
It is clear from our investigations that they are not.
> > > even 20 or 30 even though you misstate that I did over and over again.
> > > As I have detailed to you before, even with a population of 100
> > > trillion (or even a trillion trillion) and a high mutation rate per
> > > generation, the impassable wall becomes insurmountable this side of
> > > trillions upon trillions upon trillions of years (i.e., zillions) when
> > > the minimum fairly specified sequence requirement reaches several
> > > hundred to a few thousand for a given type of function.
> >
> > This is FALSE. The number of possble mutants for a letter-string of
length
> > 1000 is upper-bounded by 1000^3 or about a billion per generation.
>
> Again, this is only from the perspective of a single individual in
> just one generation. This is not from the perspective of population
> numbering 100 trillion or a trillion trillion where each individual
> can cover a different sequence. With an average mutation rate of one
> per individual, population of 100 trillion can cover up to 100
> trillion new sequences in just one generation and population of a
> trillion trillion can cover up to a trillion trillion new sequences in
> just one generation.
I have been very clear as to what constitutes a valid mutation. It includes
a single point-mutation, a delete mutation, an insert mutation, or a
recombination of a single snippet from one string into a point within
another string.
You are obfuscating and trying to create confusion. I have been specific.
Please read the rules earlier in the thread. If you have a problem with
those, you could have let us know several weeks ago. As far as I can tell,
you think mutation is where every single letter is stripped away and
rearranged, and that no information can proceed from one generation to the
next.
> You are wrong Zach. You must think from the perspective of the
> population, not the individual. From this perspective your "about a
> billion per generation" calculation is way way off given the size of
> the population.
Absolutely false under the posted rules.
Here are the Extended Rules, posted 3/14/04
http://tinyurl.com/2mjy9
There are only so many mutations of a word. Here are the surviving (valid)
1st generation mutations of "O".
O, i, a, ox, ok, ho, of, oh, do, go, lo, no, on, or, so, to
That's all of them, Sean. There ain't no more in our Dictionary.
> > > I have made this same sort of predictive statement many times in this
> > > forum and on my website if you care to look. Evidently though, you
> > > prefer to ignore such statements so that you can build your own straw
> > > man representation of my position.
> >
> > Absolutely not. Your position is clearly represented on Google-Groups.
You
> > made an analogy to words. I pointed out that your analogy was faulty.
You
> > insisted you were right. I created a poem to give you some indication
that
> > it was quite easy to evolve between words.
>
> You haven't shown this to be true beyond the lowest levels of English
> language system complexity - as I have predicted.
No, you predicted that a 14-letter word would require an exploration of a
hundred million trillion mutations and that there "is no selectable
difference between any of the meaningless words in the ocean that surrounds
the scattered islands of meaningful [14]-letter words. Therefore any change
or "evolution" between these meaningless words will be purely random. So,
all that I am left with to get across this ocean of meaningless words is a
blind 'random walk'."
This is FALSE as has been demonstrated.
> > You kept insisting your were
> > right. You could have abandoned the analogy--it's just an analogy--but
you
> > insisted. You reap what you sow.
>
> I haven't abandoned the analogy at all. And, you haven't sown
> anything that I haven't already predicted.
Just because you keep saying it doesn't make it true.
> > > My argument is that EVEN if you could
> > > monitor such a huge population in computer simulation (which you can't
> > > owing to a lack of memory as well as speed), you would never evolve a
> > > meaningful English text the size of a small Shakespearean sonnet.
> >
> > No. You made a specific challenge. Now you have changed your
requirements to
> > some impossible simulation. "Start with a short 2 or 3-letter word and
see
> > how many words you can evolve that require greater and greater minimum
> > sequence requirements . . . " You are now claiming that your challenge
was
> > specifically designed to be impossible.
>
> Exactly. My challenge is impossible and that is the whole point.
> Evolution is impossible beyond the lowest levels of language system
> complexity. You think that because I said to start with a 2- or
> 3-letter words and see how far you can go that you would win by simply
> getting to the level of just a dozen or so letters?! How insane is
> that especially given the enormous reproductive rate and mutation rate
> of your simulation?!
You keep saying that too. My simulation can only create a few thousand
mutants a second. Nature deals in numbers on the order of 10^14, the number
of bugs in your gut.
> You need to read what I my specific challenge really was again Zach.
> I know you are disappointed that your strawman just isn't holding up
> very well since you really did put a lot of work into making this
> strawman. But, in the end, it really is and always was just a
> strawman version of my position and nothing more.
Shall I quoteth thee again?
"evolve a new 7-letter word starting with meaningful 7-letter word
"swim through this ocean of meaningless words"
> > Either you have moved the goal-posts, or have repeatedly put up a false
> > challenge. Or both.
>
> I have done neither. You have just assumed a non-reality, which
> anyone who is interested can easily validate.
Ok, as you keep insisting. The big quote with link again.
"What this means is that on average each meaningful 7-letter word is
surrounded like an island by well over 300,000 meaningless words. If I want
to evolve a new 7-letter word starting with meaningful 7-letter word, I will
have to swim through this ocean of meaningless words. . . . There is no
selectable difference between any of the meaningless words in the ocean that
surrounds the scattered islands of meaningful 7-letter words. Therefore any
change or "evolution" between these meaningless words will be purely random.
So, all that I am left with to get across this ocean of meaningless words is
a blind "random walk". With a population of 1, this random walk will take,
on average, over 300,000 mutations to arrive at a new meaningful word at the
level of 7-letters."
Here is your post with the Pitman Number(14) highlighted:
http://tinyurl.com/2rx8g
> > > What I am saying here is that your "O Sean" poem and anything else of
> > > equivalent size would not evolve using truly random rules of mutation
> > > combined with meaning/function based selection as I have previously
> > > detailed.
> >
> > You keep saying that. But you have refused to admit that this challenge
has
> > been met. "Start with a short 2 or 3-letter word and see how many words
you
> > can evolve that require greater and greater minimum sequence
requirements .
> > .. . "
>
> Where has anything the size of your complete "O Sean Pitman" poem been
> evolved? Hmmmmm . . . That is and was my challenge and you have not
> met it in even the most remote sense.
No you made a specific challenge. Here it is (ad nauseum):
"Start with a short 2 or 3-letter word and see how many words you can evolve
that require greater and greater minimum sequence requirements"
Guess what? We can evolve lots of words, and in very little time, and with
very few calculations.
> > Well, I did. I do it all the time. I put words into the Word Mutator and
out
> > pops all sorts of novel words, some long, some short, some with high
> > Scrabble score, some words I didn't even know existed.
>
> They are all "short" relatively speaking. You have no "long"
> sequences at all.
>
> > > Even according to your rules, if you extrapolate them, evolving
> > > "qqqqqq" should be no problem since a path does actually exist - as
> > > you envision paths existing that is. For example, consider a
> > > population of six sequences in a population of 6 reading, "queen,
> > > quiet, quite, quick, quilt, and quiz". Lets say that in a single
> > > generation they all recombined in the following fashion before the
> > > selection process took place:
> > >
> > > "Quiet" recombined with "queen" to read, "qquieteen" and then "quite"
> > > recombined with "qquieteen" to read "qqquiteuieteen", and etc., until
> > > you ended up with "qqqqqquizuiltuickuiteuieteen." Aha! Successful
> > > pathway established!
> >
> > You are very confused. None of those recombinations are allowed.
>
> But they are allowed in my version since they are allowed in real
> life.
What the heck are you talking about? The mutational rules were posted a
month ago. Indeed, they were made in response to your specific issues. You
wanted to take into account not only point-mutations but recombinations.
This was done. Now what is your problem?
Please be specific. What are the valid mutations allowed? Let's start with
something simple:
* We can mutate any single letter.
* We can delete any single letter.
* We can insert any single letter.
* We can snip any portion of a string.
* The snip can be reinserted into another string.
Start with the word "sean" and tell us what you think constitutes a valid
mutations. Does "xxxx" represent a valid mutation?
Point mutations
---------------------
Xean, sXan, seXn, seaX (*26)
seanX, Xsean (*26)
ean, san, sen, sea
Snips
-------
s, e, a, n
se, ea, an
sea, ean
sean
Remainders
----------------
ean, san, sen
an, sn, se
n, s
Insertions
-------------
Ssean, sSean, seSan, seasn, seanS
Esean, seean, seEan, seaEn, seanE
Asean, sAean, seAan, seaAn, seanA
Nsean, sNean, seNan, seaNn, seanN
SEesean, sSEean, seSEan, seaSEn, seanSE
EAsean, sEAan, seEAan, seaEAn, seanEA
ANsean, sANean, seANan, seaANn, seanAN
SEAsean, sSEAean, seSEAan, seaSEAn, seanSEA
EANsean, sEANean, seEANan, seaEANn, seanEAN
SEANsean, sSEANean, seSEANan, seaSEANn, seanSEAN
What other mutations do you think should be considered?
> > Don't you
> > remember the derivation of "O Sean Pitman"?
> >
> > O
> > a
> > an
> > can
> > scan
> > sean
> >
> > Every word must be valid to be available to the next generation (just as
in
> > life, a mutant must be able to grow to maturity and then breed before
its
> > genes can be carried forward to the next generation). Only one mutation
or
> > recombination is allowed and then the mutants must be subject to
validation.
>
> This is quite wrong. The mutation rate can be higher than one per
> individual genome. In fact, consider humans, for example. In every
> generation each human genome (offspring) experiences well over 200
> mutations. And, this is all BEFORE selection takes place for that
> individual. See:
Most of those mutations are not significant. In our small strings, we are
considering only one mutation per string. Are you now changing the rules?
Of course you are!
By the way, 200 mutations per hundreds of millions of bases means the
average soup of words will experience only rare single-mutations, much less
double mutations, or triple mutations.
The Word Mutagenator, being randomly based, could easily simulate the
possibility of double-mutations, but the results would be so rare as to have
negligible effects on the final result. If this is the only change you need
then it is really no change at all.
> http://naturalselection.0catch.com/Files/dnamutationrates.html
>
> > > As I see it, this is one of your problems. You calculate the number
> > > 646 based on the perspective of a single individual 7-letter sequence
> > > over the course of just one generation. What you need to do to
> > > calculate the total number of possible mutants that could be realized,
> > > even in one generation, is to consider _all_ members of your
> > > population.
> > >
> > > For example, say you had a population of 10 different
> > > 7-letter sequences. With each of these 10 sequences in the population
> > > being able to go to any one of 646 sequences, the population as a
> > > whole would be able to cover 6,460 sequences in one generation -
> > > right?
> >
> > No, your calcuation is incorrect. You have not accounted for
recombinations
> > between different strings. There are 26920 possible mutants.
>
> Fine. The actual numbers don't really matter as much as the concept
> here. The concept is that the population can cover much more ground
> that a single individual per generation.
Is this an admission of sorts?
> > > Now, this isn't what really happens of course since there are
> > > only 10 individuals. At most they can only reach 10 different
> > > sequences per generation with a mutation rate of one mutation per
> > > sequence per generation.
> >
> > You really need to understand the computer simulation work. Each word in
the
> > Word Mutator represents a population.
>
> This is not exactly true as I currently understand your program. You
> have a steady state population of 25. Those 25 different sequences
> are your "population". In each of your "generations" each of these 25
> sequences produces thousands of offspring to put into a "next
> generation pool". Those thousands of offspring are then "selected"
> for "fitness" and another 25 of the most "fit" sequences are chosen.
> Those 25 are now your new "population" in a steady state population
> situation of 25 in your particular computer environment.
Yes, that is correct.
> > It doesn't matter how many are in that
> > population.
>
> Oh yes, it very much matters how many individuals are in your
> "population".
>
> > Somewhere sometime in that population a mutation occurs. That
> > mutation may occur today or in a thousand years. It doesn't matter. In
Word
> > Mutator, we try just one mutation on one word. If it is a valid word, it
is
> > potentially added to the population.
>
> This is called your "reproduction rate", but these offspring are not
> "added to the population" yet. They are put into a "next generation
> bin" for future selection - correct? This is like a bunch of
> fertilized eggs that have mutations but have not been subject to
> "natural selection" yet.
According to the rules, each generation was to be resolved first. This is a
common method in computers to simulate simultaneous events. They represent
the results of mutations over a population occurring simultaneously.
However, forget the Word Mutator. Use the Word Mutagenator, if you find it
easier to comprehend. Each new mutant is considered for entry into the
population immediately.
> > If it is invalid, it is immediately
> > deselected.
>
> That is not what you said before. You said that selection takes place
> in "batches" to save time in each generation.
If it is not a valid word, it's just tossed. It's a still-born. If it is a
valid word, we keep in aside until all the mutants have been generated.
Think of it this way. Each word on the spreadsheet represents a population.
Within that population they make babies. If one of them is a mutant, and not
still-born, they must first mature before they can reproduce. We allow all
the mutants to mature simultaneously, and then prune the Pond. The advantage
of "playing in turns" is that it allows us to look at every mutant for a
given population. If you were really interested in seeing how evolution can
evolve new structures, this program can be fascinating.
If you don't like it this way, use the Word Mutagenator, which continuously
introduces new mutants as they are created.
646. That is all the unique mutations available. There may be a bunch of any
particular mutation, but we are only concerned with unique ones.
The first Sean couldn't compete. It had a low-Scrabble number. However, when
the second Sean was discovered, its Scrabble number was found in the
Dictionary, which I set at 99. The program is designed so that you can set a
meaningfulness quotient for each word, or you can play with the Scrabble
table and make B's more important, or make God-words have a higher score.
The selection is arbitrary after all, but if you want you can stick to
length. Scrabble score and altered scoring systems are for the advanced
student.
> Do you see the problem
> here? If you did the elimination, then it was you who DIRECTED the
> evolutionary process via intelligent design. If you let the computer
> do it by it self with random chance alone, you must calculate the odds
> that two words will be chosen that can actually join together in a
> meaningful way, and these odds translate into average time.
Um. That's the whole point of the program. The only "intelligent design" is
pruning for Scrabble score (or length).
That's not how the program works. It tries every single possible
recombination.
> The
> computer on the other hand, without your "intelligent" help, cannot do
> what you have done. The computer, left to itself, would take a whole
> lot longer to come up with the united meaningful combination that you
> helped it come up with in a much shorter period of time.
I didn't help it. It figured it out. It tried all the available mutations
and kept the ones with the highest Scrabble score (or length).
> In our experiment, the computer IS supposed to be the breeder who
> selects based on the "meaning" of character sequences. In our
> computer scenario no one type of meaning is given preference over any
> other type of meaning. You therefore cannot step in and interfere
> with your intelligent mind and select based on your personal
> preference. That is called "cheating" or "intelligent evolution".
> Which, is basically my whole point. Evolution just won't work without
> intelligent direction.
If you want, I'll put "Sean" back to a standard Scrabble score, or delete it
entirely. But your point is faulty. Meaning is something human place on
things, not computers. If we select for length, its because that's
meaningful for us. However, the Word Mutator can be set to selection for
length, Scrabble score, short words, words with "Z" in them, whatever
well-defined rule you want. However, we can stick to length in the future.
> > > Now, say we get or "pit" and "man", each of these will mutate
> > > separately down different paths - right? How many generations will it
> > > take, on average, before both of these paths come to new sequences
> > > that are not only meaningful independently, but would also be
> > > meaningful IF they happened to be united by a recombination mutation?
> > > I'm not sure what the answer is, but it wouldn't be too hard to find
> > > out I'm sure.
> >
> > That's right. It isn't hard to figure. We have to figure every point
> > mutation, every snippet, every remainder, and every possible insertion
of
> > every possible snippet at every point in the string. The Word Mutator
does
> > this quite well (with a little bit of overlapping for technical
reasons).
> >
> > > But, for now, let's just say that the odds of this
> > > happening are around 1 in 20. The problem here is that it is not
> > > enough to get two populations at the same time that COULD recombine to
> > > form a meaningful sequence. What needs to happen is that a CORRECT
> > > recombination mutation DOES happen exactly when it is beneficial.
> > > Now, what are the odds of that?
> >
> > Well, without a breeder making the selection, then we wouldn't
necessarily
> > expect "beware" to pop out.
>
> Exactly my point . . .
No. That wasn't your point. If you keep this up, I'll be forced to quote you
again! You said to go from one 7- or 14-letter word to another 7- or
14-letter word meant crossing an ocean of meaningless words. Well, that
ocean is sprinkled with archipelagos.
Breeders manipulate species by selecting from essentially random mutations.
Breeding was one of Darwin's main pieces of evidence.
> > I think that's your point, and you would be
> > right. (We wouldn't necessarily expect Poodles to occur without a
breeder's
> > eye either!)
>
> So you admit that without intelligent design that significant
> meaningful evolution is impossible? Your computer just can do much
> without your input? Is that what you really want to say here?
To get a particular word, such as "beware" takes someone culling the
population for particular combinations of traits--just as a breeder selects
from random mutations. To get novel long words take nothing but selecting
for length.
> > However, without a breeder, we can still expect some mutants
> > will be valid, and this is exactly what happens. "Pitman" evolves into
> > "pinpricking", a longer word, without the intervention of a breeder.
>
> Yes, your computer can do some things very well all by itself just by
> random mutation and meaning-based selection. But, without your help,
> it is much more limited now isn't it?! Certainly then, without your
> help, the computer would never come up with your whole "O Sean Pitman"
> poem in a gazillion years or generations . . . whichever one you
> prefer.
No, probably not. But we will come up with novel words and phrase.
Biological evolution might never come up with poodles, but can and did come
up with wolves.
This is your word game. You claimed we couldn't cross the oceans of
meaningless words, and this has been shown to be FALSE. That ocean is
scattered with archipelagoes of meaningful words.
> > > Well, there are several ways that "be" and "ware" could recombine, but
> > > few of these possibilities are "meaningful" in the English language
> > > system. You could get "wbeare" or "wabere" or "warbee" or "bwaree" or
> > > "warebe" or "beware". So, the odds of getting a meaningful
> > > recombination is 1 in 6. Then, you must also consider the odds that a
> > > recombination event will occur right at this time instead of another
> > > possible type of mutation for an additional odds ratio of 1 in 5.
> >
> > Sean, Sean, that's all been considered.
>
> By intelligent design - right?
You made a challenge. The challenge has been met. I crossed the ocean of
meaningless words to arrive from one 7-letter word to another in less than
the Pitman Number(7).
> > > So, the total odds of successful recombination would be 1/6 * 1/5 *
> > > 1/20 = 1 in 600 generations. And, this is only for very short
> > > sequences with very high ratios of non-recombined meaning vs.
> > > non-meaning. This problem gets exponentially worse with each step of
> > > the ladder of complexity.
> > >
> > > Do you see the problem? Just because it CAN happen does not mean that
> > > it WILL happen all that often.
> >
> > It does happen. It did happen. It happens everytime someone runs the
Word
> > Mutator.
>
> Every time you are there to direct your mutator on just what words to
> select for "recombination".
Um, I do no such thing. I just click the button that says Generate. It does
everything. It creates every possible mutation, and selects the "best" to
fit the give size of the Pond. If I want a specific word, then I have to
artificially select, just like a breeder. If I want long words, the Mutator
does fine on its own.
> You are just getting more and more
> hilarious Zach. Don't you realize that this only proves my point?
> Your little mutator, if left to itself, wouldn't come up with much of
> anything beyond the lowest levels of English language system
> complexity (i.e., probably no more than a meaningful 50-character
> phrase and certainly no more than a 500 character phrase). Poor
> little mentally challenged mutator .
It's a Word Mutator. It sails the ocean of meaningless words on a voyage of
discovery. It navigates from one word to another. It requires no input to
create long words.
> > > Does your computer program take this
> > > little problem into account?
> >
> > Certainly. It's all there. Perhaps you should study the documentation a
bit
> > more carefully, and with an open mind. The source code can be found
here:
> >
> > Zachriel's Special Pudding Recipe
> > http://www.zachriel.com/mutagenation/Pudding.asp
>
> Oh, I have studies your document pretty carefully and I have found
> your admissions that you yourself do quite a bit of selecting, helping
> your little mutator along, quite enlightening to this whole
> discussion.
I do no such thing. I put in a "seed" word or two, and hit Generate. Try it.
Start with "O".
> > > You certainly don't in your written out
> > > evolutionary scenarios. You simply assume that the path will be
> > > easily found if it exists, but this is a fallacy.
> >
> > In the long-string examples, I calculated the number of mutants
available in
> > each generation. The selection is for meaning and is done by a
"breeder".
>
> By the _breeder_?! Don't you see my point here?! Your computer
> program couldn't do it by itself because it is not intelligent.
To create a poem of specific meaning, then we have to select from our
available options. However, the Word Mutator just selects for length.
> You
> are the breeder here when the breeder in our scenario is supposed to
> be limited to the computer in the computer's selection for meaning,
> not yours.
My computer doesn't really care about your pecidillos. However, if I ask it,
it will generate mutations and select the longest ones, or the ones with the
highest Scrabble score, or it will present me with a list of viable mutants
from which I can select.
Selective breeding was one of Darwin's main evidences.
> When you do the selection you bypass a great many possible
> non-ideal paths that could have been taken and therefore you
> dramatically shorten the required time involved for evolution to take
> place via your insertion of intelligence into the equation. You
> basically cheated and by doing so only demonstrated more convincingly
> that intelligence is required for evolution to do much of anything.
Um. Let me try something. I'll put "O" into the Word Mutator and press
Generate a few times. . . . Hm. "cookbooks", "chowchows", "hoopoes", a
crested
Old World nonpasserine bird. Never knew that.
Guess what Sean. Anyone can do what I just did. The Word Mutator does
everything. Let's try the Word Mutagenator and see what random mutation and
selection for Scrabble score can do. Oh, and I'll erase "sean" from the
Dictionary. Now, I'll put "O" into the Word Mutagenator and press Mutagenate
Continuous and let's see what happens. . . . After a few seconds we have
"champaks", Scrabble score 21. an Asian tree of the magnolia family with
yellow flowers. Never knew that either.
> > > See above descriptions of the problem with this "a path exists and
> > > therefore evolution will be rapid" assumption.
> >
> > That's not an assumption. The number of available mutants is on the
order of
> > L^3, where L is the length of the string. With L=100, the number of
possible
> > mutants per generation will be about a million. And we can have some
very
> > meaningful expression in a hundred letters.
>
> If you yourself do the selecting . . . I'm truly blown away.
That's what it's all about Sean. Random mutation only provides the raw
material for selection. We can select manually, we can have a specific rule,
or in natural biology it's natural selection. After all, selecting for
length is just as arbitrary as any other rule we might use.
> > > Actually, there is a very good way of knowing, beyond a reasonable
> > > doubt that is, seeing as how no known language/information system, is
> > > lined up as nicely as would be required for Darwinian-style evolution
> > > to get beyond the lowest levels of existing complexity found in such
> > > language systems.
> >
> > You have failed to provide any such argument. Your only argument has
been
> > that there are 26^100 possible arrangements of a hundred letters. You
have
> > absolutely no idea how many of those form valid English expressions, nor
how
> > those expressions are connected in the space of possible permutations.
>
> I do have a very good idea of how many there are and how they are
> arranged in sequence space, at least to the degree necessary for the
> purposes of my argument. You have only supported my argument all the
> more by your demonstration of the limits of evolutionary processes to
> the lowest levels of English language complexity without the input of
> intelligent help.
The Pitman Number tells us nothing about the distribution of words in the
ocean of "sequence space".
>
> > > Why then should the genetic language/information
> > > system found in living things be any different?
> >
> > You are reaching a conclusion from a faulty premise.
>
> Not at all. It is you who can't seem to understand that intelligence
> is not allowed in this equation if you are arguing for evolution. A
> breeder who selects based on phenotypic expression is not selecting
> based on the idea that a combination of traits may yield a brand new
> type of combined function with an entirely new phenotype.
Are you then claiming that breeders selecting from random mutation can
create evolution in organisms? This was, after all, one of Darwin's most
important evidences.
> That is
> impossible, even for human breeders to do, without actually looking at
> the genetic sequences involved with the phenotypic expression - which
> is what you are doing when you help your mutator out.
If you want dogs with nice soft, curly hair, you'll have to use artificial
selection, just like breeders. If you don't select, dogs'll still get
selected, selected by nature, but they probably won't be cute and cuddly.
> > > And, in fact it is
> > > not. Real life experiments have proved as much. In real life
> > > evolution stalls at the lowest levels of functional complexity so that
> > > there simply are no examples of a cellular function evolving that
> > > requires more than a few hundred fairly specified amino acids working
> > > together at the same time. There are examples of less complex
> > > cellular functions evolving all the time, but evolution stalls out as
> > > one looks higher than the few hundred fairly specified amino acid
> > > level.
> >
> > Evolution of new traits has been directly observed. Large-scale
adaptation
> > only occurs on geological time-scales, but is apparent from the fossil
> > record.
>
> Not at all. Nothing beyond systems requiring more than a few hundred
> specified amino acids has ever been shown to evolve despite direct
> observation for over a million generations. Relatively speaking, this
> is not "large-scale" evolution here. Systems requiring a few or even
> a few thousand fairly specified amino acids are rather low-level
> systems, relatively speaking.
Funny how AIDS evolved a way to invade the human immune system.
> In short Zach, I find it very interesting and even amusing that you
> actually admit to directing the evolutionary process of your computer
> program. What it can do, it does only to very low levels of English
> language complexity and rapidly stalls out as it tries to progress
> upwards. Then, in cases where it seems to need a little help by human
> directed intelligence, you freely step in and provide the needed help.
> Please. This is getting ridiculous.
Gee Willikers, Sean. That's a bunch of hooey. Have you even tried the
software?
> It would be much more ingenious if you would simply admit the obvious
> limits of evolutionary processes instead of trying to help it along
> via intelligent design. Actually, I'm starting to wonder if you
> aren't really a creationist in disguise who is not so secretly trying
> to help me prove my case.
When I built the Word Mutator I designed it to falsify your notion of oceans
of disconnected words per your quoted material below. Please don't deny what
is plain for everyone to see.
You are not capable of admitting error, but you have more-or-less pulled
away from that position. That is probably all we can hope for today.
"What this means is that on average each meaningful 7-letter word is
surrounded like an island by well over 300,000 meaningless words. If I want
to evolve a new 7-letter word starting with meaningful 7-letter word, I will
have to swim through this ocean of meaningless words. . . . There is no
selectable difference between any of the meaningless words in the ocean that
surrounds the scattered islands of meaningful 7-letter words. Therefore any
change or "evolution" between these meaningless words will be purely random.
So, all that I am left with to get across this ocean of meaningless words is
a blind "random walk". With a population of 1, this random walk will take,
on average, over 300,000 mutations to arrive at a new meaningful word at the
level of 7-letters."
Zachriel
"Sean Pitman" <seanpi...@naturalselection.0catch.com> wrote in message
news:80d0c26f.04050...@posting.google.com...
>
> The mutation rate can be higher than one per
> individual genome. In fact, consider humans, for example. In every
> generation each human genome (offspring) experiences well over 200
> mutations. And, this is all BEFORE selection takes place for that
> individual. See:
>
> http://naturalselection.0catch.com/Files/dnamutationrates.html
>
I have updated the Word Mutagenator, so it runs nearly as fast as the Word
Mutator. There was a bigger penalty than expected in updating the counters
on the spreadsheet. Now they just update when the screen updates. The
frequency of the screen updates can be set on the new Variables spreadsheet.
The current algorithm is running at about 25,000 mutants processed per
second, or a million or so per minute (on my 250MHz P4).
The Word Mutagenator has several advantages over the Word Mutator. For
instance, it more closely mimics nature in that mutations are random. In
addition, it can more easily simulate multiple mutations. I was thinking of
adding a slider that would increase the mutation rate. Minimum would be just
one mutation as it is now, while maximum would be virtual disintegration of
the genome.
Just as when Sean suggested (insisted) I include every single possible
recombination, what started as a problem became one of the driving forces of
the Mutagenation Engine. Including a small chance of multiple mutations has
the possibility of speeding up the evolution dramatically, and also allowing
the creation of heretofore impossible mutants. This may be crucial if we
proceed with the Phrasenator Project.
Thanks Sean!
Bennett Standeven
>
> On my 250MHz P4, Word Mutator only does about 40,000 mutants per second,
> while the latest (just uploaded!) version of Word Mutagenator does about
> 25,000 mutants per second, hardly a huge number when we have to supposedly
> explore a space of 100 million trillion. Yet, we have explored that space
> sufficiently to find 14-letter and longer words.
>
> With a reasonable algorithm for recognizing valid phrases, a Phrasenator
> could easily handle dozens of phrases of reasonable length.
>
[...]
I have written up a modified version of the Mutagenator (in C); it
generates valid sequences of brackets, instead of words. Thus, by a
simple change in parameters, it can produce arbitrarily long "words".
The code follows:
#include <stdio.h>
#include <string.h>
#include <random.h>
#include <time.h>
#define MAXLEN 80
#define POPVAL 500
char Mutation[2*MAXLEN + 2];
char * Pop[POPVAL];
int reCombine = 100, debug;
char chararr[8] = "()[]{}<>";
int Validate(void);
// Return a random number between a and b, inclusive.
int Random(int a, int b) {
unsigned int c;
if(b < a) { c = b; b = a; a = c; }
c = random();
c %= b-a+1;
c += a;
return c;
}
void debug_print(char err[])
{
if(debug == 1) puts(err);
}
/* ------------------------
* MUTAGENATOR
* for a random Word in population
* Random for Mutation or Recombination
* return 1 if mutation is valid, 0 otherwise.
*/
int Mutagenator(const char * Word)
{
int c, lengthWord, i, j, q;
lengthWord = strlen(Word);
if((random() % 128) < reCombine) {
// MUTATIONS
// Random type of Mutation
c = Random(1, 5);
switch(c) {
case 1: //Delete Mutation
i = Random(0, lengthWord - 2);
strncpy(Mutation, Word, i);
strcat(Mutation, Word + i+2);
break;
case 2: //Two Point Mutation
i = Random(0, lengthWord - 1);
j = Random(0, 7);
strcpy(Mutation, Word);
Mutation[i] = chararr[j];
i = Random(0, lengthWord - 1);
j = Random(0, 7);
Mutation[i] = chararr[j];
break;
case 3: //Insert Mutation
i = Random(0, lengthWord);
strncpy(Mutation, Word, i);
strcat(Mutation, Word + i-2);
break;
case 4: //Remainders
i = Random(0, lengthWord-2);
j = Random(2, lengthWord - i);
j -= j%2; // j should be even.
strncpy(Mutation, Word, i);
strcat(Mutation, Word + j + i);
break;
case 5: //Snippets
i = Random(0, lengthWord-2);
j = Random(2, lengthWord - i);
j -= j%2; // j should be even.
strncpy(Mutation, Word + i, j);
Mutation[j] = 0; // Mutation must be null-terminated.
break;
}
}
else {
char Snippet[MAXLEN+2];
int lengthInsert;
// RECOMBINATIONS
i = Random(0, lengthWord-2);
j = Random(2, lengthWord - i);
j -= j%2; // j should be even.
strncpy(Snippet, Word + i, j); // Take a snippet from Word
Snippet[j] = 0; // ensure Snippet is null-terminated.
// Select another word from existing population
i = Random(0, POPVAL-1);
lengthInsert = strlen(Pop[i]);
// Pick a random point in this subject word
q = Random(0, lengthInsert);
strncpy(Mutation, Pop[i], q);
strcat(Mutation, Snippet);
strcat(Mutation, Pop[i] + q);
}
if(strlen(Mutation) < 2) return 0; // don't allow empty strings.
if(strlen(Mutation) >= MAXLEN) return 0; // Mutation is too long.
return Validate(); // check Mutation against chosen language.
} // End of Mutagenator.
void paren_remove(char *Temp, int j)
{
int i;
for(i=0; Temp[i+1]; i++)
{
if(i>=j) Temp[i] = Temp[i+2];
}
}
void test(char *Temp)
{
int i;
for(i=0; i < strlen(Temp); i++)
{
if(Temp[i] == 0 || Temp[i+1] == 0) return;
if(Temp[i] == '(' && Temp[i+1] == ')') {
paren_remove(Temp, i); test(Temp);
}
if(Temp[i] == '[' && Temp[i+1] == ']') {
paren_remove(Temp, i); test(Temp);
}
if(Temp[i] == '{' && Temp[i+1] == '}') {
paren_remove(Temp, i); test(Temp);
}
if(Temp[i] == '<' && Temp[i+1] == '>') {
paren_remove(Temp, i); test(Temp);
}
}
}
int Validate(void)
{
char Temp[MAXLEN];
strcpy(Temp, Mutation);
test(Temp);
if(strlen(Temp)) return 0; // there were unmatched brackets.
return 1; // there were no unmatched brackets.
}
int main()
{
int i, k;
long int j;
i=rawclock();
srandom(i);
for(i = 0; i < POPVAL; i++) {
Pop[i] = malloc(MAXLEN);
if(Pop[i] == NULL) return 1; // Out of memory
switch(i%4) {
case 0: strcpy (Pop[i], "()"); break;
case 1: strcpy (Pop[i], "[]"); break;
case 2: strcpy (Pop[i], "{}"); break;
case 3: strcpy (Pop[i], "<>"); break;
}
}
for(j = 0; j < 10000; j++) {
i = Random(0, POPVAL-1);
if(Mutagenator(Pop[i])) strcpy(Pop[i], Mutation);
for(k=0; k<MAXLEN; k++) {
Mutation[k] = 0;
}
}
for(i = 0; i < POPVAL; i++) {
puts(Pop[i]);
}
return 0;
}
Zachriel
"Bennett Standeven" <be...@pop.networkusa.net> wrote in message
news:24c3076b.04050...@posting.google.com...
> "Zachriel" <sp...@zachriel.com> wrote in message
news:<4uednQu8fq9...@adelphia.com>...
> >
> > On my 250MHz P4, Word Mutator only does about 40,000 mutants per second,
> > while the latest (just uploaded!) version of Word Mutagenator does about
> > 25,000 mutants per second, hardly a huge number when we have to
supposedly
> > explore a space of 100 million trillion. Yet, we have explored that
space
> > sufficiently to find 14-letter and longer words.
> >
> > With a reasonable algorithm for recognizing valid phrases, a Phrasenator
> > could easily handle dozens of phrases of reasonable length.
> >
>
> [...]
>
> I have written up a modified version of the Mutagenator (in C); it
> generates valid sequences of brackets, instead of words. Thus, by a
> simple change in parameters, it can produce arbitrarily long "words".
> The code follows:
Cool. Very cool. If I were to do this again, I would probably write the
engine in C using VBA just as a wrap-around for the user-interface. However
I am working in a temporary location and don't have access to a C compiler
at the present moment. Plus I had never written in VBA and just wanted to
see what it could do. It's major deficiency is lack of an array
searcher/sorter. Fortunately, a binary search / insert sort works quite
efficiently with arrays which are mostly sorted, so it worked out reasonably
well.
Though more power would be handy, it wasn't really necessary to demonstrate
the the Pitman Number was an exaggeration of the computational difficulties
involved. Writing in C takes a lot more time, too. I doubt if I'll do a
rewrite of the core code at this late date, but you never know. I'll look
more closely at your code.
Thanks for the tip. My email box has been full of helpful advice.
Sean Pitman
> > Notice, Zach, that I used the pleural form "words" to indicate
> > multiple words in what you call a "war of words."
>
> Sigh. I've generated multiple words. The Word Mutator deals in populations
> of dozens or hundreds of word species.
I'm not talking about multiple single words, but about sequences of a
given length using one or more words for a combined meaningful
sequence. This is exactly what you were trying to do when you started
this very thread with the title of your poem "O Sean Pitman". My
argument was and is that such a meaningful sequence, in fact no
meaningful sequence of any kind of such a length an interdependence
within the English language system, can be evolved using random
mutation and non-intelligent function-based selection.
> It is also obvious you once believed that 14-letter words were out of reach
> of evolution. Let's look again at what you wrote.
>
> You claimed that "the potential space of a 14-letter word or phrase is over
> 109,418,989,131,512,359,209 (over 100 million trillion)." This is very close
> to the Pitman Zillion and certainly beyond the capability of any computer to
> explore in a reasonable time. My Dictionary contains exactly 1643 (~10^3)
> 14-letter words. According to your "calculations", my program would have to
> explore 10^19 / 10^3 or 10^16 mutants before having a decent chance of
> finding such a word. I invite everyone to read your "analysis" of the
> problem for themselves.
> http://tinyurl.com/2rx8g
>
> And yet, the Word Mutator can solve this problem in minutes. How is it
> possible? Can Sean Pitman please explain how the Word Mutator is capable of
> doing this.
The sequence space of 14-letter words is indeed over 100 million
trillion in size. The _average_ distance between each meaningful
14-letter single word is also about 66 million billion non-defined
sequences.
My purpose in pointing these numbers out was to show the contrast
between the average distance at this level as compared to lower
levels, such as 2-, 3-, and 7-letter words. I was trying to show the
exponential expansion in average distance as one moves up the ladder
of complexity. My purpose was NOT to propose the drawing of an
uncrossable line at the level of 14-characters. Not at all. My
purpose was ONLY to show the progression of the average gap and how
the islands and interconnections between meaningful islands decreased
in an exponential manner with each step up the ladder of complexity.
And, this is exactly what happens.
Notice, if you will, that the 14-letter islands of meaningful words
are much smaller than they are at the 3-letter level and their
interconnections are much more rare. Consider the ratio and the time
involved for your computer to evolve 3-letter words. I bet it was
able to evolve all or nearly all 3-letter words in just "seconds".
However, how many 14-letter words was it able to evolve, without your
outside "direction" as a "breeder", in the same amount of time? What
ratio of 14-letter words did your computer evolve vs. the ratio of
3-letter words or 7-letter words that it evolved - in the same amount
of time?
On your website you make mention that your program was able to evolve
one third of all the words in the dictionary that you used. Tell me
though, what _ratio_ of words were evolved at each of the levels of
complexity listed in your dictionary? I don't really care about what
scrabble score they might have. I only care about their total sequence
length. If the program found all meaningful 3-letter words, that
would be a ratio of 1:1 for the 3-letter level. What was the ratio
for the 6-letter level? The 10-letter level? etc? In other words,
you say that there are 1,643 words listed in your dictionary at the
level of 14-characters. What ratio of these 14-letter words did your
program evolve in given amount of time relative to the ratio of the
lower levels?
Why does this matter? It matters because if the ratio is
significantly lower for each step up the ladder of complexity, it
shows that the islands of meaningful sequences are not nicely lined up
at all, but are indeed becoming more and more widely separated from
each other, on average, in the exponentially expanding vastness of the
potential sequence space at each higher level of complexity.
For example, say that 1,000 of the 1,643 possible 14-letter words in
the dictionary were all clustered together in a nice little bunch in
one tiny area of 14-letter sequence space. Would your demonstration
that evolution between these closely spaced 1,000 sequences is very
rapid disprove my assertion that the average time required must still
take into account the other 643 sequences? What if these 643
sequences form another closely packed island far far away from the
other island of 1,000 sequences? Now, evolution within each island
will be rapid, but what about getting from the one island to the other
island? This must also be factored into the "average time" equation.
Basically, it comes down to the odds that each of the islands of
beneficial sequences will have a connecting bridge or bridges to
islands within the same level of complexity as well as to islands
within lower and higher levels of complexity. At relatively low
levels of complexity, these bridges are quite common and can be found
fairly quickly - depending upon the size of the population and its
mutation rate of course.
Another thing is, outside help by intelligent design is not allowed in
these experiments Zach. You have foresight that evolutionary
processes do not have. Natural selection, as a purely _mindless_
process, can only select based on what works right now. A mindless
function based selector cannot select to keep a sequence simply
because it may work in combination with something else sometime in the
future. Only an intelligence that has insight and the ability to
predict the future, like you have, can do this sort of selecting. So
please, you cannot be helping your computer out here. You must let it
select based on meaning that is current. It cannot select short
meaningful sequences over other short meaningful sequences based on
the chance that a future recombination event would produce something
meaningful in certain short sequences - as you have done in your
"poem" evolution scenarios.
> > Obviously, it is
> > very easy to see, from all that I have written on this topic, to
> > include the papers on my own website, that I'm talking about
> > meaningful sequences made up of one or many words as long as the
> > sequence has beneficial meaning. It doesn't matter at all whether the
> > sequence is one word or divided up into many words of the same length
> > - and I never said or indicated otherwise.
> >
> > In fact, you seemed to fully recognize this fact _initially_ since you
> > wrote out long multi-word "poems" in your attempt to challenge my
> > position. You even have many multi-word poem on your website. Even
> > the title of this thread is the multi-word title to your poem, "O Sean
> > Pitman". Yet, you haven't evolved anything even close to the size of
> > one of these many hundred-character poems now have you? The very best
> > that you have evolved, even with extraordinary reproduction and
> > mutation rates, is no longer than a couple dozen characters in size
> > (truly tiny in comparison to your grandiose claims for the powers of
> > evolution).
>
> As has been explained many times, the number of mutants for 1000 characters
> is on the order of a billion per generation, too large to easily simulate on
> a desktop computer, but much, much less than the "zillions" you claim.
Actually, the number of possible mutants, to include meaningful as
well as non-meaningful, for a 1,000-character sequence is the number
of individuals in a population times the average mutation rate per
individual, per generation. Given the potential sequence space for a
1,000-character sequence, this could be way over a "billion".
Say, for example, that we had a 10^24 individual sequences/genomes in
our population - each of them with a different 1,000 character
sequence and an _average_ mutation rate of one mutation per individual
per generation. How many new 1,000-character sequences would this
population come across, on average, in one generation? Obviously, the
answer is 10^24, which is far greater than a billion.
You see, in my scenario, not all characters in a 1,000-character
sequence need to be "meaningful" in order for that sequence to be
selected as more "meaningful" than another 1,000 character sequence.
In my scenario, selection is based on the greatest sequential length
of the longest meaningful stretch of characters contained within the
larger 1,000-character sequence. This allows for neutral evolution to
occur as well as meaningful to meaningful evolution. Those
meaningless portions of the 1,000-character sequence can still mutate
and happen to come across a meaningful sequence by random walk. It is
just that some part of the 1,000-character sequence must be selectable
via function-based selection over other 1,000-character sequences in
each generation.
Of course, since 1,000 character sequences require a great deal of
computer processing power, you might have to use a smaller population
or a smaller genome cap length (such as 100 character sequences) if
you use a larger steady state population. You could also use a higher
mutation rate or reproductive rate, but then you would also have a
higher death rate per generation. But, a higher reproductive rate and
death rate would be required in order to keep a higher mutation rate
from destroying your "good" mutations faster than they can be
maintained by the selection process of each generation.
> > Come on now Zach, in your war of words are you can't be seriously
> > accusing me of ever thinking to draw the line at short one-word-only
> > sequences? - Can you?!
>
> Yes. You did. "the potential space of a 14-letter word or phrase is over
> 109,418,989,131,512,359,209 (over 100 million trillion)." What did you mean
> by that?
I meant just that. The potential space of a 14-letter word or phrase
is indeed over 100 million trillion potential sequences in size. I
mentioned this as a means of comparison to the sequence space of
smaller and larger sequence sizes to show the exponential nature of
the expansion as one moves up the ladder of complexity. I did not say
this to indicate that this was the level at which all evolution for
all colonies and all starting points must end. This thought never
even crossed my mind and that can be clearly seen from all that I have
written in this forum and on my website well before you came on the
scene. In fact, I _specifically_ drew my line of practical
impossibility over and over again at the level of at least several
_hundred_ to a couple _thousand_ fairly specified characters
sequences. Why don't you reference these statements on your website?
Hmmmm? I think it is because you are trying to make your case
stronger than it really is - and you know it. You just cannot accept
the fact that you may actually be off base here. You can't even seem
to consider that possibility - can you?
> > You are really reaching for straws Zach. It
> > really does seem very desperate of you, really it does, to accuse me
> > of "moving goal posts" here when I clearly said over and over again
> > that my limits were dependent upon population and genome size as well
> > as mutation rate and nowhere did I ever say that sequence lengths as
> > short as one or two dozen where "the limit". In fact, over and over
> > again I clearly drew the limit for genetic evolution at a couple of
> > thousand amino acids working together at the same time. I am truly at
> > a loss to see how you could have read what I actually wrote and assume
> > that my "goalposts" were at the level of 7- to 14-characters in size -
> > especially considering the enormous reproduction rates and mutation
> > rates that you used in your computer simulation!
>
> On my 250MHz P4, Word Mutator only does about 40,000 mutants per second,
> while the latest (just uploaded!) version of Word Mutagenator does about
> 25,000 mutants per second, hardly a huge number when we have to supposedly
> explore a space of 100 million trillion. Yet, we have explored that space
> sufficiently to find 14-letter and longer words.
Again, this has nothing to do with my predictions. I never that with
such a mutation rate that you could not evolve a 14-letter word. You
even acknowledge that fact yourself. You have said yourself that you
know that I never specifically drew the line at 14-characters
sequences. This acknowledgement, combined with the fact that I did
_specifically_ draw the line at a couple thousand characters in many
different places should tell you something.
> With a reasonable algorithm for recognizing valid phrases, a Phrasenator
> could easily handle dozens of phrases of reasonable length.
No it couldn't _if_ by "reasonable" you mean greater than 500 or so
characters in length. To be honest though, I don't think you can even
reach the 100-character level, and probably not even the 50-character
level (based on a steady state population of less than 10,000
individuals/genomes with a high average mutation rate and high
reproductive rate and death rate).
> > You yourself recognized the fact that I never drew the line at such
> > low levels, so how can you possibly say that I've moved my goalposts?
> > They have only been moved relative to your misstatements about my
> > position. The real goalposts have not been moved at all. They are
> > right where I put them well over a year ago now and have remained
> > there, not even remotely challenged by anyone to include you, to this
> > day.
> >
> > And, if you are really honest about this whole thing, you will reflect
> > my real position on your website - but I am not holding my breath on
> > that one. You seem too attached to your strawman version of reality.
>
> I have linked to your website, and to many of your posts, including this
> thread. You have ample opportunity for rebuttal.
Yes, at least you link in a very general way to my threads in this
forum. What is interesting to me though is that what you have written
directly on your website is completely counter to my actual position.
You used my descriptions and attempts to illustrate an expanding
sequence space and average intra-word distances to say that I actually
draw my line of "impossibility" at very low levels of sequence
complexity - such as 7- or 14- character sequences. This is at best a
dramatic overstatement and at worst an deliberate mischaracterization
of my actual position. Either way, it is a strawman version of the
real thing, and you really should have been able to pick up on that
from even a superficial reading of my previous threads and what is
presented on my own website.
Your evolutionary scenarios of long sequence evolution, such as your
"O Sean Pitman" poem, are based on nothing but intelligent
manipulation of short sequences that no computer could ever do this
side of a practical eternity of time without the input of intelligent
guidance. You seem to recognize this because you insert the needed
guidance all the time and call it "selective breeding".
You also talk about the evolution of HIV resistance as something
spectacular when it involves nothing more than a very few (i.e., one
or two) point mutations to cause a block or interference with a
pre-established interaction. This sort of evolution is at the very
lowest levels of functional evolution. Nothing new is created beyond
the interference of a pre-established function or interaction. Of
those evolutionary scenarios that actually do create novel
_independent_ functions, such as the evolution of certain enzymes like
lactase or nylonase, none of these examples goes beyond the level of a
few hundred fairly specified amino acids working together at the same
time. Considering that this level is extremely low relative to the
much higher levels that exist in every living thing, evolution is
obviously extremely limited in what it can do this size of a practical
eternity of time (i.e., zillions and gazillions of years of average
time).
And you think you have done something by getting evolution to produce
a meaningful (not even considering "beneficial" vs. "non-beneficial")
sequence less than 20-characters in size?! Please . . . think again!
Sean Pitman
> Just as when Sean suggested (insisted) I include every single possible
> recombination, what started as a problem became one of the driving forces of
> the Mutagenation Engine. Including a small chance of multiple mutations has
> the possibility of speeding up the evolution dramatically, and also allowing
> the creation of heretofore impossible mutants. This may be crucial if we
> proceed with the Phrasenator Project.
>
> Thanks Sean!
You're most welcome Zach, and good luck with your "Phrasenator
Project"!
If programmed as I have suggested, I predict that an evolutionary
scenario based on true random mutation and meaning/function based
non-intelligent selection will rapidly come to walls beyond which
meaningful evolution simply will not occur this side of a practical
eternity of time. Specifically, so as you don't get confused this
time, I predict that the wall beyond which no meaningful evolution
occurs will be found well before the 1,000-character level is reached.
This level is well short of the bold "5,000-character" assertion
listed on your website as well as your "O Sean Pitman" poem. In fact,
I'd be quite surprised if you ever passed the 100-character level.
My suggested parameters for this experiment are as follows:
Population Size:
Anything maximum population size that you think your computer can
easily handle - perhaps a steady state of 100
individuals/genomes/sequences?
Types of Sequence Characters:
All 26-letters of the English alphabet plus whatever punctuation marks
you wish to include, such as a space, period, comma, etc . . .
Reproduction Rate:
I think it would be good if we at least tried to make this one at
least somewhat realistic. For example, lets limit the average
reproduction rate per individual in our population to less than 100
offspring per generation. Fair enough? For example, this means that
a population of 100 different genomes will not collectively produce
more than 10,000 different genomes/offspring in each generation on
average.
Selection:
Any sequence or any portion of a sequence (made up of single or
multiple words) that is meaningful according to standard rules of
English usage and grammar may be selected as advantageous relative to
its peers. Those sequences having a higher sequence score will be
rewarded accordingly by being allowed to produce an equivalently
greater number of offspring in the next generation, though the total
number of offspring will not exceed the above stated limit on average
over the course of the generations.
Sequence Value:
The sequence with the longest consecutive internal sequence that has
unified meaning will receive the highest scores. For example,
consider the sequence, "toy, tree, ear, glove, run". This sequence
does not have a unified meaning that is greater than the sum of all of
its internal parts. Since the longest part of this sequence that does
carry a complete unified meaning is only 5-characters in length, the
maximum selectability score of this sequence is only "5". On the
other hand, consider the sequence, "See the little boy play in the
dirt." This sequence does have a unified meaning that is provided by
all parts of the sequence working together. Therefore, this sequence
gets a selectability score of "36", which is far greater than the
score of "5" earned by the first sequence. However, if there were no
sequences with a score higher than "5" in the population, the first
sequence would still be the most selectable. But, just because it has
5 obviously meaningful words does not make it more selectable than an
apparently more random string that also has a complexity score of "5",
such as "wh okras irhoijtc tizmp". Although it seems like most of
this sequence has no meaning at all, there are several portions of it
that do have English-language meaning. Internal sequences like "ok"
and "as" and "tiz" and "ho" all have collective individual
English-language meaning. However, the longest internal meaningful
sequence is "okras". Since this is the longest internal sequence with
meaning, the sequence as a whole would also get a complexity score of
"5". Of course, as previously mentioned, the higher the score, the
more offspring will be produced by that sequence relative to its 100
peers in the population.
Types of Mutations:
Each type of the following listed mutations can be given whatever
weight value of occurrence you want - although in real life point
mutations are far more common than certain other types of mutations,
such as recombination mutations. But, that doesn't really make much
of a difference for the purpose of this experiment.
Point mutations - A single character change in one position of a
character sequence.
Deletion mutations - The loss of one or more character positions
from an individual genome. The number of characters lost must be
random per deletion mutation..
Insertion mutations - The random insertion of one or more random
characters at a random position within an individual genome. The
number of characters inserted must also be random per insertion
mutation.
Recombination mutations - Any sequence may randomly recombine at a
random location within its own genome with any other sequence,
randomly chosen, at a random site within that genome. The
recombination must be balanced between the two recombining sequences
and may destroy the meaning of a previously meaningful word or phrase
in the genomes of one or both of the involved genomes.
Cut and paste mutations - A random portion of any genome (not
limited to intact words or meaningful sequences), chosen at random, my
be cut out and pasted into another genome, chosen at random, in a
random location (not limited to certain ideal locations at the
beginning or ends of intact words or phrases). In other words, the
cut and paste mutation could destroy the meaning of a previously
meaningful word or phrase in the genomes of one or both of the
involved genomes.
NOTE - pay special attention to the definitions of recombination and
cut and paste mutations listed here since you did not program you
computer to work like this. Instead, you programmed your computer to
always select fully intact meaningful sequences (or "words" in your
case) to insert into other words at various places. Although this can
happen in real life, real life mutations do not have to work like this
and in fact usually do not work like this. Allowing for partial
recombination and copying of sequence of origin greatly increases the
average time required to achieve a meaningful mutation event.
Mutation Rate:
As long as the other rules listed here are followed, the average
mutation rate per individual genome length can be pretty much anything
you want it to be. Remember though that if the mutation rate gets too
high, it will end up destroying higher levels of meaningful complexity
faster than they can be built and your population as a whole will head
downhill in complexity. Also note that the mutation rate is an
_average_ rate per given length of a genome. This means that it is
indeed possible for a higher number of mutations to affect a given
region of a genome in a given offspring in a given generation.
Starting Point:
Start with the above-determined number of individual genomes (lets say
100 for now, but it can be whatever you want) in your steady state
population. They can all be the same exact sequence or they can each
be very different sequences. Just for kicks, lets say that they must
all be worth less than 3 selectability points to start out with. They
can be short or long to start with, it really doesn't matter. A given
sequence may even be made up of a long stretch of just one letter
repeated over and over again. For example, the sequence,
"AAAAAAAAAAAAA" would be accepted as valid and would have a
selectability score of 1 point since the longest meaningful internal
sequence in this hypothetical genome is the English word, "A".
Generations Required to Reach each Level of Complexity:
Keep track of the number of generations it takes your population as a
whole to reach each level of complexity as defined above.
Winning the Game:
You will win the game if and when your population evolves a meaningful
English language sequence in any one of its individual genomes that is
worth just 1,000 selectability points as defined above. Coming short
of this level, I will reward you with major brownie points for
achieving the level of just 100 selectability points and even raise an
eyebrow if you reach 50 selectability points.
Good luck to you! May all the forces of evolution and mindless
creativity be with you!
Zachriel
"Sean Pitman" <seanpi...@naturalselection.0catch.com> wrote in message
news:80d0c26f.04050...@posting.google.com...
news:<HamdndTfVL0...@adelphia.com>...
>
> > Just as when Sean suggested (insisted) I include every single possible
> > recombination, what started as a problem became one of the driving
forces of
> > the Mutagenation Engine. Including a small chance of multiple mutations
has
> > the possibility of speeding up the evolution dramatically, and also
allowing
> > the creation of heretofore impossible mutants. This may be crucial if we
> > proceed with the Phrasenator Project.
> >
> > Thanks Sean!
>
> You're most welcome Zach, and good luck with your "Phrasenator
> Project"!
>
> If programmed as I have suggested, I predict that an evolutionary
> scenario based on true random mutation and meaning/function based
> non-intelligent selection will rapidly come to walls beyond which
> meaningful evolution simply will not occur this side of a practical
> eternity of time. Specifically, so as you don't get confused this
> time, I predict that the wall beyond which no meaningful evolution
> occurs will be found well before the 1,000-character level is reached.
> This level is well short of the bold "5,000-character" assertion
> listed on your website as well as your "O Sean Pitman" poem.
It you read the website, I placed an upper-bound of about 10^11 (100
billion) mutations per generation for a 5000 character string.
Unfortunately, my computer can't handle that computation in a reasonable
time. Why would you expect it could? However, that number is well within
range of biology which regularly deals in such large numbers. There are
about 10^14 microbes in the average human gut. There are about 10^9 humans,
and each microbe as about 10^3 or so bases, for a total of 10^25
gut-bug-bases.
To test my calcuations (already done), you can either count the numbers of
mutations (already done), or build a simulator which tests them (already
done). The number of available mutations per generation is easy to calculate
for a combined string (all unique string species in consideration) of length
L (already done), where S is the number of symbols in the language.
point mutations
L*S
point deletions
L
point insertions
(L+2)*S
snippets
(L+1)*L/2
remainders
(L+1)*L/2
insertions
snippets*(L+1)=(L+1)^2*L/2
For large L, only the last number is significant. So we can make a
reasonable determination of the (upper-bound) number of available mutations
and insertions by taking L^3.
> In fact,
> I'd be quite surprised if you ever passed the 100-character level.
100^3 is a million per generation.
> My suggested parameters for this experiment are as follows:
>
<snip>
Thank you for your suggestions.
> NOTE - pay special attention to the definitions of recombination and
> cut and paste mutations listed here since you did not program you
> computer to work like this. Instead, you programmed your computer to
> always select fully intact meaningful sequences (or "words" in your
> case) to insert into other words at various places. Although this can
> happen in real life, real life mutations do not have to work like this
> and in fact usually do not work like this.
This is incorrect. The code does not select meaningful snips. Rather it
tries every possible snip then inserts it into every possible point in every
word (Word MutatorWord Mutator); or tries a random snip (Word Mutagenator),
then inserts it into a random point in a random string (Word Mutagenator).
It only displays the surviving strings, so it often looks like it has
purposefully selected "chow" to recombine as "chowchow". It does not.
The appearance of purposefulness strongly resembles biological evolution in
this respect. Isn't that interesting.
> Allowing for partial
> recombination and copying of sequence of origin greatly increases the
> average time required to achieve a meaningful mutation event.
>
<snip more ideas>
Actually your ideas are pretty good. You ought to build a program. For the
Phrasenator, however, I don't want long strings of nonsense with some
meaningful expression buried within. Rather, I want complete phrases,
spelled correctly. The grammar might be a bit wooden, though, due to the
limitations of computer algorithms in this regard.
Zachriel
"Sean Pitman" <seanpi...@naturalselection.0catch.com> wrote in message
news:80d0c26f.04050...@posting.google.com...
news:<4uednQu8fq9...@adelphia.com>...
>
> > > Notice, Zach, that I used the pleural form "words" to indicate
> > > multiple words in what you call a "war of words."
> >
> > Sigh. I've generated multiple words. The Word Mutator deals in
populations
> > of dozens or hundreds of word species.
>
> I'm not talking about multiple single words, but about sequences of a
> given length using one or more words for a combined meaningful
> sequence.
That's was not your claim. You claimed we had to cross oceans of meaningless
strings to find the few meaningful strings which are scattered randomly in
that ocean. You have modified your claim that "all that I am left with to
get across this ocean of meaningless words is
a blind 'random walk'. "
I am satisfied that you have abandoned that claim. We know that it is not a
random distribution.
> This is exactly what you were trying to do when you started
> this very thread with the title of your poem "O Sean Pitman". My
> argument was and is that such a meaningful sequence, in fact no
> meaningful sequence of any kind of such a length an interdependence
> within the English language system, can be evolved using random
> mutation and non-intelligent function-based selection.
So you think it possible for intelligent selection of random mutations to
cause the evolution of species. Good. That was one of Darwin's main pieces
of evidence. Selecting for length is just as arbitrary as any other type of
selection, yet that was the selection criteria you chose. We could just as
easily select words for their Scrabble score.
Bill Gates walks into a bar. The mean average wealth shoots up to a billion
per person. This mean average is extremely misleading because it doesn't
tell us anything about the distribution of that wealth.
> My purpose in pointing these numbers out was to show the contrast
> between the average distance at this level as compared to lower
> levels, such as 2-, 3-, and 7-letter words. I was trying to show the
> exponential expansion in average distance as one moves up the ladder
> of complexity. My purpose was NOT to propose the drawing of an
> uncrossable line at the level of 14-characters. Not at all. My
> purpose was ONLY to show the progression of the average gap and how
> the islands and interconnections between meaningful islands decreased
> in an exponential manner with each step up the ladder of complexity.
> And, this is exactly what happens.
>
> Notice, if you will, that the 14-letter islands of meaningful words
> are much smaller than they are at the 3-letter level and their
> interconnections are much more rare. Consider the ratio and the time
> involved for your computer to evolve 3-letter words. I bet it was
> able to evolve all or nearly all 3-letter words in just "seconds".
> However, how many 14-letter words was it able to evolve, without your
> outside "direction" as a "breeder", in the same amount of time? What
> ratio of 14-letter words did your computer evolve vs. the ratio of
> 3-letter words or 7-letter words that it evolved - in the same amount
> of time?
Never said they did. I said they didn't vary according to the Pitman Number.
More complex genomes take longer to evolve. In biology, it's the difference
between millions of years and "zillions" of years.
> On your website you make mention that your program was able to evolve
> one third of all the words in the dictionary that you used.
That's just when I stopped the program.
> Tell me
> though, what _ratio_ of words were evolved at each of the levels of
> complexity listed in your dictionary? I don't really care about what
> scrabble score they might have. I only care about their total sequence
> length. If the program found all meaningful 3-letter words, that
> would be a ratio of 1:1 for the 3-letter level. What was the ratio
> for the 6-letter level? The 10-letter level? etc? In other words,
> you say that there are 1,643 words listed in your dictionary at the
> level of 14-characters. What ratio of these 14-letter words did your
> program evolve in given amount of time relative to the ratio of the
> lower levels?
Trying to evolve every word is very inefficient. To evolve long words, you
need mutation and *selection*.
> Why does this matter? It matters because if the ratio is
> significantly lower for each step up the ladder of complexity, it
> shows that the islands of meaningful sequences are not nicely lined up
> at all, but are indeed becoming more and more widely separated from
> each other, on average, in the exponentially expanding vastness of the
> potential sequence space at each higher level of complexity.
No, it shows that it takes a heck of a lot of time to evolve anything
without some selection mechanism.
> For example, say that 1,000 of the 1,643 possible 14-letter words in
> the dictionary were all clustered together in a nice little bunch in
> one tiny area of 14-letter sequence space. Would your demonstration
> that evolution between these closely spaced 1,000 sequences is very
> rapid disprove my assertion that the average time required must still
> take into account the other 643 sequences? What if these 643
> sequences form another closely packed island far far away from the
> other island of 1,000 sequences? Now, evolution within each island
> will be rapid, but what about getting from the one island to the other
> island? This must also be factored into the "average time" equation.
Sure, and the average wealth in the bar is a billion bucks. You're missing
the point. Some words probably can't be evolved. I never saw "Zachriel" pop
out even though I selected for Scrabble score and set "Zachriel" to 99.
That's because there are probably few words similar to "Zachriel" in our
Dictionary.
"The biological Theory of Evolution does not claim that every imaginable
creature can be evolved, and certainly not that every imaginable creature
must evolve and co-exist. Rather, like our game, evolution is opportunistic;
and though every conceivable creature may not be evolvable, the diversity of
life on Earth clearly indicates that the range of evolvable organic forms is
vast."
A Pond of Doggerel
http://www.zachriel.com/mutagenation/Doggerel.asp
> Basically, it comes down to the odds that each of the islands of
> beneficial sequences will have a connecting bridge or bridges to
> islands within the same level of complexity as well as to islands
> within lower and higher levels of complexity. At relatively low
> levels of complexity, these bridges are quite common and can be found
> fairly quickly - depending upon the size of the population and its
> mutation rate of course.
Funny that I've found bridges all the way out to "denominationalists" at
length 18. It turns out there is a limit to the length of word we can
evolve. The longest word in our Dictionary is "antiparliamentarianisms" at
length 23. Of course, I haven't run the Word Mutagenator for a "zillion
years", or even a single year.
> Another thing is, outside help by intelligent design is not allowed in
> these experiments Zach. You have foresight that evolutionary
> processes do not have.
The selection criteria (length) was arbitrarily selected by yourself. It
could just as well been animal-words, or z-words, short words, words with
double-letters, Scrabble score, whatever.
> Natural selection, as a purely _mindless_
> process, can only select based on what works right now. A mindless
> function based selector cannot select to keep a sequence simply
> because it may work in combination with something else sometime in the
> future.
That's correct. When Word Mutagenator selects for length, it doesn't know if
these particular words will lead to longer words, or whether they are
deadends. Funny how it worked out.
> Only an intelligence that has insight and the ability to
> predict the future, like you have, can do this sort of selecting.
Funny how Word Mutagenator always seems to find words that lead to longer
words that lead to longer words.
> So
> please, you cannot be helping your computer out here. You must let it
> select based on meaning that is current. It cannot select short
> meaningful sequences over other short meaningful sequences based on
> the chance that a future recombination event would produce something
> meaningful in certain short sequences - as you have done in your
> "poem" evolution scenarios.
If I build a Phrasenator, I will be certain to not let the computer peek
ahead. That's way too much work to program. It will work just like the Word
Mutagenator, which selects the longest words without regard to their ability
to "bridge" to even longer words. Only we will use the rules of grammar for
selection.
Um, according to your own figures, for the human genome there are an average
of 200 mutations per generation. There are about a half billion bases in the
human genome. So for any string of 1000, there is much less than one
mutation per generation. Double mutations would be exceedingly rare. I'll
probably include multi-mutations anyway--just for fun.
> Say, for example, that we had a 10^24 individual sequences/genomes in
> our population - each of them with a different 1,000 character
> sequence and an _average_ mutation rate of one mutation per individual
> per generation. How many new 1,000-character sequences would this
> population come across, on average, in one generation? Obviously, the
> answer is 10^24, which is far greater than a billion.
Sorry, that's wrong. If there are only 1000 characters, most of those
mutations would not be unique.
> You see, in my scenario, not all characters in a 1,000-character
> sequence need to be "meaningful" in order for that sequence to be
> selected as more "meaningful" than another 1,000 character sequence.
> In my scenario, selection is based on the greatest sequential length
> of the longest meaningful stretch of characters contained within the
> larger 1,000-character sequence. This allows for neutral evolution to
> occur as well as meaningful to meaningful evolution. Those
> meaningless portions of the 1,000-character sequence can still mutate
> and happen to come across a meaningful sequence by random walk. It is
> just that some part of the 1,000-character sequence must be selectable
> via function-based selection over other 1,000-character sequences in
> each generation.
Well, that would make an interesting program actually.
> Of course, since 1,000 character sequences require a great deal of
> computer processing power, you might have to use a smaller population
> or a smaller genome cap length (such as 100 character sequences) if
> you use a larger steady state population. You could also use a higher
> mutation rate or reproductive rate, but then you would also have a
> higher death rate per generation. But, a higher reproductive rate and
> death rate would be required in order to keep a higher mutation rate
> from destroying your "good" mutations faster than they can be
> maintained by the selection process of each generation.
>
> > > Come on now Zach, in your war of words are you can't be seriously
> > > accusing me of ever thinking to draw the line at short one-word-only
> > > sequences? - Can you?!
> >
> > Yes. You did. "the potential space of a 14-letter word or phrase is over
> > 109,418,989,131,512,359,209 (over 100 million trillion)." What did you
mean
> > by that?
>
> I meant just that. The potential space of a 14-letter word or phrase
> is indeed over 100 million trillion potential sequences in size. I
> mentioned this as a means of comparison to the sequence space of
> smaller and larger sequence sizes to show the exponential nature of
> the expansion as one moves up the ladder of complexity. I did not say
> this to indicate that this was the level at which all evolution for
> all colonies and all starting points must end.
We should drop this, but you were quite specific about how to use the Pitman
Number(7) to determine how many mutations it requires to evolve new words.
"With a population of 1, this random walk will take, on average, over
300,000 mutations to arrive at a new meaningful word at the level of
7-letters."
This assertion is incorrect. It takes an average of much less than 300,000
mutations. Give me a 7-letter word, and I'll tell you how many mutations it
takes to evolve some other 7-letter word. Just for fun, we know that
"Zachriel" has never evolved in the Word Mutagenator. Let's try plugging it
in and see what happens.
"Zachriel"
Pond Size = 25
4 Generations
"chitchat" at 8
"mahatma" at 7
58751 mutations
Pitman Number(8) = 16 million
Plug some numbers into the Word Mutator and let it rip. You won't find any
starting word that requires a Pitman Number to do anything. Sterile string
do exist. Can you find any? Are there any sterile words?
> This thought never
> even crossed my mind and that can be clearly seen from all that I have
> written in this forum and on my website well before you came on the
> scene. In fact, I _specifically_ drew my line of practical
> impossibility over and over again at the level of at least several
> _hundred_ to a couple _thousand_ fairly specified characters
> sequences. Why don't you reference these statements on your website?
> Hmmmm? I think it is because you are trying to make your case
> stronger than it really is - and you know it. You just cannot accept
> the fact that you may actually be off base here. You can't even seem
> to consider that possibility - can you?
Oh please. This specific statement is unsupported by the evidence:
"With a population of 1, this random walk will take, on average, over
300,000 mutations to arrive at a new meaningful word at the level of
7-letters."
This assertion is incorrect. Let's move on.
> > > You are really reaching for straws Zach. It
> > > really does seem very desperate of you, really it does, to accuse me
> > > of "moving goal posts" here when I clearly said over and over again
> > > that my limits were dependent upon population and genome size as well
> > > as mutation rate and nowhere did I ever say that sequence lengths as
> > > short as one or two dozen where "the limit". In fact, over and over
> > > again I clearly drew the limit for genetic evolution at a couple of
> > > thousand amino acids working together at the same time. I am truly at
> > > a loss to see how you could have read what I actually wrote and assume
> > > that my "goalposts" were at the level of 7- to 14-characters in size -
> > > especially considering the enormous reproduction rates and mutation
> > > rates that you used in your computer simulation!
> >
> > On my 250MHz P4, Word Mutator only does about 40,000 mutants per second,
> > while the latest (just uploaded!) version of Word Mutagenator does about
> > 25,000 mutants per second, hardly a huge number when we have to
supposedly
> > explore a space of 100 million trillion. Yet, we have explored that
space
> > sufficiently to find 14-letter and longer words.
>
> Again, this has nothing to do with my predictions. I never that with
> such a mutation rate that you could not evolve a 14-letter word.
You said it would require an average of the Pitman Number(14), which for our
dictionary is 10^16. This is incorrect.
> You
> even acknowledge that fact yourself. You have said yourself that you
> know that I never specifically drew the line at 14-characters
> sequences. This acknowledgement, combined with the fact that I did
> _specifically_ draw the line at a couple thousand characters in many
> different places should tell you something.
Well, it depends on what a "zillion" is. However, it would take the Word
Mutator thousands of years to churn through a Pitman Number(14) number of
mutations. It doesn't take that long to find 14-letter words. Take a
14-letter word and plug it in. Try it. (Better set it to a decent Pond Size.
You can't grow mice in a petri dish.)
"absentmindedly", length 14
Pond Size = 100
5 Generations
"interdependent", length 14
6657484 mutations
Pitman Number(8) = 10,000,000,000,000,000
My 2500MHz P4 took about 5 minutes, which is somewhat less than thousands of
years. The advantage of the Word Mutator (over the Word Mutagenator) is that
you can exactly replicate the results.
> > With a reasonable algorithm for recognizing valid phrases, a Phrasenator
> > could easily handle dozens of phrases of reasonable length.
>
> No it couldn't _if_ by "reasonable" you mean greater than 500 or so
> characters in length. To be honest though, I don't think you can even
> reach the 100-character level, and probably not even the 50-character
> level (based on a steady state population of less than 10,000
> individuals/genomes with a high average mutation rate and high
> reproductive rate and death rate).
>
> > > You yourself recognized the fact that I never drew the line at such
> > > low levels, so how can you possibly say that I've moved my goalposts?
> > > They have only been moved relative to your misstatements about my
> > > position. The real goalposts have not been moved at all. They are
> > > right where I put them well over a year ago now and have remained
> > > there, not even remotely challenged by anyone to include you, to this
> > > day.
> > >
> > > And, if you are really honest about this whole thing, you will reflect
> > > my real position on your website - but I am not holding my breath on
> > > that one. You seem too attached to your strawman version of reality.
> >
> > I have linked to your website, and to many of your posts, including this
> > thread. You have ample opportunity for rebuttal.
>
> Yes, at least you link in a very general way to my threads in this
> forum. What is interesting to me though is that what you have written
> directly on your website is completely counter to my actual position.
Everyone has read my posts, and everyone has read your rebuttals. But if you
want to write a short rebuttal, I would be happy to link it on my website,
or link to a rebuttal posted on your website.
"this random walk will take, on average, over Pitman Number(L) mutations to
arrive at a new meaningful word at the level of L-letters."
> You used my descriptions and attempts to illustrate an expanding
> sequence space and average intra-word distances to say that I actually
> draw my line of "impossibility" at very low levels of sequence
> complexity - such as 7- or 14- character sequences. This is at best a
> dramatic overstatement and at worst an deliberate mischaracterization
> of my actual position. Either way, it is a strawman version of the
> real thing, and you really should have been able to pick up on that
> from even a superficial reading of my previous threads and what is
> presented on my own website.
Everyone has read my posts, and everyone has read your rebuttal. But if you
want to write a short rebuttal, I would be happy to link it on my website,
or link to a rebuttal posted on your website.
"What this means is that on average each meaningful 7-letter word is
surrounded like an island by well over 300,000 meaningless words. If I want
to evolve a new 7-letter word starting with meaningful 7-letter word, I will
have to swim through this ocean of meaningless words"
> Your evolutionary scenarios of long sequence evolution, such as your
> "O Sean Pitman" poem, are based on nothing but intelligent
> manipulation of short sequences that no computer could ever do this
> side of a practical eternity of time without the input of intelligent
> guidance. You seem to recognize this because you insert the needed
> guidance all the time and call it "selective breeding".
Selective breeding was one of Darwin's main pieces of evidence.
> You also talk about the evolution of HIV resistance as something
> spectacular when it involves nothing more than a very few (i.e., one
> or two) point mutations to cause a block or interference with a
> pre-established interaction. This sort of evolution is at the very
> lowest levels of functional evolution. Nothing new is created beyond
> the interference of a pre-established function or interaction.
It created an epidemic.
Bill Rogers
I completely agree that this is not how evolution works, but according
to your model, real evolution should be easier, not harder, than this.
A sonnet has about 1000 characters, so, by your calculations, to come
upon a particular sonnet, the program would have to search a space of
26^1000 sequence strings. Now your claim has always been that vast
oceans of meaningless sequences separate any meaningful strings.
Surely vast oceans of meaninglessness separate the single character
string, "O", from any chosen Shakespearean sonnet. Surely the set of
shakespearean sonnets is a tiny, tiny subset of the set of 1000
character strings meaningful in English. If crossing the vast oceans
of meaningless strings is a "wall" to evolution of complexity, surely
it will be even harder if the only archipelago possible is composed of
fragments of meaning from a Shakespearean sonnet, as opposed to all
possible meaningful English strings.
Your argument is based on the difficulty of searching sequence space,
not on the nature of the selection acting on the very rare beneficial
mutations that crop up once in a while. Using "homology to 'Shall I
compare thee to a summer's day'" as the selection criterion is no more
'unnatural' than devising a complex algorithm to detect grammatical
meaning. And if the problem for evolution is the number of
non-beneficial mutants that must be weeded through to arrive at
anything meaningful I honestly cannot see why you object to "Methinks
it is like a weasel," or any other chosen phrase. Indeed, with that
challenge there is vastly more "ocean" than in you original challenge.
It should be harder, not easier, if you are correct that crossing vast
neutral gaps is the key problem for evolution.
Andrew Arensburger
> Selection:
> Any sequence or any portion of a sequence (made up of single or
> multiple words) that is meaningful according to standard rules of
> English usage and grammar may be selected as advantageous relative to
> its peers.
This seems hopelessly vague to me. How can a computer program
tell whether a sequence of words is "meaningful according to standard
rules of English usage"?
If you had a table that said which words are verbs, which ones
are nouns, and so forth, then you could define a grammar that roughly
approximates that used in English. This would tell us that "John eats
wood" is grammatically correct, but that "John eat apple" isn't.
But how can the program tell whether a given sequence of words
is meaningful, as opposed to merely being grammatically correct? How
can it know that "John vacations at the beach" is meaningful, but that
"Horseshoe paints for an arena" isn't?
I think that if you could write a program that makes this
determination, you'd be well on your way to winning an award in AI. So
I suggest that you come up with a different criterion, one of equal or
greater difficulty, but such that a program can easily determine
whether the criterion has been met.
--
Andrew Arensburger, Systems guy University of Maryland
arensb.no-...@umd.edu Office of Information Technology
Good sex means being told, "Stop and I'll kill you!"
Zachriel
"Andrew Arensburger" <arensb.no-...@umd.edu> wrote in message
news:c78vdd$la8$1...@grapevine.wam.umd.edu...
> In talk.origins Sean Pitman <seanpi...@naturalselection.0catch.com>
wrote:
> > Selection:
> > Any sequence or any portion of a sequence (made up of single or
> > multiple words) that is meaningful according to standard rules of
> > English usage and grammar may be selected as advantageous relative to
> > its peers.
>
> This seems hopelessly vague to me. How can a computer program
> tell whether a sequence of words is "meaningful according to standard
> rules of English usage"?
> If you had a table that said which words are verbs, which ones
> are nouns, and so forth, then you could define a grammar that roughly
> approximates that used in English. This would tell us that "John eats
> wood" is grammatically correct, but that "John eat apple" isn't.
Poetic license? Here are a few turns of phrase from the master of phrase
turning. As literal statements, as on the first hearing by Shakespeare's
audience, they are, well, quite unusual. ;-)
Eaten out of house and home
The world's (my) oyster
To run upon the Sharp winde of the North.
we stand upon our guard
A laughing stock
Screw your courage to the sticking-place
I will wear my heart upon my sleeve
In a pickle
Friends, Romans, Countrymen, lend me your ears
In stiches
Love is blind
Tower of strength
Drown an eye
Sean Pitman
> > I'm not talking about multiple single words, but about sequences of a
> > given length using one or more words for a combined meaningful
> > sequence.
>
> That's was not your claim. You claimed we had to cross oceans of meaningless
> strings to find the few meaningful strings which are scattered randomly in
> that ocean. You have modified your claim that "all that I am left with to
> get across this ocean of meaningless words is
> a blind 'random walk'. "
>
> I am satisfied that you have abandoned that claim. We know that it is not a
> random distribution.
Although there certainly are "islands" or "clusters" of meaningful
sequences, which I have always recognized, these islands are indeed
fairly random in their location in sequence space and this randomness
becomes ever more pronounced and apparent as one moves up the ladder
of meaningful sequence complexity.
> > This is exactly what you were trying to do when you started
> > this very thread with the title of your poem "O Sean Pitman". My
> > argument was and is that such a meaningful sequence, in fact no
> > meaningful sequence of any kind of such a length an interdependence
> > within the English language system, can be evolved using random
> > mutation and non-intelligent function-based selection.
>
> So you think it possible for intelligent selection of random mutations to
> cause the evolution of species. Good. That was one of Darwin's main pieces
> of evidence. Selecting for length is just as arbitrary as any other type of
> selection, yet that was the selection criteria you chose. We could just as
> easily select words for their Scrabble score.
What you are trying to do by looking directly at the genotype is much
much different than what Darwin thought he was doing by looking only
at the phenotype. We know now that the variations Darwin observed
where all pretty much based on Mendelian variation - which is not the
evolution of anything really informationally new at all.
A phenotypic change in Mendelian expression does not add or take away
any information or novel potential from the gene pool of a particular
type of creature. Because of the way in which Mendelian genetics
works, you can breed all kinds of different looking cats, dogs, pigs,
cows, gerbils, horses etc., without requiring any new genetic
information or mutational "errors" at all. However, using Mendelian
genetics alone, you will never be able to get a cat to evolve into a
dog or a lizard into a bird, etc. For the sorts of changes that
purportedly go beyond the informational limits of a set gene pool,
additional information is needed. The only way to get this additional
information is either from an outside source of pre-established
genetic material or via random mutation and natural selection acting
on the genetic material already contained within the gene pool.
So you see, breeding that is phenotypically based, such as dog or
horse breeding, is not really "evolution" - in the sense that we are
talking about evolution as the arrival of new information and meaning
into a gene pool. Darwin didn't know this (since Darwin didn't know
about Mendel's work), but we know it now because we understand the
code behind the changes that Darwin observed as being primarily
Mendelian in nature. Therefore, this sort of breeding, though
intelligently directed, would not speed up the evolutionary process at
all beyond the other non-directed selection mechanisms already in
place in nature.
You, on the other hand, are trying to "manually" select genotypic
sequences based on your knowledge how various genotypic combinations
work together that are not yet present in the gene pool of options.
This is much different than selecting based on function alone with no
knowledge of the workings or meaning of the underlying coded symbols.
It would be like starting with a calculator program, which you see on
your computer monitor, and having the underlying code for this program
produce several offspring programs with underlying code mutations, and
you picking between the underlying codes based ONLY on the changes in
calculator function that you see on your screen. No understanding of
the arbitrary definitions of the underlying codes or observation of
the interaction of these coded character strings is allowed. Using
this process of phenotypic selection alone, how long do you think it
would take to evolve a brand new software function at an equal level
of complexity (like opening the CD player on command)?
Now, wouldn't this be a much harder evolutionary scenario compared to
one in which you get to see, understand, and manipulate a coded
sequence in a very direct manner based on an understanding of code
function combined with intelligent foresight?
> > The sequence space of 14-letter words is indeed over 100 million
> > trillion in size. The _average_ distance between each meaningful
> > 14-letter single word is also about 66 million billion non-defined
> > sequences.
>
> Bill Gates walks into a bar. The mean average wealth shoots up to a billion
> per person. This mean average is extremely misleading because it doesn't
> tell us anything about the distribution of that wealth.
Ah, but it does tell us something. It tells us that the distribution
is not perfectly clustered into just one little corner of sequence
space or nicely lined up in perfect little rows within sequence space
- now doesn't it? It tells us that the clusters that are present are
very irregular in size, shape, and even location within sequence
space. It also appears that these clusters get relatively smaller and
smaller and more and more widely distributed, in a rather random way,
throughout sequence space with each step up the ladder of minimum
meaningful complexity/size that involves the same degree of
specificity.
> > My purpose in pointing these numbers out was to show the contrast
> > between the average distance at this level as compared to lower
> > levels, such as 2-, 3-, and 7-letter words. I was trying to show the
> > exponential expansion in average distance as one moves up the ladder
> > of complexity. My purpose was NOT to propose the drawing of an
> > uncrossable line at the level of 14-characters. Not at all. My
> > purpose was ONLY to show the progression of the average gap and how
> > the islands and interconnections between meaningful islands decreased
> > in an exponential manner with each step up the ladder of complexity.
> > And, this is exactly what happens.
> >
> > Notice, if you will, that the 14-letter islands of meaningful words
> > are much smaller than they are at the 3-letter level and their
> > interconnections are much more rare. Consider the ratio and the time
> > involved for your computer to evolve 3-letter words. I bet it was
> > able to evolve all or nearly all 3-letter words in just "seconds".
> > However, how many 14-letter words was it able to evolve, without your
> > outside "direction" as a "breeder", in the same amount of time? What
> > ratio of 14-letter words did your computer evolve vs. the ratio of
> > 3-letter words or 7-letter words that it evolved - in the same amount
> > of time?
>
> Never said they did. I said they didn't vary according to the Pitman Number.
> More complex genomes take longer to evolve. In biology, it's the difference
> between millions of years and "zillions" of years.
You seem to fail to recognize the exponential decline in the rate of
evolution produced by your own experiment. The more complex genomes
don't just take longer to evolve; they take _exponentially_ longer to
evolve as compared to lower levels of complexity. The exponential
nature of this whole process quickly flies by the mark for "millions"
and even "billions" of years for very low levels of complexity and,
with just a few more steps, a gene pool suddenly finds itself needing
a minimum of trillions upon trillions upon trillions of years to do
much of anything.
> > On your website you make mention that your program was able to evolve
> > one third of all the words in the dictionary that you used.
>
> That's just when I stopped the program.
Yes . . . But I'm more interested in the ratio of sequences that
evolved within each level when you stopped to program. You don't seem
to mention that the average length of the sequences that you evolved
were, what? - 4 or 5 letters long? You see, the ratio rapidly dropped
off from low to high levels. Compared to all the meaningful words
listed in your dictionary, you probably evolved a higher ratio of 3-
vs. 7-letter words - right? And, you no doubtably evolved a higher
ratio of 7-letter words than 10- or 14-letter words - right? Also,
not only did the ratio drop off, but the time it took to reach each
higher level increased exponentially - right? Hmmmm . . . How many
levels do _you_ think it would take, in the light of this obvious
exponential increase in required time with each level, to surpass the
"million" or "billion" or "zillion" year mark?
> > Why does this matter? It matters because if the ratio is
> > significantly lower for each step up the ladder of complexity, it
> > shows that the islands of meaningful sequences are not nicely lined up
> > at all, but are indeed becoming more and more widely separated from
> > each other, on average, in the exponentially expanding vastness of the
> > potential sequence space at each higher level of complexity.
>
> No, it shows that it takes a heck of a lot of time to evolve anything
> without some selection mechanism.
Even with a function-based non-intelligent selection mechanism it
still takes exponentially more and more time to evolve at each higher
level of complexity.
> > For example, say that 1,000 of the 1,643 possible 14-letter words in
> > the dictionary were all clustered together in a nice little bunch in
> > one tiny area of 14-letter sequence space. Would your demonstration
> > that evolution between these closely spaced 1,000 sequences is very
> > rapid disprove my assertion that the average time required must still
> > take into account the other 643 sequences? What if these 643
> > sequences form another closely packed island far far away from the
> > other island of 1,000 sequences? Now, evolution within each island
> > will be rapid, but what about getting from the one island to the other
> > island? This must also be factored into the "average time" equation.
>
> Sure, and the average wealth in the bar is a billion bucks. You're missing
> the point. Some words probably can't be evolved. I never saw "Zachriel" pop
> out even though I selected for Scrabble score and set "Zachriel" to 99.
> That's because there are probably few words similar to "Zachriel" in our
> Dictionary.
Now think carefully here Zach. If some words "can't be evolved"
_because_ they aren't close enough to the starting cluster, what do
you think would happen if the clusters got smaller and smaller and
farther and farther apart? Wouldn't that result in relatively fewer
and fewer sequences that actually "could" be evolved without having to
cross significant neutral gaps of non-meaningful sequences? Well,
this is exactly what happens with each step up the ladder of
meaningful complexity. Even your experiment, as non-realistic as it
is, demonstrates this rather nicely.
> "The biological Theory of Evolution does not claim that every imaginable
> creature can be evolved, and certainly not that every imaginable creature
> must evolve and co-exist. Rather, like our game, evolution is opportunistic;
> and though every conceivable creature may not be evolvable, the diversity of
> life on Earth clearly indicates that the range of evolvable organic forms is
> vast."
What evolutionists claim is that there is no limit in the ability of
evolution to create higher and higher functional/meaningful complexity
via mindless processes of random mutation and natural selection. That
means, basically, that each meaningful sequence in one level of
complexity is not very far away from another meaningful sequence in
the next higher level of complexity and that this rule remains true as
one moves up from very low to extremely high levels of meaningful
complexity. The problem with this notion is that it simply makes no
logical sense and it is not observed in real time either.
Statistically, evolution should and in fact does in real life stall
out on relatively low rungs of the ladder of complexity. This means
that evolvable organic forms are not "vast" at all - relatively
speaking. In fact, much of what many people think of as a "vast"
array of different forms are nothing more than Mendelian variation of
a pretty static gene pool of allelic options with no significant gain
to these options (more likely a loss) over time.
> > Basically, it comes down to the odds that each of the islands of
> > beneficial sequences will have a connecting bridge or bridges to
> > islands within the same level of complexity as well as to islands
> > within lower and higher levels of complexity. At relatively low
> > levels of complexity, these bridges are quite common and can be found
> > fairly quickly - depending upon the size of the population and its
> > mutation rate of course.
>
> Funny that I've found bridges all the way out to "denominationalists" at
> length 18.
Funny that you found exponentially fewer and fewer bridges - isn't it?
> It turns out there is a limit to the length of word we can
> evolve. The longest word in our Dictionary is "antiparliamentarianisms" at
> length 23. Of course, I haven't run the Word Mutagenator for a "zillion
> years", or even a single year.
That is because you are limiting yourself to single word sequences.
But, there is no technical limit to the length of a meaningful
sequence you could evolve if you do not limit your selection criteria
to sequences made up only of single words.
> > Another thing is, outside help by intelligent design is not allowed in
> > these experiments Zach. You have foresight that evolutionary
> > processes do not have.
>
> The selection criteria (length) was arbitrarily selected by yourself. It
> could just as well been animal-words, or z-words, short words, words with
> double-letters, Scrabble score, whatever.
Whatever the criteria, intelligent input and foresight is not allowed
as a basis for selecting one genotype over another (for previously
detailed reasons).
The reason I selected increasing length and English language meaning
as selection criteria, is because it is my position that with
increasing minimum length requirements for a meaningful English
sequence (at a given level of specificity) comes an exponentially
expanding ocean of non-functional, non-beneficial sequences. This
ocean of "non-beneficence" pushes the relatively small islands farther
and farther apart, stretching and straining the bridges that connect
these islands until they break from each other completely in their
headlong rush toward hopeless isolation and the rapid death of
evolutionary progress.
> > Natural selection, as a purely _mindless_
> > process, can only select based on what works right now. A mindless
> > function-based selector cannot select to keep a sequence simply
> > because it may work in combination with something else sometime in the
> > future.
>
> That's correct. When Word Mutagenator selects for length, it doesn't know if
> these particular words will lead to longer words, or whether they are
> deadends. Funny how it worked out.
Funny how it showed good evidence of stalling out. And, funny how you
felt the need to do some "manual" selection yourself to get some of
your more "creative" evolutionary scenarios to "work".
> > Only an intelligence that has insight and the ability to
> > predict the future, like you have, can do this sort of selecting.
>
> Funny how Word Mutagenator always seems to find words that lead to longer
> words that lead to longer words.
Again, this is only to be expected considering the relatively low
level of meaningful complexity that your "Mutagenator" is working on
with the use of a very high reproductive rate and mutation rate. Keep
going though. Without intelligent input, your computer will not be
able to evolve very much farther (predicted limits previously detailed
according to my own stated parameters of how the program should work).
> > So
> > please, you cannot be helping your computer out here. You must let it
> > select based on meaning that is current. It cannot select short
> > meaningful sequences over other short meaningful sequences based on
> > the chance that a future recombination event would produce something
> > meaningful in certain short sequences - as you have done in your
> > "poem" evolution scenarios.
>
> If I build a Phrasenator, I will be certain to not let the computer peek
> ahead. That's way too much work to program. It will work just like the Word
> Mutagenator, which selects the longest words without regard to their ability
> to "bridge" to even longer words. Only we will use the rules of grammar for
> selection.
Well then, without intelligent input and with a reasonable steady
state population, reproduction rate, mutation rate, death rate,
mutation types, etc, as I have previously detailed, your "Phrasenator"
will stall well short of my predictions.
Remember though, your computer cannot analyze more potential sequences
in a given generation than the rate of reproduction and mutation rate
allows. For example, your current computer program analyses every
possible mutation for a given generation from the perspective of each
individual in your population, which quickly runs into the thousands
at higher levels. With a limited reproduction rate of say, 100
offspring per individual, your computer is only allowed to produce and
analyze 100 new sequences per individual in your population regardless
of the potential sequences that could be had in that generation. Each
offspring sequence produced is mutated and batched with the other
offspring before the selection process. Then, of the 100 new
offspring sequences, the top scoring sequence is selected.
> > Actually, the number of possible mutants, to include meaningful as
> > well as non-meaningful, for a 1,000-character sequence is the number
> > of individuals in a population times the average mutation rate per
> > individual, per generation. Given the potential sequence space for a
> > 1,000-character sequence, this could be way over a "billion".
>
> Um, according to your own figures, for the human genome there are an average
> of 200 mutations per generation. There are about a half billion bases in the
> human genome.
As an aside, you are just slightly off here. There are actually over 6
billion base pairs (diploid) in the human genome.
> So for any string of 1000, there is much less than one
> mutation per generation.
That's true. So you see, even your use of an average of just 1
mutation per generation for such a short string of 1,000 characters is
an extremely high mutation rate when compared to what happens in real
life. In fact, in real life, such a high mutation rate would be
lethal, wiping out far more useful information than it created (given
the limits of reproductive rates even in bacteria).
> Double mutations would be exceedingly rare.
Like I said before, I would agree with you when you argued this point.
Although, "exceedingly rare" is not the same thing as impossible.
However, "exceedingly rare" does translate into a significant increase
in the average time involved. Starting to see my point?
> I'll
> probably include multi-mutations anyway--just for fun.
What you really need to do is include the _potential_ for multiple
mutations, although the _average_ rate can still be set to a
reasonable level so as you don't destroy faster than you create and
turn your population into homogenous mush - just like in real life.
> > Say, for example, that we had a 10^24 individual sequences/genomes in
> > our population - each of them with a different 1,000 character
> > sequence and an _average_ mutation rate of one mutation per individual
> > per generation. How many new 1,000-character sequences would this
> > population come across, on average, in one generation? Obviously, the
> > answer is 10^24, which is far greater than a billion.
>
> Sorry, that's wrong. If there are only 1000 characters, most of those
> mutations would not be unique.
It certainly doesn't seem to be as wrong as your limit of just a
"billion" new sequences per generation calculation regardless of
population size. Why don't we just think this thing through again
Zach?
Starting with 10^24 different, fairly evenly spaced, 1,000-character
sequences in our steady state population, each mutating with an
average rate of one mutation per generation, the average generation
would produce 10^24 unique sequences compared to the population of
10^24 sequences in the generation that came before. This is because
the odds than any one unique individual line in our population of
10^24 would cross any other line within that population is 10^24 /
26^1000 or about 1 in 10^1390 generations. Even if you started with
the same sequence in all 10^24 individuals, a mutation rate of 1
mutation per genome per generation would cause a rapid neutral drift
divergence of all the sequences so that very rapidly you would reach
the "10^24 new sequences per generation" mark with your population.
Again, this is far greater than a billion is it not?
Think of it as 10^24 checker pieces on a huge checkerboard (~10^1414
squares in size) where each square on the checkerboard represents a
novel sequence in sequence space. If all the checkers stared out on
very widely spaces squares, how often would they end up on the same
square if each of them moved, on average, one square per round?
> > You see, in my scenario, not all characters in a 1,000-character
> > sequence need to be "meaningful" in order for that sequence to be
> > selected as more "meaningful" than another 1,000 character sequence.
> > In my scenario, selection is based on the greatest sequential length
> > of the longest meaningful stretch of characters contained within the
> > larger 1,000-character sequence. This allows for neutral evolution to
> > occur as well as meaningful to meaningful evolution. Those
> > meaningless portions of the 1,000-character sequence can still mutate
> > and happen to come across a meaningful sequence by random walk. It is
> > just that some part of the 1,000-character sequence must be selectable
> > via function-based selection over other 1,000-character sequences in
> > each generation.
>
> Well, that would make an interesting program actually.
Yes, it would since it would mirror real life evolutionary potential
much more closely than your computer program currently does.
> > Of course, since 1,000 character sequences require a great deal of
> > computer processing power, you might have to use a smaller population
> > or a smaller genome cap length (such as 100 character sequences) if
> > you use a larger steady state population. You could also use a higher
> > mutation rate or reproductive rate, but then you would also have a
> > higher death rate per generation. But, a higher reproductive rate and
> > death rate would be required in order to keep a higher mutation rate
> > from destroying your "good" mutations faster than they can be
> > maintained by the selection process of each generation.
> >
> > > > Come on now Zach, in your war of words are you can't be seriously
> > > > accusing me of ever thinking to draw the line at short one-word-only
> > > > sequences? - Can you?!
> > >
> > > Yes. You did. "the potential space of a 14-letter word or phrase is over
> > > 109,418,989,131,512,359,209 (over 100 million trillion)." What did you
> > > mean by that?
> >
> > I meant just that. The potential space of a 14-letter word or phrase
> > is indeed over 100 million trillion potential sequences in size. I
> > mentioned this as a means of comparison to the sequence space of
> > smaller and larger sequence sizes to show the exponential nature of
> > the expansion as one moves up the ladder of complexity. I did not say
> > this to indicate that this was the level at which all evolution for
> > all colonies and all starting points must end.
>
> We should drop this, but you were quite specific about how to use the Pitman
> Number(7) to determine how many mutations it requires to evolve new words.
Again, just like with your "Trump walks into a bar" situation, I was
talking about averages, not absolute lines of impossibility or the
lack of all bridges. This position of mine should have been very
clear to you from all that I had already written on this topic before
you came along.
> > Your evolutionary scenarios of long sequence evolution, such as your
> > "O Sean Pitman" poem, are based on nothing but intelligent
> > manipulation of short sequences that no computer could ever do this
> > side of a practical eternity of time without the input of intelligent
> > guidance. You seem to recognize this because you insert the needed
> > guidance all the time and call it "selective breeding".
>
> Selective breeding was one of Darwin's main pieces of evidence.
See above for discussion of "selective breeding" and Darwin's mistaken
use of it as "evolution in action" when it was nothing more than
Mendelian variation.
> > You also talk about the evolution of HIV resistance as something
> > spectacular when it involves nothing more than a very few (i.e., one
> > or two) point mutations to cause a block or interference with a
> > pre-established interaction. This sort of evolution is at the very
> > lowest levels of functional evolution. Nothing new is created beyond
> > the interference of a pre-established function or interaction.
>
> It created an epidemic.
Like antibiotic resistance, some very low levels of meaningful
evolution can and do significantly affect a lot of people and other
creatures. This does not mean evolution can create significantly
higher levels of functional complexity. It simply doesn't and it
can't.
See the following discussions for more detail about the such mutations
as those that cause HIV and antibiotic resistance:
http://naturalselection.0catch.com/Files/antibioticresistance.html
http://naturalselection.0catch.com/Files/steppingstones.html
> > Of
> > those evolutionary scenarios that actually do create novel
> > _independent_ functions, such as the evolution of certain enzymes like
> > lactase or nylonase, none of these examples goes beyond the level of a
> > few hundred fairly specified amino acids working together at the same
> > time. Considering that this level is extremely low relative to the
> > much higher levels that exist in every living thing, evolution is
> > obviously extremely limited in what it can do this side of a practical
> > eternity of time (i.e., zillions and gazillions of years of average
> > time).
> >
> > And you think you have done something by getting evolution to produce
> > a meaningful (not even considering "beneficial" vs. "non-beneficial")
> > sequence less than 20-characters in size?! Please . . . think again!
Bill Rogers
> "Andrew Arensburger" <arensb.no-...@umd.edu> wrote in message
> news:c78vdd$la8$1...@grapevine.wam.umd.edu...
> > In talk.origins Sean Pitman <seanpi...@naturalselection.0catch.com>
> wrote:
> > > Selection:
> > > Any sequence or any portion of a sequence (made up of single or
> > > multiple words) that is meaningful according to standard rules of
> > > English usage and grammar may be selected as advantageous relative to
> > > its peers.
> >
> > This seems hopelessly vague to me. How can a computer program
> > tell whether a sequence of words is "meaningful according to standard
> > rules of English usage"?
> > If you had a table that said which words are verbs, which ones
> > are nouns, and so forth, then you could define a grammar that roughly
> > approximates that used in English. This would tell us that "John eats
> > wood" is grammatically correct, but that "John eat apple" isn't.
> <snip>
>
> Poetic license? Here are a few turns of phrase from the master of phrase
> turning. As literal statements, as on the first hearing by Shakespeare's
> audience, they are, well, quite unusual. ;-)
I agree with Andrew. I think you should go for a simpler test of
meaningfulness. E.g., is the character string found in "The Decline
and Fall of the Roman Empire," say, or Shakespeare's sonnets? Sean may
gripe that "this is not how evolution works," but according to his
model these tasks should be much, much harder, not easier, than
evolving "any" meaningful English string. Shakespearean meaningful
strings are only a tiny, tiny (one in a zillion) subset of all
possible meaningful strings (which are, of course just one in a
zillion zillion of all possible strings), so if the barrier to
evolution is the vastness of the meaningless spaces between islands of
meaning, then it should be harder to evolve phrases or verse from
Shakespeare than to evolve any random meaningful phrase. That would
make your program doable I think. It should be possible to automate a
search of each mutant against a large text and provide a finess score
that depends on the length of the match.
I am afraid that Andrew is correct that trying to automate a routine
to determine whether a character string is meaningful in English is a
very hard problem in linguistics and AI. All you need is an automated
selection that does not "look ahead" to see whether something has
"potential" to evolve further, and asking whether a candidate
character string is found in some long literary text is as good a
selection as any. Sort of like trying to evolve a specific cytochrome
c, rather than anything that could work as one. This is an argument
about whether "seas of non-beneficialness" rapidly form a "wall" to
evolution of complexity. It would be too bad to get sidetracked into
AI modeling of grammar, interesting as that is.
Bill
Sean Pitman
> > Selection:
> > Any sequence or any portion of a sequence (made up of single or
> > multiple words) that is meaningful according to standard rules of
> > English usage and grammar may be selected as advantageous relative to
> > its peers.
>
> This seems hopelessly vague to me. How can a computer program
> tell whether a sequence of words is "meaningful according to standard
> rules of English usage"?
Consider that I said "meaningful", not necessarily "beneficial". Now,
I realize that I am using the term "meaningful" rather loosely here.
So I will explain what I mean by "meaningful" in the current sense. I
will accept as "meaningful" any sequence that may be understood to
have English language meaning in some, although possibly a very
remote, context. In other words, one must be able to present some
scenario where, if a particular sequence were written or spoken, it
would be understood in English as having "beneficial" meaning.
> If you had a table that said which words are verbs, which ones
> are nouns, and so forth, then you could define a grammar that roughly
> approximates that used in English. This would tell us that "John eats
> wood" is grammatically correct, but that "John eat apple" isn't.
Actually, both phrases would probably be accepted as meaningful in
generally understood English in some context or another.
> But how can the program tell whether a given sequence of words
> is meaningful, as opposed to merely being grammatically correct? How
> can it know that "John vacations at the beach" is meaningful, but that
> "Horseshoe paints for an arena" isn't?
That would be very difficult I would think. That is why I haven't
based this test on the detection of what is "beneficial" given a
certain context, but have limited selection criteria only to what is
"meaningful" without regard to context.
Now why am I able to do this as part of my argument proposing a very
limited evolutionary potential? Consider that there are far more
"meaningful" (in the current sense) possibilities in English compared
to those that are both "meaningful" and "beneficial", with respect to
a _particular_ context. This means that if evolutionary scenarios
show significant low level limitations with regard to meaning alone
that the additional requirement of "beneficial meaning" would only
worsen the evolutionary outlook. Since selection based on meaning
alone shows an exponential decline in the ratio of meaningful vs.
non-meaningful in the English language system, the ratio of
"beneficial meaning" vs. "non-beneficial meaning" would only result in
a significantly increased exponential decline in evolutionary
potential.
> I think that if you could write a program that makes this
> determination, you'd be well on your way to winning an award in AI. So
> I suggest that you come up with a different criterion, one of equal or
> greater difficulty, but such that a program can easily determine
> whether the criterion has been met.
I think that it is possible to program a computer to recognize English
language meaning (in the present sense) if it does not have to also
recognize "beneficial meaning" with regard to a particular situation /
environment.
I can't really think of any other equivalent selection criteria that
would actually be helpful to resolving the discussion at hand.
However, if you can think of such an equivalent selection criterion,
please do let me know!
Andrew Arensburger
> Poetic license? Here are a few turns of phrase from the master of phrase
> turning. As literal statements, as on the first hearing by Shakespeare's
> audience, they are, well, quite unusual. ;-)
These just illustrate the difficulty of the problem. Phrases
like "lend me your ears" are grammatically correct (and a computer
might be able to recognize this).
We as humans notice, through some mechanism that is as yet not
well understood, that they literal meaning of "lend me your ears" is
absurd. This prompts us to look for some other, non-literal meaning,
and we manage--again, though some poorly-understood mechanism--to
translate this into "pay attention to me for a while."
I'm pretty sure that the unknown mechanisms above involve
natural language processing, which perforce requires an awful lot of
knowledge about the world (such as the fact that ears aren't
detachable, which computers generally don't know). In short, if you
manage to write a program that detects meaning as well as a human
would, then you're a stone's throw from writing one that can pass the
Turing test.
Obviously, you don't want to spend a lot of time doing that
just for the sake of answering Sean Pitman's challenge (and you
certainly don't want to do it in Visual Basic!). That's why I
suggested using some other, more easily verifiable criteria. Beyond
requiring that a sentence consist solely of English words, you could
require that it contain a prime number of vowels, or an equal number
of risers and descenders (i.e., each 'b' or 'd' would have to be
balanced by a 'q' or 'g'). Or require the sentence to be a palindrome,
or that the second half be an anagram of the first half.
--
Andrew Arensburger, Systems guy University of Maryland
arensb.no-...@umd.edu Office of Information Technology
Evil Mentalist I think, therefore you aren't.
Sean Pitman
Let's say that you start with sequence "Me" and the goal is to evolve
longer and longer Shakespearean sequences. You can select for any
sequence as long as it is found in the works of Shakespeare. By these
rules alone, the sequence "methi" would be positively selectable,
according to your rules, since it is part of a Shakespearean work -
even though the sentence fragment "methi", by itself, has no evident
meaning in the English language system. Using "Methinks it is like a
weasel" as a template were each and every single character change that
matches this template is selectable, evolution would proceed at
lightning speed - relatively speaking. This is because the odds of
"successful mutation" of each character position in a sequence are
only 1 in 27 (including a spacing character).
Do you see the problem with little scenario? It is a little bit
tricky. After all, it fooled Dawkins and many other very intelligent
people into thinking that a selection process based on sequence
comparison alone could also explain the evolution of highly complex
genetic _information_ systems. The fact is though, selection based
only on sequence comparison, without regard to understood meaning or
function, would produce very rapid evolution. Unfortunately for
evolutionists, real life a mindless non-directed nature does not
usually have an "ideal" sequence with which to compare evolving
sequences. Most of the time, with regard to most functional genetic
systems, all that nature has available is an ideal function, not an
actual sequence, with which to compare all other functions without
regard to futuristic goals.
There are those relatively few cases, however, where nature does
actually have a sequence of sorts with which to compare evolving
sequences. One prominent illustration of this is the evolution of
antibodies to match foreign antigens for a better immune response.
The antigen acts as a sequence ideal. All the immune system has to do
to be more selectability "fit" is to get its antibodies to match the
pre-established "ideal" antigen sequence more and more closely (in a
mirror image-type way of course). I discuss this particular concept a
bit more at:
http://naturalselection.0catch.com/Files/immunesystem.html
This function-based selection is very interesting in that those
sequences that are defined as "meaningfully" functional via this
method become more and more rare, in an exponential manner, at
increasing levels of complexity. And, not only do they become more
and more rare, they become more and more widely dispersed throughout
the potential sequence space (which is quite different from sequence
based selection). Because of this, the finding of something
meaningful in the next higher level of complexity is not as easy as it
was in the previous level. It is not always 1/26 for each additional
character addition as it was in Dawkins's "Methinks it is like a
weasel" scenario. The requirement for the detection of "meaning" in a
language system starts to separate meaningful stretches of characters
into more and more widely spaced blocks of characters at each internal
level of complexity. This makes it much much more difficult to get
from "Me" to "Methinks it is like a weasel" by the simple addition or
change of one character at a time in a nice sequence of unbroken
positive selectability.
So, although maybe more difficult, all scenarios that are used to
model true evolutionary processes, must be based on _meaningful_
selectability criteria, not _sequence_ selectability criteria.
If you wanted to limit selection to fully intact meaningful sections
of Shakespeare, that would be perfectly fine, but extremely limiting
to your evolutionary hopes. You would no doubt find your computer
unable to evolve much at all from Shakespeare, as far as sequence
length is concerned, with the limitation of meaningful selection in
place.
Zachriel
"Sean Pitman" <seanpi...@naturalselection.0catch.com> wrote in message
news:80d0c26f.04050...@posting.google.com...
Funny how the people who are actually decoding the Dog genome don't know
about the Pitman Conjecture of Evolution.
"Minor differences arise between individuals in a species through natural
processes of mutation. Most mutations are harmful and decrease the chance of
survival. However, for those few mutations that cause a favorable change
that enhance survival, the mutations will spread throughout the population
due to the enhanced survival of the individuals with the mutation. The
accumulation of mutations over time leads to the creation of new species."
http://mendel.berkeley.edu/dog/manifesto.html
Or breeders themselves who wait generations (in dog years) for
attractive mutations.
"When creating a new breed from an attractive mutation, the gene pool is
initially necessarily small with frequent matings between related dogs."
http://www.petpeoplesplace.com/Care/Cats/004/17p3.htm
http://www.dogbreedinfo.com/inbreeding.htm
> You, on the other hand, are trying to "manually" select genotypic
> sequences based on your knowledge how various genotypic combinations
> work together that are not yet present in the gene pool of options.
The Word Mutator does not require human intervention, though it is certainly
one option available if you so desire to control the process. Or you could
change the code if you prefer z-words, if you want. Or just leave it set to
length and let the process operate "naturally".
> This is much different than selecting based on function alone with no
> knowledge of the workings or meaning of the underlying coded symbols.
It's your analogy, not mine. Beware a war of words.
> It would be like starting with a calculator program, which you see on
> your computer monitor, and having the underlying code for this program
> produce several offspring programs with underlying code mutations, and
> you picking between the underlying codes based ONLY on the changes in
> calculator function that you see on your screen.
That's what the Word Mutator does. It just picks the longest ones without
regard to their future utility in creating even longer words. There is no
way for the program to know if a particular word is a dead-end. It does not
anticipate. Indeed, animal breeders are in a similar position. When
selecting for a large dog, they don't know if other problems of design will
inhibit further increases in size. Large dogs have problems with hips, for
instance.
> No understanding of
> the arbitrary definitions of the underlying codes or observation of
> the interaction of these coded character strings is allowed. Using
> this process of phenotypic selection alone, how long do you think it
> would take to evolve a brand new software function at an equal level
> of complexity (like opening the CD player on command)?
Using our rules of mutation it's L^3 per generation.
> Now, wouldn't this be a much harder evolutionary scenario compared to
> one in which you get to see, understand, and manipulate a coded
> sequence in a very direct manner based on an understanding of code
> function combined with intelligent foresight?
Word Mutator has no vision of the future. It ruthlessly culls short words
regardless of their future utility.
> > > The sequence space of 14-letter words is indeed over 100 million
> > > trillion in size. The _average_ distance between each meaningful
> > > 14-letter single word is also about 66 million billion non-defined
> > > sequences.
> >
> > Bill Gates walks into a bar. The mean average wealth shoots up to a
billion
> > per person. This mean average is extremely misleading because it doesn't
> > tell us anything about the distribution of that wealth.
>
> Ah, but it does tell us something. It tells us that the distribution
> is not perfectly clustered into just one little corner of sequence
> space or nicely lined up in perfect little rows within sequence space
> - now doesn't it?
The mean average doesn't tell us anything about that.
> It tells us that the clusters that are present are
> very irregular in size, shape, and even location within sequence
> space. It also appears that these clusters get relatively smaller and
> smaller and more and more widely distributed, in a rather random way,
> throughout sequence space with each step up the ladder of minimum
> meaningful complexity/size that involves the same degree of
> specificity.
Actually that is not the distribution of wealth in the bar. There is a
serious discontinuity in the distribution.
The difference between L^3 and 26^L is vast as L increases. You are wrong on
this point, and that has been demonstrated.
> The more complex genomes
> don't just take longer to evolve; they take _exponentially_ longer to
> evolve as compared to lower levels of complexity.
Yes, however the difference is millions of years, not zillions of years.
Your improper use of mathematics has misled you.
> The exponential
> nature of this whole process quickly flies by the mark for "millions"
> and even "billions" of years for very low levels of complexity and,
> with just a few more steps, a gene pool suddenly finds itself needing
> a minimum of trillions upon trillions upon trillions of years to do
> much of anything.
You continue to point to the mathematics, but never argue them. The function
is on the order of L^3, not 26^L or S^L or anything ^L.
> > > On your website you make mention that your program was able to evolve
> > > one third of all the words in the dictionary that you used.
> >
> > That's just when I stopped the program.
>
> Yes . . . But I'm more interested in the ratio of sequences that
> evolved within each level when you stopped to program. You don't seem
> to mention that the average length of the sequences that you evolved
> were, what? - 4 or 5 letters long?
Why do you keep belaboring the point? Yes, the number of required mutations
increases geometrically as L increases. But your number is off by zillions.
> You see, the ratio rapidly dropped
> off from low to high levels. Compared to all the meaningful words
> listed in your dictionary, you probably evolved a higher ratio of 3-
> vs. 7-letter words - right? And, you no doubtably evolved a higher
> ratio of 7-letter words than 10- or 14-letter words - right? Also,
> not only did the ratio drop off, but the time it took to reach each
> higher level increased exponentially - right? Hmmmm . . . How many
> levels do _you_ think it would take, in the light of this obvious
> exponential increase in required time with each level, to surpass the
> "million" or "billion" or "zillion" year mark?
On the order of L^3 per generation. This has always been on the website,
posted on this thread, and is the point of the whole exercise. In addition,
the real number of usually much less than L^3. That's because we have been
treating ten 10-length strings as a single string 100 in length. In fact,
the former has 67150 possible mutants, the latter has 525475. The L^3 figure
is an upper-limit.
> > > Why does this matter? It matters because if the ratio is
> > > significantly lower for each step up the ladder of complexity, it
> > > shows that the islands of meaningful sequences are not nicely lined up
> > > at all, but are indeed becoming more and more widely separated from
> > > each other, on average, in the exponentially expanding vastness of the
> > > potential sequence space at each higher level of complexity.
> >
> > No, it shows that it takes a heck of a lot of time to evolve anything
> > without some selection mechanism.
>
> Even with a function-based non-intelligent selection mechanism it
> still takes exponentially more and more time to evolve at each higher
> level of complexity.
Your math is wrong. So what else is new?
> > > For example, say that 1,000 of the 1,643 possible 14-letter words in
> > > the dictionary were all clustered together in a nice little bunch in
> > > one tiny area of 14-letter sequence space. Would your demonstration
> > > that evolution between these closely spaced 1,000 sequences is very
> > > rapid disprove my assertion that the average time required must still
> > > take into account the other 643 sequences? What if these 643
> > > sequences form another closely packed island far far away from the
> > > other island of 1,000 sequences? Now, evolution within each island
> > > will be rapid, but what about getting from the one island to the other
> > > island? This must also be factored into the "average time" equation.
> >
> > Sure, and the average wealth in the bar is a billion bucks. You're
missing
> > the point. Some words probably can't be evolved. I never saw "Zachriel"
pop
> > out even though I selected for Scrabble score and set "Zachriel" to 99.
> > That's because there are probably few words similar to "Zachriel" in our
> > Dictionary.
>
> Now think carefully here Zach. If some words "can't be evolved"
> _because_ they aren't close enough to the starting cluster, what do
> you think would happen if the clusters got smaller and smaller and
> farther and farther apart?
Well, this brings up another problem with your false notion of averages.
Let's assume a word is completely isolated. Our evolutionary process can
neither find the word or evolve away from the word. Let's say "zzzz" is a
word. Now what is the number of mutations involved? It's infinite (or more
properly undefined). Your average is therefore infinite (or more properly
undefined). So you are wrong again, but for a different reason.
Do you know of such a word?
> Wouldn't that result in relatively fewer
> and fewer sequences that actually "could" be evolved without having to
> cross significant neutral gaps of non-meaningful sequences? Well,
> this is exactly what happens with each step up the ladder of
> meaningful complexity. Even your experiment, as non-realistic as it
> is, demonstrates this rather nicely.
No, it clearly demonstrates that for any word in our dictionary is takes
much less than the Pitman Number to evolve other words. Have you found a
word which is completely sterile? I asked before, but you never answered.
All words and combinations of words will result in the evolution of new
words, some long, some short, some with high Scrabble score, some with z's.
We can select according to any rule we choose, but you yourself chose
length.
The problem is to start with a word of length N and find any other word of
length N. So far I have always been able to evolve other such words in less
than the Pitman Number, most of the time in much less than the Pitman
Number.
> > "The biological Theory of Evolution does not claim that every imaginable
> > creature can be evolved, and certainly not that every imaginable
creature
> > must evolve and co-exist. Rather, like our game, evolution is
opportunistic;
> > and though every conceivable creature may not be evolvable, the
diversity of
> > life on Earth clearly indicates that the range of evolvable organic
forms is
> > vast."
>
> What evolutionists claim is that there is no limit in the ability of
> evolution to create higher and higher functional/meaningful complexity
> via mindless processes of random mutation and natural selection.
Sure there are limits. The limits are set by the available time (billions of
years), the environment, and the previous history of evolution.
> That
> means, basically, that each meaningful sequence in one level of
> complexity is not very far away from another meaningful sequence in
> the next higher level of complexity and that this rule remains true as
> one moves up from very low to extremely high levels of meaningful
> complexity.
No one in science claims this. Large adaptive changes in large species may
take millions of years, but large adaptive changes in viruses may only take
days. (Of course there are reasons why adaptive changes can sometimes occur
quickly in larger species, too.)
> The problem with this notion is that it simply makes no
> logical sense and it is not observed in real time either.
> Statistically, evolution should and in fact does in real life stall
> out on relatively low rungs of the ladder of complexity. This means
> that evolvable organic forms are not "vast" at all - relatively
> speaking. In fact, much of what many people think of as a "vast"
> array of different forms are nothing more than Mendelian variation of
> a pretty static gene pool of allelic options with no significant gain
> to these options (more likely a loss) over time.
Constantly repeating it doesn't make it so.
> > > Basically, it comes down to the odds that each of the islands of
> > > beneficial sequences will have a connecting bridge or bridges to
> > > islands within the same level of complexity as well as to islands
> > > within lower and higher levels of complexity. At relatively low
> > > levels of complexity, these bridges are quite common and can be found
> > > fairly quickly - depending upon the size of the population and its
> > > mutation rate of course.
> >
> > Funny that I've found bridges all the way out to "denominationalists" at
> > length 18.
>
> Funny that you found exponentially fewer and fewer bridges - isn't it?
I found no such limit except the limit of time as set by (at most) L^3 and
the size of the Pond. Your math is wrong. It's as simple as that. You
claimed that to discover a 14-letter word required a hundred million
trillion mutations. You were wrong. Please admit this and move on.
> > It turns out there is a limit to the length of word we can
> > evolve. The longest word in our Dictionary is "antiparliamentarianisms"
at
> > length 23. Of course, I haven't run the Word Mutagenator for a "zillion
> > years", or even a single year.
>
> That is because you are limiting yourself to single word sequences.
> But, there is no technical limit to the length of a meaningful
> sequence you could evolve if you do not limit your selection criteria
> to sequences made up only of single words.
That was the challenge.
Just try a little experiment yourself. Start with a short 2 or 3-letter word
and see how many words you can evolve that require greater and greater
minimum sequence requirements. No doubt you will quickly find yourself
coming to walls of meaningless or non-beneficial potential options that
separate you from every other meaningful and beneficial option."
This was the claim.
"Getting from one meaningful 7-letter phrase to a different meaningful
7-letter phrase requires, on average, a fairly long random walk through
250,000 meaningless options."
http://tinyurl.com/ypos7
You were wrong. We don't have to walk through all that space. We can
navigate the ocean like ancient Polynesian explorers. Get over it.
> > > Another thing is, outside help by intelligent design is not allowed in
> > > these experiments Zach. You have foresight that evolutionary
> > > processes do not have.
> >
> > The selection criteria (length) was arbitrarily selected by yourself. It
> > could just as well been animal-words, or z-words, short words, words
with
> > double-letters, Scrabble score, whatever.
>
> Whatever the criteria, intelligent input and foresight is not allowed
> as a basis for selecting one genotype over another (for previously
> detailed reasons).
The Word Mutator does not see the future. It ruthlessly eliminates short
words when longer ones are found. The initial criteria was your suggestion.
> The reason I selected increasing length and English language meaning
> as selection criteria, is because it is my position that with
> increasing minimum length requirements for a meaningful English
> sequence (at a given level of specificity) comes an exponentially
> expanding ocean of non-functional, non-beneficial sequences. This
> ocean of "non-beneficence" pushes the relatively small islands farther
> and farther apart, stretching and straining the bridges that connect
> these islands until they break from each other completely in their
> headlong rush toward hopeless isolation and the rapid death of
> evolutionary progress.
Your specific claim was that they spread out according to a calculation I
call the Pitman Number, for length L, and N the number of words in the
Dictionary of length L, it is 26^L / N. Using our dictionary of about 80K
words, these are the first few Pitman Numbers.
1- 9
2- 16
3- 29
4- 192
5- 2,522
6- 39,034
7- 714,828
8- 16,813,773
9- 468,545,364
10-14,460,878,473
11- 516,949,927,745
12- 19,782,122,027,712
13- 835,686,383,699,473
14- 39,263,526,904,015,300
15- 1,869,854,339,226,000,000
Apply these numbers to the evolution of words is a gross miscalculation.
> > > Natural selection, as a purely _mindless_
> > > process, can only select based on what works right now. A mindless
> > > function-based selector cannot select to keep a sequence simply
> > > because it may work in combination with something else sometime in the
> > > future.
> >
> > That's correct. When Word Mutagenator selects for length, it doesn't
know if
> > these particular words will lead to longer words, or whether they are
> > deadends. Funny how it worked out.
>
> Funny how it showed good evidence of stalling out. And, funny how you
> felt the need to do some "manual" selection yourself to get some of
> your more "creative" evolutionary scenarios to "work".
That's just silly. I added some features for fun and for the benetif of the
advanced student. You have yet to answer the objections raised. Of course,
you never will as long as you block the sight.
Could it be that you could see the light
But choose instead to close your eyes and block
The sight?
> > > Only an intelligence that has insight and the ability to
> > > predict the future, like you have, can do this sort of selecting.
> >
> > Funny how Word Mutagenator always seems to find words that lead to
longer
> > words that lead to longer words.
>
> Again, this is only to be expected considering the relatively low
> level of meaningful complexity that your "Mutagenator" is working on
> with the use of a very high reproductive rate and mutation rate.
Um. This was your challenge and your claim. They have been met, though I
realize you are incapable of seeing that.
This was the challenge.
Just try a little experiment yourself. Start with a short 2 or 3-letter word
and see how many words you can evolve that require greater and greater
minimum sequence requirements. No doubt you will quickly find yourself
coming to walls of meaningless or non-beneficial potential options that
separate you from every other meaningful and beneficial option."
This was the claim.
"Getting from one meaningful 7-letter phrase to a different meaningful
7-letter phrase requires, on average, a fairly long random walk through
250,000 meaningless options."
http://tinyurl.com/ypos7
You were wrong. We don't have to walk through all that space. We can
navigate the ocean like ancient Polynesian explorers. Get over it.
> Keep
> going though. Without intelligent input, your computer will not be
> able to evolve very much farther (predicted limits previously detailed
> according to my own stated parameters of how the program should work).
>
> > > So
> > > please, you cannot be helping your computer out here. You must let it
> > > select based on meaning that is current. It cannot select short
> > > meaningful sequences over other short meaningful sequences based on
> > > the chance that a future recombination event would produce something
> > > meaningful in certain short sequences - as you have done in your
> > > "poem" evolution scenarios.
> >
> > If I build a Phrasenator, I will be certain to not let the computer peek
> > ahead. That's way too much work to program. It will work just like the
Word
> > Mutagenator, which selects the longest words without regard to their
ability
> > to "bridge" to even longer words. Only we will use the rules of grammar
for
> > selection.
>
> Well then, without intelligent input and with a reasonable steady
> state population, reproduction rate, mutation rate, death rate,
> mutation types, etc, as I have previously detailed, your "Phrasenator"
> will stall well short of my predictions.
Well, you want a population of a million (or is it 10^24) letters. That
would require more calculations than my computer is capable in a reasonable
time. You have moved the goal-posts. Indeed, if I build the Phrasenator, it
will be for the enjoyment of our readers. I am under no illusion that you
will admit any error.
> Remember though, your computer cannot analyze more potential sequences
> in a given generation than the rate of reproduction and mutation rate
> allows. For example, your current computer program analyses every
> possible mutation for a given generation from the perspective of each
> individual in your population, which quickly runs into the thousands
> at higher levels. With a limited reproduction rate of say, 100
> offspring per individual, your computer is only allowed to produce and
> analyze 100 new sequences per individual in your population regardless
> of the potential sequences that could be had in that generation. Each
> offspring sequence produced is mutated and batched with the other
> offspring before the selection process. Then, of the 100 new
> offspring sequences, the top scoring sequence is selected.
The Word Mutagenator works on the different principle (random changes), but
please note that the results are comparable.
> > > Actually, the number of possible mutants, to include meaningful as
> > > well as non-meaningful, for a 1,000-character sequence is the number
> > > of individuals in a population times the average mutation rate per
> > > individual, per generation. Given the potential sequence space for a
> > > 1,000-character sequence, this could be way over a "billion".
> >
> > Um, according to your own figures, for the human genome there are an
average
> > of 200 mutations per generation. There are about a half billion bases in
the
> > human genome.
>
> As an aside, you are just slightly off here. There are actually over 6
> billion base pairs (diploid) in the human genome.
>
> > So for any string of 1000, there is much less than one
> > mutation per generation.
>
> That's true. So you see, even your use of an average of just 1
> mutation per generation for such a short string of 1,000 characters is
> an extremely high mutation rate when compared to what happens in real
> life. In fact, in real life, such a high mutation rate would be
> lethal, wiping out far more useful information than it created (given
> the limits of reproductive rates even in bacteria).
You apparently don't understand how simulations work. Consider the Word
Mutagenator. We wait for a mutation. It might be an hour, or a week or a
year. Mutations are relatively rare. That's what counts. When the mutation
occurs, we select whether it is beneficial or not. That's it. That's the
entire process.
> > Double mutations would be exceedingly rare.
>
> Like I said before, I would agree with you when you argued this point.
> Although, "exceedingly rare" is not the same thing as impossible.
> However, "exceedingly rare" does translate into a significant increase
> in the average time involved. Starting to see my point?
No. Your point is false. I can easily add a percentage of double mutation to
the Word Mutagenator. Are you going to predict a significantly different
result? It won't. But I'm not going to keep changing the code because you
raise new and irrelevant objections.
The rules were posted. Single mutations is in keeping with the concept of
rare mutation, and reasonble numbers of multiple mutations won't
significantly change the results.
> > I'll
> > probably include multi-mutations anyway--just for fun.
>
> What you really need to do is include the _potential_ for multiple
> mutations, although the _average_ rate can still be set to a
> reasonable level so as you don't destroy faster than you create and
> turn your population into homogenous mush - just like in real life.
>
> > > Say, for example, that we had a 10^24 individual sequences/genomes in
> > > our population - each of them with a different 1,000 character
> > > sequence and an _average_ mutation rate of one mutation per individual
> > > per generation. How many new 1,000-character sequences would this
> > > population come across, on average, in one generation? Obviously, the
> > > answer is 10^24, which is far greater than a billion.
> >
> > Sorry, that's wrong. If there are only 1000 characters, most of those
> > mutations would not be unique.
>
> It certainly doesn't seem to be as wrong as your limit of just a
> "billion" new sequences per generation calculation regardless of
> population size. Why don't we just think this thing through again
> Zach?
>
> Starting with 10^24 different, fairly evenly spaced, 1,000-character
> sequences in our steady state population, each mutating with an
> average rate of one mutation per generation, the average generation
> would produce 10^24 unique sequences compared to the population of
> 10^24 sequences in the generation that came before.
This is not true. There are not that many valid mutations of
1000-characters. Perhaps after a number of generations the various members
of the collection would diverge. What you are positing is a vast ensemble of
meaningless letters. Where did this come from? This wasn't the challenge.
You would have to change the rules. Is that what you want to do? If so,
please go back a few weeks in this thread, find the rules and suggest
changes. But the rules are clearly established. We consider point-mutations,
delete-mutations, insert mutations, snips, remainders and recombinations. As
mutations are relatively rare, we only consider a single mutation per
generation. Each string must consist of a valid word.
I would be happy to analyze your new scenario, but only after you completely
and utterly repudiate your previous word analogy. This endless moving of the
goal-posts is futile.
> This is because
> the odds than any one unique individual line in our population of
> 10^24 would cross any other line within that population is 10^24 /
> 26^1000 or about 1 in 10^1390 generations. Even if you started with
> the same sequence in all 10^24 individuals, a mutation rate of 1
> mutation per genome per generation would cause a rapid neutral drift
> divergence of all the sequences so that very rapidly you would reach
> the "10^24 new sequences per generation" mark with your population.
> Again, this is far greater than a billion is it not?
<snip>
You said to start with a 2- or 3-letter word, and changing one letter at a
time, etc. etc. Now you want me to start with 10^24 number of strings of
length 1000 composed of meaningless and disconnected symbols.
Don't you think you've changed the rules a wee bit.
Sean Pitman
> > So you see, breeding that is phenotypically based, such as dog or
> > horse breeding, is not really "evolution" - in the sense that we are
> > talking about evolution as the arrival of new information and meaning
> > into a gene pool. Darwin didn't know this (since Darwin didn't know
> > about Mendel's work), but we know it now because we understand the
> > code behind the changes that Darwin observed as being primarily
> > Mendelian in nature. Therefore, this sort of breeding, though
> > intelligently directed, would not speed up the evolutionary process at
> > all beyond the other non-directed selection mechanisms already in
> > place in nature.
>
> Funny how the people who are actually decoding the Dog genome don't know
> about the Pitman Conjecture of Evolution.
The people decoding the dog genome are not the people who were
responsible for dog breeding for thousands of years. Generally
speaking, breeding has been done and is being done without any
understanding of the underlying genetic code. Breeding is purely
phenotypically based.
> "Minor differences arise between individuals in a species through natural
> processes of mutation. Most mutations are harmful and decrease the chance of
> survival. However, for those few mutations that cause a favorable change
> that enhance survival, the mutations will spread throughout the population
> due to the enhanced survival of the individuals with the mutation. The
> accumulation of mutations over time leads to the creation of new species."
> http://mendel.berkeley.edu/dog/manifesto.html
Again, if a phenotypically expressed mutation happens to occur, a
breeder can select for the expressed phenotypic change, but this
selection is not based on a genotypic understanding or ability to
predict that the genotypic change will be able to combine with some
other underlying genotype for another desirable trait to form a new
unified trait. Being able to read and select based on genotype and
genotypic combinations with futuristic intent is far far different
from what breeders do.
> Or breeders themselves who wait generations (in dog years) for
> attractive mutations.
>
> "When creating a new breed from an attractive mutation, the gene pool is
> initially necessarily small with frequent matings between related dogs."
> http://www.petpeoplesplace.com/Care/Cats/004/17p3.htm
> http://www.dogbreedinfo.com/inbreeding.htm
The creation of new "breeds" from the same gene pool, is not based on
anything more than Mendelian genetics. It is not based to any
significant degree on mutations, but on the specific recombination of
a limited variety of alleles for specific allelic positions in a
specific type of gene pool. No new information is created here. The
only thing that happens is that a different part of the potential a
fairly fixed gene pool is reflected or expressed. That is all. Take
for example me and my brother. We look very different from each other
even though we came from the exact same gene pool. Our differences
could be selected and enhanced within the limits of our gene pool
options, but this does NOT entail the evolution of any new genetic
information at all. Therefore, this sort of change over time, which
is the same as what Darwin observed, is not enough, by itself, to
explain those high level differences between life forms that do
actually require novel information differences between gene pools.
> > You, on the other hand, are trying to "manually" select genotypic
> > sequences based on your knowledge how various genotypic combinations
> > work together that are not yet present in the gene pool of options.
>
> The Word Mutator does not require human intervention, though it is certainly
> one option available if you so desire to control the process. Or you could
> change the code if you prefer z-words, if you want. Or just leave it set to
> length and let the process operate "naturally".
The problem here is that you actually _did_ select changes based on
your knowledge of how the genotype, not just the phenotype, works and
interacts phenotypically according to futuristic goals. Nature cannot
do this. Even human breeders cannot do this if, as is usually done,
they based all of their selections on phenotypic changes alone.
Certainly the genotypes of many creatures are being investigated and
understood to a greater and greater degree, but whenever changes are
selected on the basis of a direct understanding of the genotypic
changes that are taking place as well as what these changes mean
phenotypically, this is not purely phenotypically-based evolution, but
genotypically _designed_ selection. Genotypic selection is out of the
question since natural processes of lesser complexity than human
intelligence do not have access to this ability.
> > It would be like starting with a calculator program, which you see on
> > your computer monitor, and having the underlying code for this program
> > produce several offspring programs with underlying code mutations, and
> > you picking between the underlying codes based ONLY on the changes in
> > calculator function that you see on your screen.
>
> That's what the Word Mutator does. It just picks the longest ones without
> regard to their future utility in creating even longer words. There is no
> way for the program to know if a particular word is a dead-end. It does not
> anticipate.
That is not what I am talking about. I am talking about your own
admission that you directly selected for changes "manually" to achieve
certain results. That "manual" selection by you is not allowed. And,
the computer can only select based on what works right now (according
to definition of "meaningful"). Of course you haven't programmed the
computer to select for futuristic goals, but I mention this because
other people have set up their evolutionary scenarios based on
pre-established futuristic goals.
> Indeed, animal breeders are in a similar position. When
> selecting for a large dog, they don't know if other problems of design will
> inhibit further increases in size. Large dogs have problems with hips, for
> instance.
Exactly. This is my whole point. Without a direct knowledge of the
genotype and the ability to foresee how various genotypic selections
will probably interact if combined, animal breeders are in exactly the
same position as any other phenotypic-only selection based system.
> > No understanding of
> > the arbitrary definitions of the underlying codes or observation of
> > the interaction of these coded character strings is allowed. Using
> > this process of phenotypic selection alone, how long do you think it
> > would take to evolve a brand new software function at an equal level
> > of complexity (like opening the CD player on command)?
>
> Using our rules of mutation it's L^3 per generation.
That is completely wrong. Your L^3 number is simply ludicrous since
it doesn't take into account the size of sequence space or the
location of meaningful sequences within that space. Also, it doesn't
take into account the population as a whole or the limitation of the
reproductive rate of that population. The maximum number of sequences
that can be searched in one generation is not L^3, but is equivalent
to the total number of offspring (O), if given a mutation rate greater
than 1. So, the formula for the total number of analyzed mutations
many generations is O*G. It is NOT L^3. This notion of yours is
simply off the wall and so obviously wrong that I am wondering how
strong your conceptual math background really is?
> > The more complex genomes
> > don't just take longer to evolve; they take _exponentially_ longer to
> > evolve as compared to lower levels of complexity.
>
> Yes, however the difference is millions of years, not zillions of years.
> Your improper use of mathematics has misled you.
LOL - You are the one who seems absolutely clueless about the math
involved. And, an exponential increase over time would quickly reach
far past the millions, billions, and even trillions upon trillions of
years. The best you evolutionists can hope for is that the decline is
linear, because a truly exponential decline in evolutionary abilities
with increasing functional complexity would be lethal to your theory.
> > The exponential
> > nature of this whole process quickly flies by the mark for "millions"
> > and even "billions" of years for very low levels of complexity and,
> > with just a few more steps, a gene pool suddenly finds itself needing
> > a minimum of trillions upon trillions upon trillions of years to do
> > much of anything.
>
> You continue to point to the mathematics, but never argue them. The function
> is on the order of L^3, not 26^L or S^L or anything ^L.
Again, the L^3 calculation is meaningless. The sequence space is
definitely C^L (C = total number of characters). The maximum
sequences that may be analyzed per generation is not L^3 * G, but O*G
(O = offspring per generation) assuming an average of at least 1
random mutation per genome per generation. With this formula, the
average success rate is strictly dependent upon the density of
selectable sequences in sequence space, the average randomness of
their distribution within sequence space, and the starting point(s) of
the initial population.
> > > > On your website you make mention that your program was able to evolve
> > > > one third of all the words in the dictionary that you used.
> > >
> > > That's just when I stopped the program.
> >
> > Yes . . . But I'm more interested in the ratio of sequences that
> > evolved within each level when you stopped to program. You don't seem
> > to mention that the average length of the sequences that you evolved
> > were, what? - 4 or 5 letters long?
>
> Why do you keep belaboring the point? Yes, the number of required mutations
> increases geometrically as L increases. But your number is off by zillions.
Actually, it is your "L" formula that is off by "zillions" since it
has nothing to do with the actual problem (see above).
> > You see, the ratio rapidly dropped
> > off from low to high levels. Compared to all the meaningful words
> > listed in your dictionary, you probably evolved a higher ratio of 3-
> > vs. 7-letter words - right? And, you no doubtably evolved a higher
> > ratio of 7-letter words than 10- or 14-letter words - right? Also,
> > not only did the ratio drop off, but the time it took to reach each
> > higher level increased exponentially - right? Hmmmm . . . How many
> > levels do _you_ think it would take, in the light of this obvious
> > exponential increase in required time with each level, to surpass the
> > "million" or "billion" or "zillion" year mark?
>
> On the order of L^3 per generation. This has always been on the website,
> posted on this thread, and is the point of the whole exercise. In addition,
> the real number of usually much less than L^3. That's because we have been
> treating ten 10-length strings as a single string 100 in length. In fact,
> the former has 67150 possible mutants, the latter has 525475. The L^3 figure
> is an upper-limit.
L^3 is not an upper limit at all. The upper technical limit is C^L.
Given a population that is C^L in size (i.e., total number of
offspring produced in a give period of time), all of the C^L
possibilities could be reached in very short order. With a lesser
population undergoing selection, the C^L possibilities would take a
lot longer to reach.
> > Even with a function-based non-intelligent selection mechanism it
> > still takes exponentially more and more time to evolve at each higher
> > level of complexity.
>
> Your math is wrong. So what else is new?
Why don't you check with some of your evolutionist buddies and ask
them whose math is "wrong" here. Or, you could read some interesting
papers on the topic, such as the one I previously suggested by Lenski
et. al. on computer code evolution. At least they got their _math_
right.
> > That is because you are limiting yourself to single word sequences.
> > But, there is no technical limit to the length of a meaningful
> > sequence you could evolve if you do not limit your selection criteria
> > to sequences made up only of single words.
>
> That was the challenge.
That was not the challenge. The challenge was to start with a
meaningful short sequence like a 2 or 3-letter word or words and
evolve longer and longer meaningful sequences made up of "words" . . .
and see how far you could go (with my prediction that you would not be
able to make it past several hundred to a few thousand fairly
specified character sequences). I'm very sorry if you misunderstood
my position, but this has been my position and my challenge far before
you arrived on the scene. Check out what I wrote before you arrived
and see if this is not a true statement of reality. It might help you
to read up on what my real position is on my website as well.
> Your specific claim was that they spread out according to a calculation I
> call the Pitman Number, for length L, and N the number of words in the
> Dictionary of length L, it is 26^L / N. Using our dictionary of about 80K
> words, these are the first few Pitman Numbers.
>
> 1- 9
> 2- 16
> 3- 29
> 4- 192
> 5- 2,522
> 6- 39,034
> 7- 714,828
> 8- 16,813,773
> 9- 468,545,364
> 10-14,460,878,473
> 11- 516,949,927,745
> 12- 19,782,122,027,712
> 13- 835,686,383,699,473
> 14- 39,263,526,904,015,300
> 15- 1,869,854,339,226,000,000
>
> Apply these numbers to the evolution of words is a gross miscalculation.
Not at all. Meaningful sequence islands do actually spread out like
this, but this does not mean that all bridges between islands in one
level and the next higher level are broken at such low levels. In
order for significantly complete bridge collapse to be realized,
especially with the extraordinarily high reproductive rates and
mutation rates that you are using, impassable bridge collapse would be
realized at less than 1,000 characters and probably less than 100
characters, which is still very "quick", relatively speaking.
> > Well then, without intelligent input and with a reasonable steady
> > state population, reproduction rate, mutation rate, death rate,
> > mutation types, etc, as I have previously detailed, your "Phrasenator"
> > will stall well short of my predictions.
>
> Well, you want a population of a million (or is it 10^24) letters.
Giving you opportunity to use such a population, as suggested on your
own website, is generous on my part. The larger the population, the
more that helps you, not me. If you use a much smaller population and
reproductive rate, evolution will be that much harder for your
population.
> That
> would require more calculations than my computer is capable in a reasonable
> time. You have moved the goal-posts.
I haven't moved the goalposts at all. Whatever sized population and
reproductive rate that your little computer can handle. It won't
really matter as long as you follow the rules of the game as I have
listed them in this thread and to which you made the comment that they
seemed like good rules to you.
> Indeed, if I build the Phrasenator, it
> will be for the enjoyment of our readers. I am under no illusion that you
> will admit any error.
I have admitted error many times in this forum when it has been made
clear to me that I actually made an error. Simply saying that another
person is incapable of recognizing a personal error is meaningless
especially since you yourself have admitted none of the many errors
you have obviously made in your discussions with me.
> > That's true. So you see, even your use of an average of just 1
> > mutation per generation for such a short string of 1,000 characters is
> > an extremely high mutation rate when compared to what happens in real
> > life. In fact, in real life, such a high mutation rate would be
> > lethal, wiping out far more useful information than it created (given
> > the limits of reproductive rates even in bacteria).
>
> You apparently don't understand how simulations work. Consider the Word
> Mutagenator. We wait for a mutation. It might be an hour, or a week or a
> year. Mutations are relatively rare. That's what counts. When the mutation
> occurs, we select whether it is beneficial or not. That's it. That's the
> entire process.
You don't seem to realize that in your analyzing mutations per
"generation", ever mutation that you subject to analysis represents a
new offspring. Your computer program is analyzing up to tens to
hundreds of thousands of mutations in each "generation". That
translates into an equivalent number of offspring. Having so many
offspring per generation basically makes your notion of "generation
time" irrelevant as a comparison to anything that can be achieve in a
real life scenario.
> > > Double mutations would be exceedingly rare.
> >
> > Like I said before, I would agree with you when you argued this point.
> > Although, "exceedingly rare" is not the same thing as impossible.
> > However, "exceedingly rare" does translate into a significant increase
> > in the average time involved. Starting to see my point?
>
> No. Your point is false. I can easily add a percentage of double mutation to
> the Word Mutagenator. Are you going to predict a significantly different
> result? It won't. But I'm not going to keep changing the code because you
> raise new and irrelevant objections.
You evidently don't understand my point here. Why am I not surprised.
No, it will not significantly change the result. But this was not my
point here. My point was that finding certain sequences is not
actually "impossible" as you had claimed. The finding of all
sequences should be made at least "possible" if you are thinking to
model real evolution. This is exactly what my model provides -
possibility even if unlikely possibility.
> The rules were posted. Single mutations is in keeping with the concept of
> rare mutation, and reasonble numbers of multiple mutations won't
> significantly change the results.
The single mutation limitation, as you yourself noted, removes from
possibility many sequences that are actually possibly reached in real
life. You should therefore add this possibility even if it wouldn't
change things significantly.
> > > I'll
> > > probably include multi-mutations anyway--just for fun.
> >
> > What you really need to do is include the _potential_ for multiple
> > mutations, although the _average_ rate can still be set to a
> > reasonable level so as you don't destroy faster than you create and
> > turn your population into homogenous mush - just like in real life.
Exactly . . .
> > Starting with 10^24 different, fairly evenly spaced, 1,000-character
> > sequences in our steady state population, each mutating with an
> > average rate of one mutation per generation, the average generation
> > would produce 10^24 unique sequences compared to the population of
> > 10^24 sequences in the generation that came before.
>
> This is not true. There are not that many valid mutations of
> 1000-characters.
Yes there are. There are C^1000 of them. All of these are valid
mutations of 1000-Characters (C).
> Perhaps after a number of generations the various members
> of the collection would diverge.
Yes they would, just like they do in real life.
> What you are positing is a vast ensemble of
> meaningless letters.
What I am proposing is that meaningless stretches of sequences be
allowed to be part of selectable sequences that have at least a
portion of their sequence length that is meaningful. This is exactly
what is allowed in real life. Non-meaningful stretches of DNA tag
along with meaningful stretches of DNA. So, say your sequence length
was 100 characters long, the longest internal sequence of these 100
characters that made sense in English was only 20-characters long.
All the rest of this sequence was gibberish. Well, as long as the
meaningful part of this sequence had the highest sequence score in the
population, this entire sequence would be the most selectable
sequence.
> Where did this come from? This wasn't the challenge.
If you had read much of anything from my website or from previous
posts to this forum, you would know that this has always been my
position and included in my challenge.
> You would have to change the rules. Is that what you want to do?
This is not a change of the rules at all and I really don't know why
you aren't jumping at this opportunity since it is really what real
life evolution is supposed to do. If anything, these rules that allow
neutral evolution in a non-meaningful stretch of a sequence to tag
along as part of a meaningful sequence helps your position out even
more.
> If so,
> please go back a few weeks in this thread, find the rules and suggest
> changes. But the rules are clearly established. We consider point-mutations,
> delete-mutations, insert mutations, snips, remainders and recombinations. As
> mutations are relatively rare, we only consider a single mutation per
> generation.
If you only consider a single mutation per generation, you would only
be able to analyze one new sequence per generation. This is not what
your computer program does. It analyzes thousands of mutations per
"generation". The only way you can analyze thousands of potential
mutations per generation is if you had thousands of offspring per
generation, each with a different mutation.
> Each string must consist of a valid word.
This is not realistic or to your advantage. Each string may consist
not only of a valid English language sequence, but also of sections of
non-valid sequences.
> I would be happy to analyze your new scenario, but only after you completely
> and utterly repudiate your previous word analogy. This endless moving of the
> goal-posts is futile.
The only goalposts that are moving are the ones pertaining to your
mental perception of what has always been there.
> > This is because
> > the odds than any one unique individual line in our population of
> > 10^24 would cross any other line within that population is 10^24 /
> > 26^1000 or about 1 in 10^1390 generations. Even if you started with
> > the same sequence in all 10^24 individuals, a mutation rate of 1
> > mutation per genome per generation would cause a rapid neutral drift
> > divergence of all the sequences so that very rapidly you would reach
> > the "10^24 new sequences per generation" mark with your population.
> > Again, this is far greater than a billion is it not?
> <snip>
>
> You said to start with a 2- or 3-letter word, and changing one letter at a
> time, etc. etc. Now you want me to start with 10^24 number of strings of
> length 1000 composed of meaningless and disconnected symbols.
Again, don't you see that if you could model such a scenario as this,
it would be to your advantage, not mine. The larger you can make your
population and the more offspring you can get your population to
generate, the faster evolution will proceed. And, the less
restrictions you impose on your strings as to what is and isn't
allowed, the faster evolution will proceed and the more evolutionary
possibilities there will be. It is you who are limiting yourself with
your own rules. After all, it was you who claimed that certain
"meaningful" sequences could be placed in technically "impossible"
positions - not I. Therefore, it should be obvious to you that my
rules allow for more possibilities as compared to your rules. You
should jump at the chance my man! I am trying to help you out here
and you are seeing it!
> Don't you think you've changed the rules a wee bit.
Not at all. And, even if I had, these rules are obviously to your
advantage over the ones you are currently using.
Andrew Arensburger
> Andrew Arensburger <arensb.no-...@umd.edu> wrote in message news:<c78vdd$la8$1...@grapevine.wam.umd.edu>...
>> In talk.origins Sean Pitman <seanpi...@naturalselection.0catch.com> wrote:
>> > Selection:
>> > Any sequence or any portion of a sequence (made up of single or
>> > multiple words) that is meaningful according to standard rules of
>> > English usage and grammar may be selected as advantageous relative to
>> > its peers.
>>
>> This seems hopelessly vague to me. How can a computer program
>> tell whether a sequence of words is "meaningful according to standard
>> rules of English usage"?
> Consider that I said "meaningful", not necessarily "beneficial".
Um, yeah. Who ever said anything about "beneficial"?
> Now,
> I realize that I am using the term "meaningful" rather loosely here.
> So I will explain what I mean by "meaningful" in the current sense. I
> will accept as "meaningful" any sequence that may be understood to
> have English language meaning in some, although possibly a very
> remote, context.
Okay, please explain how this can be done. Specifically, how
can a computer program determine whether a given sequence "may be
understood to have English language meaning in some [...] context"?
Please be specific. Remember that computers don't understand
English.
Also, as I understand your definition above, the sequence
"sdjfksh zooecpgk" is meaningful, in that one can imagine a situation
in which it is the correct answer to the question, "What did the
random letter generator print?" Of course, the same is true of any
sequence.
> In other words, one must be able to present some
> scenario where, if a particular sequence were written or spoken, it
> would be understood in English as having "beneficial" meaning.
What do you mean by "beneficial" here? And how would a program
come up with this scenario?
Or would you accept a program that said that "sdjfksh
zooecpgk" was meaningful, because one can imagine a context in which
that sequence of letters makes sense and is somehow beneficial to the
speaker?
[...]
>> But how can the program tell whether a given sequence of words
>> is meaningful, as opposed to merely being grammatically correct? How
>> can it know that "John vacations at the beach" is meaningful, but that
>> "Horseshoe paints for an arena" isn't?
> That would be very difficult I would think.
Yes. That's my point.
> That is why I haven't
> based this test on the detection of what is "beneficial" given a
> certain context, but have limited selection criteria only to what is
> "meaningful" without regard to context.
And that's what I'm asking about: how can a computer program
determine whether a given phrase is meaningful?
As far as I know, this is the first time anyone has mentioned
"beneficial" sequences. You've been talking about meaningful
sequences, but you haven't given any useful suggestions on how to
determine whether a given sequence of words is meaningful. All of your
responses have boiled down to "a human being would find meaning in
this sequence."
But computers and programs are not human beings. They don't
understand English. You have to explain very, very precisely and
carefully what it is that you want them to do. Now, please explain,
precisely and carefully, how a computer program can determine whether
a given sequence is "meaningful" or not.
Either that, or pick a different set of selection criteria.
[...]
> I think that it is possible to program a computer to recognize English
> language meaning (in the present sense) if it does not have to also
> recognize "beneficial meaning" with regard to a particular situation /
> environment.
Then please explain how this can be done.
You said above that you think this would be very difficult. I
agree. That's why I'm asking you. If I knew how it could be done, I'd
be writing code instead of posting here.
> I can't really think of any other equivalent selection criteria that
> would actually be helpful to resolving the discussion at hand.
> However, if you can think of such an equivalent selection criterion,
> please do let me know!
Well, we could move away from English and devise a new
language.
How about a new language, one that uses four letters. Each
possible set of three letters codes for one token. Sequences of tokens
embody instructions which can then be executed on suitable (possibly
virtual) hardware.
With some discussion, we could come up with a grammar to which
sequences of tokens must conform in order to be considered meaningful.
How about it?
--
Andrew Arensburger, Systems guy University of Maryland
arensb.no-...@umd.edu Office of Information Technology
If Bill Gates had a dime for every time a Windows box crashed...
...Oh, wait a minute, he already does.
Zachriel
"Sean Pitman" <seanpi...@naturalselection.0catch.com> wrote in message
news:80d0c26f.04050...@posting.google.com...
news:<wcydnYgx_v_...@adelphia.com>...
>
> > > So you see, breeding that is phenotypically based, such as dog or
> > > horse breeding, is not really "evolution" - in the sense that we are
> > > talking about evolution as the arrival of new information and meaning
> > > into a gene pool. Darwin didn't know this (since Darwin didn't know
> > > about Mendel's work), but we know it now because we understand the
> > > code behind the changes that Darwin observed as being primarily
> > > Mendelian in nature. Therefore, this sort of breeding, though
> > > intelligently directed, would not speed up the evolutionary process at
> > > all beyond the other non-directed selection mechanisms already in
> > > place in nature.
> >
> > Funny how the people who are actually decoding the Dog genome don't know
> > about the Pitman Conjecture of Evolution.
>
> The people decoding the dog genome are not the people who were
> responsible for dog breeding for thousands of years. Generally
> speaking, breeding has been done and is being done without any
> understanding of the underlying genetic code. Breeding is purely
> phenotypically based.
No, the people alive today have not been alive for thousands of years.
> > "Minor differences arise between individuals in a species through
natural
> > processes of mutation. Most mutations are harmful and decrease the
chance of
> > survival. However, for those few mutations that cause a favorable change
> > that enhance survival, the mutations will spread throughout the
population
> > due to the enhanced survival of the individuals with the mutation. The
> > accumulation of mutations over time leads to the creation of new
species."
> > http://mendel.berkeley.edu/dog/manifesto.html
>
> Again, if a phenotypically expressed mutation happens to occur, a
> breeder can select for the expressed phenotypic change, but this
> selection is not based on a genotypic understanding or ability to
> predict that the genotypic change will be able to combine with some
> other underlying genotype for another desirable trait to form a new
> unified trait. Being able to read and select based on genotype and
> genotypic combinations with futuristic intent is far far different
> from what breeders do.
When random mutations occur, they make use of the opportunity through
breeding and culling. Breeders certainly are concerned about the future
possibilities of their efforts, and modern science allows them to understand
and surpass the limits of their methods.
> > Or breeders themselves who wait generations (in dog years) for
> > attractive mutations.
> >
> > "When creating a new breed from an attractive mutation, the gene pool is
> > initially necessarily small with frequent matings between related dogs."
> > http://www.petpeoplesplace.com/Care/Cats/004/17p3.htm
> > http://www.dogbreedinfo.com/inbreeding.htm
>
> The creation of new "breeds" from the same gene pool, is not based on
> anything more than Mendelian genetics.
This is obviously incorrect and shows your ignorance of the history of
breeding.
> It is not based to any
> significant degree on mutations, but on the specific recombination of
> a limited variety of alleles for specific allelic positions in a
> specific type of gene pool.
This is simply false and is contrary to experts in breeding--people who have
a practical interest in the outcome of their efforts.
> No new information is created here.
Saying it doesn't make it so.
> The
> only thing that happens is that a different part of the potential a
> fairly fixed gene pool is reflected or expressed. That is all. Take
> for example me and my brother. We look very different from each other
> even though we came from the exact same gene pool. Our differences
> could be selected and enhanced within the limits of our gene pool
> options, but this does NOT entail the evolution of any new genetic
> information at all. Therefore, this sort of change over time, which
> is the same as what Darwin observed, is not enough, by itself, to
> explain those high level differences between life forms that do
> actually require novel information differences between gene pools.
You can't really be that confused, can you? Do you really think that
geneticists never considered this?
> > > You, on the other hand, are trying to "manually" select genotypic
> > > sequences based on your knowledge how various genotypic combinations
> > > work together that are not yet present in the gene pool of options.
> >
> > The Word Mutator does not require human intervention, though it is
certainly
> > one option available if you so desire to control the process. Or you
could
> > change the code if you prefer z-words, if you want. Or just leave it set
to
> > length and let the process operate "naturally".
>
> The problem here is that you actually _did_ select changes based on
> your knowledge of how the genotype, not just the phenotype, works and
> interacts phenotypically according to futuristic goals. Nature cannot
> do this. Even human breeders cannot do this if, as is usually done,
> they based all of their selections on phenotypic changes alone.
The Word Mutagenator doesn't require human intervention. Put in a 2- or
3-letter word and out it spits new and longer words.
> Certainly the genotypes of many creatures are being investigated and
> understood to a greater and greater degree, but whenever changes are
> selected on the basis of a direct understanding of the genotypic
> changes that are taking place as well as what these changes mean
> phenotypically, this is not purely phenotypically-based evolution, but
> genotypically _designed_ selection. Genotypic selection is out of the
> question since natural processes of lesser complexity than human
> intelligence do not have access to this ability.
>
> > > It would be like starting with a calculator program, which you see on
> > > your computer monitor, and having the underlying code for this program
> > > produce several offspring programs with underlying code mutations, and
> > > you picking between the underlying codes based ONLY on the changes in
> > > calculator function that you see on your screen.
> >
> > That's what the Word Mutator does. It just picks the longest ones
without
> > regard to their future utility in creating even longer words. There is
no
> > way for the program to know if a particular word is a dead-end. It does
not
> > anticipate.
>
> That is not what I am talking about. I am talking about your own
> admission that you directly selected for changes "manually" to achieve
> certain results. That "manual" selection by you is not allowed.
Fine. You will go on and on, but you keep forgetting. Anyone can download
the Mutagenator and see that manual intervention is not required. New and
long words are evolved without human intervention.
> And,
> the computer can only select based on what works right now (according
> to definition of "meaningful"). Of course you haven't programmed the
> computer to select for futuristic goals, but I mention this because
> other people have set up their evolutionary scenarios based on
> pre-established futuristic goals.
>
> > Indeed, animal breeders are in a similar position. When
> > selecting for a large dog, they don't know if other problems of design
will
> > inhibit further increases in size. Large dogs have problems with hips,
for
> > instance.
>
> Exactly. This is my whole point. Without a direct knowledge of the
> genotype and the ability to foresee how various genotypic selections
> will probably interact if combined, animal breeders are in exactly the
> same position as any other phenotypic-only selection based system.
<snip>
Yet, the Word Mutagenator uses very simple rules of random mutation and
selection to evolve long words without human intervention and without any
foresight. And it does it in less than a zillion years. Anyone can download
the Mutagenator and see for themselves.
http://www.zachriel.com/mutagenation/
Zachriel
"Sean Pitman" <seanpi...@naturalselection.0catch.com> wrote in message
news:80d0c26f.04050...@posting.google.com...
> >
> > The Word Mutator does not require human intervention, though it is
certainly
> > one option available if you so desire to control the process. Or you
could
> > change the code if you prefer z-words, if you want. Or just leave it set
to
> > length and let the process operate "naturally".
>
> The problem here is that you actually _did_ select changes based on
> your knowledge of how the genotype, not just the phenotype, works and
> interacts phenotypically according to futuristic goals. Nature cannot
> do this. Even human breeders cannot do this if, as is usually done,
> they based all of their selections on phenotypic changes alone.
No. Why do you keep saying that. You "can" select after each generation, but
it isn't required, and isn't the default behavior of the program.
<snip>
Forget the manual selection. Are you intentionally diverting attention from
the basic fact that without human intervention, Mutagenation can discover
long words in much less time that you had asserted?
http://www.zachriel.com/mutagenation/
Sean Pitman
> > That is not what I am talking about. I am talking about your own
> > admission that you directly selected for changes "manually" to achieve
> > certain results. That "manual" selection by you is not allowed. And,
> > the computer can only select based on what works right now (according
> > to definition of "meaningful"). Of course you haven't programmed the
> > computer to select for futuristic goals, but I mention this because
> > other people have set up their evolutionary scenarios based on
> > pre-established futuristic goals.
> <snip>
>
> Forget the manual selection. Are you intentionally diverting attention from
> the basic fact that without human intervention, Mutagenation can discover
> long words in much less time that you had asserted?
> http://www.zachriel.com/mutagenation/
As you yourself recognize, I never asserted that the relatively short
sequences your refer to as "long" could not be evolved in the time
your programs evolved them, especially with the use of the incredibly
high mutation rates and/or generation times that you use in your
"simulations".
If you will notice your very first post in this thread and my very
first response to that post where I wrote the following challenge:
> > So, what you
> > "start with" is quite important to determining what is and what is
> > not beneficial. Then, beyond this, say you start with a short
> > sequence, like a two or three-letter word that is defined or
> > recognized as beneficial by a much larger system of function, such as
> > a living cell or an English language system. Try evolving this short
> > word, one letter at a time, into a longer and longer word or phrase.
> > See how far you can go. Very quickly you will find yourself running
> > into walls of non-beneficial function.
Notice that I specifically challenged you to evolve a "longer and
longer word or _phrase_" beginning with a 2- or 3-letter word. You
yourself listed this challenge in your initial post as representative
of my position. Though, on your website, you represent my argument as:
"So, to evolve a three-letter word is easy, but anything longer than
seven letters or so is virtually impossible."
Where did I ever say that to evolve anything even close to a 7-letter
sequence "is virtually impossible"? This is an outright fabrication,
or at best a gross exaggeration. In fact, this did not seem to be your
initial understanding of my position at all. In your initial posts to
this thread you went even farther in clarifying what you meant in your
response my challenge with the following statement:
> First you made this challenge. I responded with a word puzzle where,
> starting with the single letter word "O", and by only changing one
> letter at a time, and with concatenation, I constructed the phrase,
> "Beware a war of words, Sean Pitman, ere you err."
>
> We can trace the "etymology" of each word used in the poem. Some
> of the more difficult words to create include "light", "choose",
> "instead" and "simple".
Notice that you talked about phrase evolution like this is what we had
been talking about all along . . . and it was. I never drew any sort
of "line of impossibility" at the level of "7-letter sequences" and
you obviously recognized this in your initial arguments. I really
don't know how your memory forgot this so quickly? What happened
Zach? After all, your own "rules" for your evolutionary scenario went
like this:
> Rules: Change only one letter at a time from any existing string.
> Can concatenate any two strings. However, only one operation at
> a time. All words, phrases and sentences must make sense in
> standard English.
Do you notice that word "phrases" as part of the description in your
rules? Clearly this was included in the challenge. The challenge is
not and never was limited to "single words" or even such relatively
short phrases as 7-letters or those even close to this extremely low
level of relative complexity. This is quite obvious from how I
responded to your initial posts. I ask you, was I bothered by your
inclusion of the word "phrases" into your rules? Clearly, I was not
bothered at all by this, as evidenced by my response. My disturbance
was not with your inclusion of "phrases" or even long "poems" into the
challenge, but your concept of "concatenation" as part of the rules.
You believed and maybe even still believe that there were only "two
ways to concatenate [join together] two phrases." I went on to point
out to you that just because you happen to have the right words in the
same population does not mean that they will just join together
correctly to form a new united meaningful sequence of combined length
since there are many possible non-meaningful ways that they could
combine (far more than just the two ways that you initially claimed).
Obviously, this fact raises the average time required for a "correct"
uniting mutation to be realized. But, you didn't seem to understand
this concept and I don't think you understand it even now. In any
case though, even in my illustration I did not use single words, but
complete sentences to prove my point. Clearly then, I was not
limiting myself to single words like "7-letter sequences" or anything
even close.
At the end of my response I even clarified by saying, "So, you simply
cannot get from "O" to "Beware a war of words, Sean Pitman, ere you
err" without crossing significant gaps of neutral or even detrimental
meaning/function."
Note that in this challenge I did not come even close to drawing the
"impassable line" at single 7-letter word sequences - or 14-characters
or even of 20-charcters in size. Notice that the "evolved" phrase of
yours that I quoted is 47 characters in size. And notice that I did
NOT say that even this line was an "impossible" gap. What I said was
that a 47-character sequence would produce a "significant" gap - even
for very large populations with very high reproductive rates and
mutation rates (such as those used in your "simulations"). And, I have
been arguing this very same point for several years, as my website and
other posts will testify to despite your continual taking of my quotes
out of context.
In fact Zach, it was in response to a long "poem evolution" scenario
of yours - via intelligent design I might add, that I made the
following challenge:
"This is a great story, but sadly, it is statistically impossible. Go
ahead and try it. Based on your rules you should be able to program a
computer to evolve new functions requiring higher and higher levels of
informational input using this method. The problem here is that there
simply is not enough time this size of zillions of years to get the
limited number of phrases to "bump together" enough times to make
anything beyond the lowest levels of functional complexity without the
input of a higher intelligence or pre-established information system.
It just won't happen. Try it and see."
You quoted only part of this challenge on your website, out of the
context of your "evolving poem" scenario, and indicated instead that I
believed the evolution of much shorter single word sequence, very
close to 7-letters in size, to be "impossible." The quote of me on
the front page of your website reads:
"The problem here is that there simply is not enough time this side
of zillions of years to get the limited number of phrases to "bump
together" enough times to make anything beyond the lowest levels of
functional complexity without the input of a higher intelligence or
pre-established information system. It just won't happen. Try it and
see."
You then immediately follow that quote up with a statement that my
line of "impossibility" is very close to 7-characters in size. What a
crock!
Notice that even here the word "phrases" is mentioned. Did you
mention to your readers _why_ I said that "phrases" could not bump
together often enough to evolve anything beyond the lowest levels of
functional complexity? Did you tell them that this statement was in
response to your claim that an entire poem with hundreds and even
thousands of characters could evolve via mindless evolutionary
mechanisms? Hmmmmm? Did you tell your readers that I very strongly
indicated that the "line of impossibility" was not even close to
7-characters for the parameters that you use in your computer
scenarios, but rather much closer to hundreds or at least a 1,000
characters in size? No. Instead, you deliberately mislead your
readers into thinking my position was and is something that it clearly
is not - and you obviously knew this when you published your website.
That, in my book, is a deliberate fabrication and outlandish strawman
building if I ever saw it.
Zachriel
"Sean Pitman" <seanpi...@naturalselection.0catch.com> wrote in message
news:80d0c26f.04050...@posting.google.com...
news:<8cidnXXWQ6b...@adelphia.com>...
>
> > > That is not what I am talking about. I am talking about your own
> > > admission that you directly selected for changes "manually" to achieve
> > > certain results. That "manual" selection by you is not allowed. And,
> > > the computer can only select based on what works right now (according
> > > to definition of "meaningful"). Of course you haven't programmed the
> > > computer to select for futuristic goals, but I mention this because
> > > other people have set up their evolutionary scenarios based on
> > > pre-established futuristic goals.
> > <snip>
> >
> > Forget the manual selection. Are you intentionally diverting attention
from
> > the basic fact that without human intervention, Mutagenation can
discover
> > long words in much less time that you had asserted?
> > http://www.zachriel.com/mutagenation/
>
> As you yourself recognize, I never asserted that the relatively short
> sequences your refer to as "long" could not be evolved in the time
> your programs evolved them, especially with the use of the incredibly
> high mutation rates and/or generation times that you use in your
> "simulations".
You clearly stated that it would take 26^L / N average number of random
mutations to, starting at a word of length L, to find another word of length
L (where N is the number of words of that length). This has been shown to be
incorrect. It is quite enough that you have repudiated this stance. Let's
leave it at that.
<snip variations on the same theme>
Pitman Series
9
16
29
192
2,522
39,034
714,828
16,813,773
468,545,364
14,460,878,473
516,949,927,745
19,782,122,027,712
835,686,383,699,473
39,263,526,904,015,300
1,869,854,339,226,000,000
100,946,164,119,048,000,000
5,107,330,249,482,660,000,000
368,493,877,500,174,000,000,000
19,653,006,800,009,300,000,000,000
1,532,934,530,400,720,000,000,000,000
64,766,483,909,430,600,000,000,000,000
4,490,476,217,720,520,000,000,000,000,000
175,128,572,491,100,000,000,000,000,000,000
Sean Pitman
> > As you yourself recognize, I never asserted that the relatively short
> > sequences your refer to as "long" could not be evolved in the time
> > your programs evolved them, especially with the use of the incredibly
> > high mutation rates and/or generation times that you use in your
> > "simulations".
>
> You clearly stated that it would take 26^L / N average number of random
> mutations to, starting at a word of length L, to find another word of length
> L (where N is the number of words of that length). This has been shown to be
> incorrect. It is quite enough that you have repudiated this stance. Let's
> leave it at that.
But I haven't "repudiated this stance" in any significant way and you
haven't shown it to be significantly in error either. Did you do the
ratio calculation that I asked you to do? What ratio change did you
find with each level of increasing complexity? What was the ratio of
meaningful vs. non-meaningful at the 3-letter level compared with the
6-letter level?
You see Zach, what you have shown is that islands of meaningful
sequences exist in sequence space where the average distance is indeed
less than 26^L/N (and yet the ratio still increases exponentially even
within these islands with each step up the ladder). I have no problem
with that at all. This has always been very obvious to me. In fact,
I have never had a problem with this notion of islands clusters.
Clearly then, your bold assertion on your website and in this thread
that my position draws an absolutely impassable line at about the
"7-character" level is nothing less than deliberate strawman building
on your part - especially given your most generous program parameters
of extremely high reproductive rates and mutation rates.
Go ahead and see if this is not true Zach. Go ahead and read the very
first post you made to start out this thread. And then, read the very
first post that I made in response and see if that doesn't jar your
memory just a bit.
Zachriel
"Sean Pitman" <seanpi...@naturalselection.0catch.com> wrote in message
news:80d0c26f.04050...@posting.google.com...
news:<6-udndtaI8i...@adelphia.com>...
>
> > > As you yourself recognize, I never asserted that the relatively short
> > > sequences your refer to as "long" could not be evolved in the time
> > > your programs evolved them, especially with the use of the incredibly
> > > high mutation rates and/or generation times that you use in your
> > > "simulations".
> >
> > You clearly stated that it would take 26^L / N average number of random
> > mutations to, starting at a word of length L, to find another word of
length
> > L (where N is the number of words of that length). This has been shown
to be
> > incorrect. It is quite enough that you have repudiated this stance.
Let's
> > leave it at that.
>
> But I haven't "repudiated this stance" in any significant way
Sure you did. You moved the goal-posts outside the reach of our VBA program.
Our desktop computer can handle about a million relevant computations per
minute, consequently, it can handle a variety of strings with a combined
length of a few hundred. This was more than sufficient to answer the
specific challenge, and to verify the general limit calculation.
I can't write code as fast as you can move the goal-posts. Fortunately, I
have no illusion of being able to convince the unconvincible. This program
was for the benefit of those who might actually take your assertions
seriously, and for that purpose, I'm sure it served its purpose. Plus it was
fun.
> and you
> haven't shown it to be significantly in error either. Did you do the
> ratio calculation that I asked you to do? What ratio change did you
> find with each level of increasing complexity?
This is simply incredible.
I analyzed an ~80K dictionary by length of word. Created a program that
calculates every possible mutation for a given length of word, even more,
calculated every possible mutation for a disparate collection of words of
varying length, then compared the posited upper-bound of (L+2)^2 with the
actual calculation, compiled the data into a spreadsheet; and yet, and yet.
.. . well, it's simply incredible. . . you actually claim I haven't provided
the information!
Here's the spreadsheet, updated with Pitman Numbers.
http://www.zachriel.com/Mutagenation/calcs.xls
> What was the ratio of
> meaningful vs. non-meaningful at the 3-letter level compared with the
> 6-letter level?
You are referring to the Pitman Number, the ratio of total permutations of
26 letters, to the permutations that actually exist in the Dictionary. Using
our ~80K Dictionary, the Pitman Number (3) = 29. The Pitman Number(6) =
39,034. You then made the claim that this means words of length six are
thousands of times less likely to evolve than words of length three. This is
a false claim. Are you really going to make me quote you again?
This was the claim:
"Getting from one meaningful 7-letter phrase to a different meaningful
7-letter phrase requires, on average, a fairly long random walk through
250,000 meaningless options."
http://tinyurl.com/ypos7
Or to reprase it:
"Getting from one meaningful L-letter phrase to a different meaningful
L-letter phrase requires, on average, a fairly long random walk through
Pitman Number(L) meaningless options."
http://tinyurl.com/ypos7
You were wrong. We don't have to walk through all that space randomly. The
average is much, much less that you claim.
# of Words
(by length)
3
43
606
2385
4712
7914
11236
12420
11588
9762
7100
4824
2969
1643
897
432
222
80
39
13
8
3
2
---------
78901
> You see Zach, what you have shown is that islands of meaningful
> sequences exist in sequence space where the average distance is indeed
> less than 26^L/N (and yet the ratio still increases exponentially even
> within these islands with each step up the ladder).
You should think of them as archipelagos. We can navigate from one end of
the ocean to the other, step-by-step. This is because words are not random
collections of letters, but closely related due to their own historical
evolution. Indeed, most words are themselves collections of shorter
word-parts, either in English or Latin. Anyone playing with the Word Mutator
can see this. One word leads to another closely related word, such as
"flinch", "flinching", "unflinching", "unflinchingly"; or consider
"denominationalists" which is made of a variety of word-parts, "de", "nom",
"in", "a", "tion", "al", "ist", "s".
> I have no problem
> with that at all. This has always been very obvious to me. In fact,
> I have never had a problem with this notion of islands clusters.
Your analogy is faulty and leads you to false conclusions. Analogies can be
aids, but shouldn't be used as crutches. Beware a war of words.
> Clearly then, your bold assertion on your website and in this thread
> that my position draws an absolutely impassable line at about the
> "7-character" level is nothing less than deliberate strawman building
> on your part - especially given your most generous program parameters
> of extremely high reproductive rates and mutation rates.
You said that it would take a random walk through hundreds-of-thousands
(Pitman Number(7)) of permutations (which is false), and that by
extrapolation, longer words and phrases would take a random walk through
"zillions" of permuations (which is also false).
> Go ahead and see if this is not true Zach. Go ahead and read the very
> first post you made to start out this thread. And then, read the very
> first post that I made in response and see if that doesn't jar your
> memory just a bit.
You said, "You must consider the odds that they will concatenate themselves
in a meaningful way vs. all the huge numbers of meaningless/non-beneficial
possibilities that also exist."
So that's what I did.
Sean Pitman
> > Did you do the
> > ratio calculation that I asked you to do? What ratio change did you
> > find with each level of increasing complexity?
>
> This is simply incredible.
>
> I analyzed an ~80K dictionary by length of word. Created a program that
> calculates every possible mutation for a given length of word, even more,
> calculated every possible mutation for a disparate collection of words of
> varying length, then compared the posited upper-bound of (L+2)^2 with the
> actual calculation, compiled the data into a spreadsheet; and yet, and yet.
> .. . well, it's simply incredible. . . you actually claim I haven't provided
> the information!
But you haven't provided the information I asked for. Look Zach, what
you provided here were the number of possible mutations according to
your setup. This is not what I asked you to do. I asked you to show
the ratio of meaningful vs. non-meaningful mutations for each level.
Only in that way could you see how many mutations it would take, on
average, to find a new meaningful word at a given level of complexity.
> Here's the spreadsheet, updated with Pitman Numbers.
> http://www.zachriel.com/Mutagenation/calcs.xls
I see no ratios of meaning vs. non-meaning listed on this spreadsheet.
> > What was the ratio of
> > meaningful vs. non-meaningful at the 3-letter level compared with the
> > 6-letter level?
>
> You are referring to the Pitman Number, the ratio of total permutations of
> 26 letters, to the permutations that actually exist in the Dictionary.
No. What I am referring to here is the average number of mutations
that _your_ computer program(s) required to find new meaningful
sequences at a given level or higher. What was the actual ratio that
your computer simulation found?
> Using
> our ~80K Dictionary, the Pitman Number (3) = 29. The Pitman Number(6) =
> 39,034. You then made the claim that this means words of length six are
> thousands of times less likely to evolve than words of length three. This is
> a false claim. Are you really going to make me quote you again?
This is not a false claim. This is exactly correct. The ratios give
you the _average_ number of mutations it would take to find a new
meaningful sequence (an English word in this case) at a minimum
sequence length. Again, what was the ratio that your computer found
for level 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 . . . ect.? I've asked you
to list this several times and you keep stalling. Don't list what you
think my ratios are. List what your ratios are.
Again, this exponentially growing average ratio of meaningful vs.
meaningless that you will find means exactly what I said it does. It
tells you the average number of mutations it takes to get from your
starting island to any other word within that island. Obviously, the
difficulty of finding a new meaningful word/sequence expands
exponentially with each step up the ladder even within islands of
words. According to your own observed ratios, even within your
clusters of islands with higher relative ratios than the surrounding
sequence space, this expansion is exponential and thus devastating to
your position.
> This was the claim:
>
> "Getting from one meaningful 7-letter phrase to a different meaningful
> 7-letter phrase requires, on average, a fairly long random walk through
> 250,000 meaningless options."
> http://tinyurl.com/ypos7
You never determined the actual overall "average" Zach. You only
determined islands and bridges having somewhat higher average ratios
than the overall average. Even here though, you have a significant
problem. Even your ratios that you have calculated yourself expand
exponentially so that you reach walls of impossibility very quickly by
extrapolation of even your numbers. Go ahead and do show your ratios
Zach. What was the ratio of meaningful vs. meaningless that your
computer programs came up with at each level that they evolved
meaningful words? For a given level, how many meaningless sequences,
on average, were sorted through before a meaningful sequence was
found?
> You were wrong. We don't have to walk through all that space randomly.
Yes, you do.
> The
> average is much, much less that you claim
For one thing Zach, even if the "average" was really "much less than I
claim", that wouldn't save your position. The fact of the matter is
that random walk exists even in your computer simulations. This
random walk also expands at an exponential rate in your computer
simulations. If it wasn't for your enormous reproductive rates and
mutation rates, your relatively small population would have to "swim
for it" much sooner than it currently does.
But, even with your parameters as your currently have them set, the
exponentially expanding random walk averages will quickly stall out
even your computer programs well shy of the 1,000-character level and
probably shy of the 100-character level. You mistakenly think that
your L^3 calculation means something as far as some sort of
extrapolation, but it means absolutely nothing since it says nothing,
even at very low levels, about the average ratios of meaningful vs.
meaningless. It therefore says nothing about random walk averages and
therefore cannot be extrapolated to say anything about the average
random walk time it will take at higher and higher levels of
meaningful complexity.
> > You see Zach, what you have shown is that islands of meaningful
> > sequences exist in sequence space where the average distance is indeed
> > less than 26^L/N (and yet the ratio still increases exponentially even
> > within these islands with each step up the ladder).
>
> You should think of them as archipelagos. We can navigate from one end of
> the ocean to the other, step-by-step. This is because words are not random
> collections of letters, but closely related due to their own historical
> evolution. Indeed, most words are themselves collections of shorter
> word-parts, either in English or Latin. Anyone playing with the Word Mutator
> can see this. One word leads to another closely related word, such as
> "flinch", "flinching", "unflinching", "unflinchingly"; or consider
> "denominationalists" which is made of a variety of word-parts, "de", "nom",
> "in", "a", "tion", "al", "ist", "s".
Certainly true. There are all kinds of little islands and
archipelagos everywhere in sequence space. The problem is that these
islands and archipelagoes start becoming smaller and smaller and more
and more isolated, in an exponential manner, with each step up the
ladder of meaningful sequence complexity. Even for very long phrases
and even 5,000-character poems there will be small islands and
archipelagos that can be easily traversed. But, on average, such
islands and archipelagoes will be extremely small and extremely
isolated from each other at such levels of complexity. They will be
clustered in the very narrow "types" of functions, widely separated
from other different potential types of meaningful functions. This
separation is so great, at fairly specified levels requiring more than
a few hundred characters or so, that getting from one type of
functional sequence to a different type of functional sequence
requires a practical eternity of average time.
This is what I have always claimed and I never intended otherwise.
This is easily seen if you just go back and read the first few posts
to this thread.
> > I have no problem
> > with that at all. This has always been very obvious to me. In fact,
> > I have never had a problem with this notion of islands clusters.
>
> Your analogy is faulty and leads you to false conclusions. Analogies can be
> aids, but shouldn't be used as crutches. Beware a war of words.
You're really something else Zach. You make the claim that my analogy
is faulty and yet your own programs show my analogy to work pretty
much as I always said it would work. You repeatedly warn me to
"Beware a war of words" - which is most amusing. You claim victory by
saying that my goalposts were in places that they obviously never
where. In fact, your own programs support my own contentions far more
than they support yours. You place your focus on relative minutia and
end up loosing the war. In fact, you effectively destroy your own
main position. You outflank yourself.
That is in fact why I am spending so much time with you. You actually
did something that supports my position, not yours. It is you who
have come up with faulty conclusions based on erroneous assumptions
and meaningless extrapolations of worthless calculations (i.e., your
L^3 calculation for example). Even you admitted yourself that the L^3
calculation says nothing about the likelihood of finding a meaningful
sequence, and yet you continue to use it in extrapolations that assume
this very thing. Does that really make much sense to you?
> > Clearly then, your bold assertion on your website and in this thread
> > that my position draws an absolutely impassable line at about the
> > "7-character" level is nothing less than deliberate strawman building
> > on your part - especially given your most generous program parameters
> > of extremely high reproductive rates and mutation rates.
>
> You said that it would take a random walk through hundreds-of-thousands
> (Pitman Number(7)) of permutations (which is false), and that by
> extrapolation, longer words and phrases would take a random walk through
> "zillions" of permuations (which is also false).
Again, you never calculated the actual average for 7-letter sequence
space. And, even if you did find that the true average was less than
a couple hundred thousand, it wouldn't be a "significant" difference.
You just don't seem to realize what you have done or what exponential
growth means. Your own computer simulations showed an exponentially
growing average neutral gap with each step up the ladder of meaningful
complexity. Don't you understand that this is very significant? It
means that your nice little lines and bridges are rapidly breaking
down between your archipelagos.
For example, for arguments sake lets just say that the average random
walk for the 7-letter level was only 1,000 mutations. The sequence
space in this setup may look like a giant grid of crisscrossing lines
of islands or archipelagos that are all obviously fairly closely
connected - relatively speaking. Lets say though that these islands
and lines separate in an exponential manner with each step up the
ladder so that with every doubling of the level number the random walk
increase by a factor of only 2. What would the random walk be at
level 14? Obviously, it would be 1,000 x 1,000 or 10^6 random walk
steps. At level 28 the average random walk would be 10^12 steps. At
level 56 the average random walk would be 10^24 steps . . . etc.
Are you starting to see the problem with the existence of
exponentially expanding neutral gaps even if they start out fairly
small? Very quickly the average neutral gaps really start to be a
very big problem, isolating most islands and breaking apart islands
from each other very quickly.
This is exactly what you will see happening with the English language
system once you start trying to evaluation longer and longer
sequences. For one thing, which should be very obvious to you,
valid/meaningful English language sentences and paragraphs and
passages, etc., just don't have the same historical "evolutionary"
history as single words do. They are not therefore going to be in such
nice little lined-up archipelagos throughout sequence space.
The same thing is true for meaningful genetic sequences of higher and
higher specified complexity. The 20 different amino acids that are
generally used by life forms are all pretty similar in structure and
even function. Like letters they often arrange themselves into various
similar families of protein domains or "words". These domains are
then combined in various orders to form single protein systems or
"phrases" or "sentences". These single protein systems can then be
combined with other protein systems to form higher unified systems of
proteins, often working together at the same time to give rise to a
particular function comparable to the interdependent function of a
English paragraph or other higher level English language work. And,
just like with the English language system, the nice interconnected
islands, bridges, and archipelagos start to quickly disintegrate, in
an exponential fashion, with each step up the ladder of functional
complexity.
> > Go ahead and see if this is not true Zach. Go ahead and read the very
> > first post you made to start out this thread. And then, read the very
> > first post that I made in response and see if that doesn't jar your
> > memory just a bit.
>
> You said, "You must consider the odds that they will concatenate themselves
> in a meaningful way vs. all the huge numbers of meaningless/non-beneficial
> possibilities that also exist."
>
> So that's what I did.
I also talked about poems the size of yours being "impossible" to
evolve. I drew the line of impossibility in these initial threads at
the size of your poem and specifically said that a 47-character
sequence would be "significantly" though not "impossibly" isolated by
neutral gaps. Please do read these initial posts again and then
compare what you actually did to my actual challenge.
Zachriel
"Sean Pitman" <seanpi...@naturalselection.0catch.com> wrote in message
news:80d0c26f.04050...@posting.google.com...
news:<iNidnWkBScA...@adelphia.com>...
>
> > > Did you do the
> > > ratio calculation that I asked you to do? What ratio change did you
> > > find with each level of increasing complexity?
> >
> > This is simply incredible.
> >
> > I analyzed an ~80K dictionary by length of word. Created a program that
> > calculates every possible mutation for a given length of word, even
more,
> > calculated every possible mutation for a disparate collection of words
of
> > varying length, then compared the posited upper-bound of (L+2)^2 with
the
> > actual calculation, compiled the data into a spreadsheet; and yet, and
yet.
> > .. . well, it's simply incredible. . . you actually claim I haven't
provided
> > the information!
>
> But you haven't provided the information I asked for.
I am simply amazed.
> Look Zach, what
> you provided here were the number of possible mutations according to
> your setup. This is not what I asked you to do. I asked you to show
> the ratio of meaningful vs. non-meaningful mutations for each level.
Amazing. Well to repeat once again and to answer your specific question, the
answer requires a Dictionary. I have provided a common dictionary of ~80K
words. The Pitman Number(L) = number of possible permutations of letters,
26^L divided by the number of valid words of that length represents the
"ratio of meaningful vs. non-meaningful" WORDS, but *not* the ratio of such
mutations. Mutations are temporal and can only be considered in relation to
change.
(As an example, and starting from any valid word, "qqqqqqq" is *not* an
available mutation. It is never a valid mutation.)
> Only in that way could you see how many mutations it would take, on
> average, to find a new meaningful word at a given level of complexity.
And this is false. You keep repeating this but provide no mathematical
justification for this leap. Indeed, it is directly contrary to the
evidence. Words are not distributed randomly, and if you start from a valid
word, you will find other words closely related, which lead to still other
words.
> > Here's the spreadsheet, updated with Pitman Numbers.
> > http://www.zachriel.com/Mutagenation/calcs.xls
>
> I see no ratios of meaning vs. non-meaning listed on this spreadsheet.
Sure you do. We have the ratio of all permutations to the number of valid
words (Pitman Number). The inverse of the Pitman number has always been on
the Dictionary page ("Chance"), but we've added the proper Pitman Number to
the Calc.xls spreadsheet as well. However, you then make this mental
substitution:
ratio of meaningful vs. non-meaningful *words*
to
ratio of meaningful vs. non-meaningful *mutations*
These are not the same numbers. And for me, this represents and "Aha!", so
that's what Sean is thinking.
> > > What was the ratio of
> > > meaningful vs. non-meaningful at the 3-letter level compared with the
> > > 6-letter level?
> >
> > You are referring to the Pitman Number, the ratio of total permutations
of
> > 26 letters, to the permutations that actually exist in the Dictionary.
>
> No. What I am referring to here is the average number of mutations
> that _your_ computer program(s) required to find new meaningful
> sequences at a given level or higher. What was the actual ratio that
> your computer simulation found?
It depends on the word. That's why I built a simulator. However, in all
cases it was less, usually much less, than the Pitman Number. We do know
that if there is a path to another word, that the maximum number of
mutations required is less than L^3 per generation. So if we know this,
peace
pace
paced
then we know that the number of mutations, including recombinations, is less
than 5^3 = 125 per generation. I could spell out every single mutation for
you, but we've been down that route already.
> > Using
> > our ~80K Dictionary, the Pitman Number (3) = 29. The Pitman Number(6) =
> > 39,034. You then made the claim that this means words of length six are
> > thousands of times less likely to evolve than words of length three.
This is
> > a false claim. Are you really going to make me quote you again?
>
> This is not a false claim. This is exactly correct. The ratios give
> you the _average_ number of mutations it would take to find a new
> meaningful sequence (an English word in this case) at a minimum
> sequence length.
This is incorrect. It gives you the ratio of all permutations to valid
words. This is not the same as the number of mutations. We don't have to
search randomly. We can use mutation and selection.
> Again, what was the ratio that your computer found
> for level 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 . . . ect.? I've asked you
> to list this several times and you keep stalling. Don't list what you
> think my ratios are. List what your ratios are.
Everybody knows that I have provided the answer. The problem isn't the
simplistic calculation of the Pitman Number, but the fact that you assert
incorrectly that only random means will find the path to other words.
> Again, this exponentially growing average ratio of meaningful vs.
> meaningless that you will find means exactly what I said it does. It
> tells you the average number of mutations it takes to get from your
> starting island to any other word within that island. Obviously, the
> difficulty of finding a new meaningful word/sequence expands
> exponentially with each step up the ladder even within islands of
> words. According to your own observed ratios, even within your
> clusters of islands with higher relative ratios than the surrounding
> sequence space, this expansion is exponential and thus devastating to
> your position.
Except that Word Mutator can find new words in much less than a Pitman
Number of attempts. This directly contradicts your assertion.
> > This was the claim:
> >
> > "Getting from one meaningful 7-letter phrase to a different meaningful
> > 7-letter phrase requires, on average, a fairly long random walk through
> > 250,000 meaningless options."
> > http://tinyurl.com/ypos7
>
> You never determined the actual overall "average" Zach.
I never claimed to be able to determine the average of every word in our
Dictionary. However, you are more than welcome to plug them all into our
Word Mutator, if you like. I claimed only to set an upper-limit on the
number mutations per generation--contary to your own
"calculations"--required for words with known paths. And it appears that
there are paths for just about every word in our Dictionary to just about
any other word.
> You only
> determined islands and bridges having somewhat higher average ratios
> than the overall average.
Yeah, just every word I've tried. You are more than welcome to look for
counterexamples. The closest I have come is made-up words like "qqqqqqq"
which are completely sterile.
What is really disappointing, Sean, is that we can't even begin to
understand the process if you keep pretending you can't see it happening
before your eyes. There really are limits to our analogous word-game, but
they are completely unavailable to your present understanding.
> Even here though, you have a significant
> problem. Even your ratios that you have calculated yourself expand
> exponentially so that you reach walls of impossibility very quickly by
> extrapolation of even your numbers.
There is an upper-limit of L^3. For a string of a hundred letters, we must
sort through at most a million mutations per generation. However, that is
considerably less than your assertion that it requires a Pitman Number(100)
or
3,142,930,641,582,940,000,000,000,000,
000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,
000,000
number of trails.
There is a significant difference between millions and zillions.
> Go ahead and do show your ratios
> Zach. What was the ratio of meaningful vs. meaningless that your
> computer programs came up with at each level that they evolved
> meaningful words? For a given level, how many meaningless sequences,
> on average, were sorted through before a meaningful sequence was
> found?
Let's take an example from your own prose.
Word Mutator
-------------------
Pond Size = 25 (default)
Starting word "sequence", length 8
1 Generations
845 mutations
Discovered "sequences", length 9
4 Generations
160862 mutations
Discovered "precedence", length 10
The Pitman Number(10) is 14,460,878,473, and yet we found new words in far
fewer trials than that. How did the Word Mutator cross through that ocean of
14 billion permutations to stumble across "precedence"? Blind luck? Well,
let's try another word from your prose.
Word Mutator
-------------------
Pond Size = 25 (default)
Starting word "computer", length 8
1 Generations
23176 mutations
Discovered "computers", length 9
4 Generations
408586 mutations
Discovered "completeness", length 12
The Pitman Number(12) is 19,782,122,027,712! Wow, we must be very, very
lucky. I should really play the horses. Anyone can play this game. If you
prefer, you can use random mutation with the Word Mutagenator.
Word Mutagenator
--------------------------
Pond Size = 100 (default)
Starting word "evolved", length 7
~2 seconds
58709 mutations
Discovered "soldered", "hideouts", length 8
~6 seconds
155283 mutations
Discovered "inversions", length 10
~14 seconds
350776 mutations
Discovered "spluttering", length 11
~ 55 seconds
1335430 mutations
Discovered "constraining", length 12
> > You were wrong. We don't have to walk through all that space randomly.
>
> Yes, you do.
Apparently not. This is the crux of your blindness.
> > The
> > average is much, much less that you claim
>
> For one thing Zach, even if the "average" was really "much less than I
> claim", that wouldn't save your position.
Sure it would. I was disputing your specific claim. If you are wrong by a
factor of a few zillion, then you should just admit it.
> The fact of the matter is
> that random walk exists even in your computer simulations.
Random mutation plus selection.
> This
> random walk also expands at an exponential rate in your computer
> simulations. If it wasn't for your enormous reproductive rates and
> mutation rates, your relatively small population would have to "swim
> for it" much sooner than it currently does.
As I have mentioned, if you don't want to compute every possible mutation
per generation, you can use the Word Mutagenator, which takes one random
mutation at a time.
> But, even with your parameters as your currently have them set, the
> exponentially expanding random walk averages will quickly stall out
> even your computer programs well shy of the 1,000-character level and
> probably shy of the 100-character level.
We have no well-defined validation method for strings longer than words. If
you have one, let us know.
> You mistakenly think that
> your L^3 calculation means something as far as some sort of
> extrapolation, but it means absolutely nothing since it says nothing,
> even at very low levels, about the average ratios of meaningful vs.
> meaningless.
What is means is that this assertion of yours is false:
"Getting from one meaningful 7-letter phrase to a different meaningful
7-letter phrase requires, on average, a fairly long random walk through
250,000 meaningless options."
http://tinyurl.com/ypos7
It's really a shame you haven't even attempted to dispute this on valid
grounds, such as by finding words that have no paths or very long paths to
their nearest words. You have never provided a single word that doesn't have
neighbors.
For instance, if any part of the word contains a smaller word, even "a" or
"i", then it probably has close neighbors. So you could look for words in
our Dictionary with "u" and "y" for its vowels. I've tried, "why" and other
such words, but to no avail.
why
way
a
and all the words that follow from "a"
The distribution of words in sequence space is not a matter of guess word,
nor of blind assertion, but a fact like the geography of North America. You
find its navigable rivers by exploration, not by sitting in your armchair
and thinking about it.
> It therefore says nothing about random walk averages and
> therefore cannot be extrapolated to say anything about the average
> random walk time it will take at higher and higher levels of
> meaningful complexity.
A meaningful counter-example would be helpful right about now. We're not
dealing with random letters, but actual words.
An easy assertion to make, but you have provided no evidence other than your
ignorance of the actual distribution.
> This is what I have always claimed and I never intended otherwise.
> This is easily seen if you just go back and read the first few posts
> to this thread.
I've read them several times. This was your claim,
"Getting from one meaningful 7-letter phrase to a different meaningful
7-letter phrase requires, on average, a fairly long random walk through
250,000 meaningless options."
http://tinyurl.com/ypos7
This is false. When you admit this and try to understand why you were wrong,
then perhaps this discussion can progress. For me, it has been worthwhile
simply because I got to play with Mutagenation.
> > > I have no problem
> > > with that at all. This has always been very obvious to me. In fact,
> > > I have never had a problem with this notion of islands clusters.
> >
> > Your analogy is faulty and leads you to false conclusions. Analogies can
be
> > aids, but shouldn't be used as crutches. Beware a war of words.
>
> You're really something else Zach. You make the claim that my analogy
> is faulty and yet your own programs show my analogy to work pretty
> much as I always said it would work.
It clearly demonstrates you were wrong. You claim the compuational
difficulty of the problem increases with the Pitman Number. It does not. It
increase with (at most) L^3. They are very, very different numbers.
> You repeatedly warn me to
> "Beware a war of words" - which is most amusing. You claim victory by
> saying that my goalposts were in places that they obviously never
> where.
This is the goalpost I played for:
"Getting from one meaningful [L]-letter phrase to a different meaningful
[L]-letter phrase requires, on average, a fairly long random walk through
[Pitman Number(L)] meaningless options."
http://tinyurl.com/ypos7
When I got there it was gone. No less than I expected though. Again, I have
no illusion of being able to convince the unconvincible.
> In fact, your own programs support my own contentions far more
> than they support yours.
Nonsense. Not all "exponential" equations are equal.
If L = 20, then L^3 = 8000, but the Pitman Number(20) =
19,653,006,800,009,300,000,000,000. That's a pretty significant difference.
> You place your focus on relative minutia and
> end up loosing the war. In fact, you effectively destroy your own
> main position. You outflank yourself.
Being off by a factor of, well, zillions, is not "relative minutia".
> That is in fact why I am spending so much time with you. You actually
> did something that supports my position, not yours. It is you who
> have come up with faulty conclusions based on erroneous assumptions
> and meaningless extrapolations of worthless calculations (i.e., your
> L^3 calculation for example). Even you admitted yourself that the L^3
> calculation says nothing about the likelihood of finding a meaningful
> sequence, and yet you continue to use it in extrapolations that assume
> this very thing. Does that really make much sense to you?
The L^3 is the upper-limit of how many possible point mutations and
recombinations of a string of length L, or a collection of strings with a
combined length of L are available per generation. The actual number of
calcuations depends on the number of strings and their lengths, and will
generally be much less than L^3 per generation.
> > > Clearly then, your bold assertion on your website and in this thread
> > > that my position draws an absolutely impassable line at about the
> > > "7-character" level is nothing less than deliberate strawman building
> > > on your part - especially given your most generous program parameters
> > > of extremely high reproductive rates and mutation rates.
> >
> > You said that it would take a random walk through hundreds-of-thousands
> > (Pitman Number(7)) of permutations (which is false), and that by
> > extrapolation, longer words and phrases would take a random walk through
> > "zillions" of permuations (which is also false).
>
> Again, you never calculated the actual average for 7-letter sequence
> space. And, even if you did find that the true average was less than
> a couple hundred thousand, it wouldn't be a "significant" difference.
Well, there you are. A millions years, a zillions years, the next thing you
know we're talking real eons.
> You just don't seem to realize what you have done or what exponential
> growth means.
I know exactly what exponential growth is, and not all exponential functions
are the same.
> Your own computer simulations showed an exponentially
> growing average neutral gap with each step up the ladder of meaningful
> complexity.
Yes, from the very beginning I claimed an upper-limit of L^3 per generation.
Your argument for both the evolution of words and the evolution of genetics
is off by a few zillion.
> Don't you understand that this is very significant? It
> means that your nice little lines and bridges are rapidly breaking
> down between your archipelagos.
It means for a hundred letters, there are at most a million possible
mutations (actually a bit less than 525,726) per generation. The number of
generations depends on the actual distribution of valid strings and the
method of selection.
> For example, for arguments sake lets just say that the average random
> walk for the 7-letter level was only 1,000 mutations. The sequence
> space in this setup may look like a giant grid of crisscrossing lines
> of islands or archipelagos that are all obviously fairly closely
> connected - relatively speaking. Lets say though that these islands
> and lines separate in an exponential manner with each step up the
> ladder so that with every doubling of the level number the random walk
> increase by a factor of only 2. What would the random walk be at
> level 14? Obviously, it would be 1,000 x 1,000 or 10^6 random walk
> steps. At level 28 the average random walk would be 10^12 steps. At
> level 56 the average random walk would be 10^24 steps . . . etc.
What you are doing is assuming that there is no order involved. There is
quite apparently order in words and their distribution through sequence
space. I'm quite sure it applies to phrases, as well, but we don't have a
systematic and well-defined method of validating phrases or I would build a
Phrasenator.
> Are you starting to see the problem with the existence of
> exponentially expanding neutral gaps even if they start out fairly
> small? Very quickly the average neutral gaps really start to be a
> very big problem, isolating most islands and breaking apart islands
> from each other very quickly.
You claim this, but why do you know this? It depends on the actual
distribution of valid words and phrases. A vast sequence space, but obvious
there are many, quite obvious relationships.
> This is exactly what you will see happening with the English language
> system once you start trying to evaluation longer and longer
> sequences. For one thing, which should be very obvious to you,
> valid/meaningful English language sentences and paragraphs and
> passages, etc., just don't have the same historical "evolutionary"
> history as single words do.
Sure they do. Whatever gave you any idea otherwise?
> They are not therefore going to be in such
> nice little lined-up archipelagos throughout sequence space.
<snip>
This is a claim (appeal from ignorance), but I don't see any evidence
provided.
Bill Rogers
Sean, your claim is that the relevant ratio, for evolution of
meaningful words (or phrases). Is # of meaningful strings/# of all
possible strings. For words of length L, this would be # entries in a
complete English dictionary/26^L, I am sure you agree that that is the
ratio your have been talking about. Call that "Sean's Ratio." It would
give you the global average distance between meaningful strings.
Zach's claim is that that ratio does not matter at all. Why not? It
does not matter because evolution always starts from somewhere. In
this analogy it might start from a specific L letter word. The real
ratio that matters, in figuring out how hard it is to evolve new words
from that starting point, is
# of meaningful words 1 mutation away from the starting word/total
number of possible mutants 1 mutational step away from the starting
word
the upper limit of the denominator is L^3 (the limit of all possible
point mutations, insertions and deletions, fragments)
the numerator depends on the particular starting word, but can be
measured empirically with the Word Mutator. Let's call this "Zach's
ratio."
Do you dispute that Zach's ratio represents "how evolution searches
sequence space" ? You start with a meaningful sequence (a word, or a
functional protein) and you search the region of sequence space that
is 1 mutational step away from your starting point. You apply your
selection criterion, and then you move on from (a) new starting
point(s). The word analogy is not perfect, in many ways, but it is
interesting as an illustration of how a random mutation/selection
algorithm searches sequence space.
Furthermore, it is possible to measure Zach's ratio as a function of
L. I do not think Zach has done it yet, but it is certainly doable
with his program.
One final point about exponential increases. Again, Zach has mentioned
this already. Both y=L^3 and z=26^L increase "exponentially." But the
limit, as L goes to infinity, of y/z = 0. That is, the number you
think limits evolution in the word analogy, (26^L), becomes infinitely
greater than the number that actually describes the sequence space
that evolution searches (L^3). So as L gets larger, the "Pitman
number" overestimates the sequence space to be searched by an
exponentially increasing factor. You are wrong about 2-3 letter words,
very wrong about 7 letter words, astronomically wrong about 12 letter
words, and unboundedly wrong about still longer words.
Bill
Bill Rogers
> bro...@noguchi.mimcom.net (Bill Rogers) wrote in message news:<8984713a.04050...@posting.google.com>...
>
>
> Let's say that you start with sequence "Me" and the goal is to evolve
> longer and longer Shakespearean sequences. You can select for any
> sequence as long as it is found in the works of Shakespeare. By these
> rules alone, the sequence "methi" would be positively selectable,
> according to your rules, since it is part of a Shakespearean work -
> even though the sentence fragment "methi", by itself, has no evident
> meaning in the English language system. Using "Methinks it is like a
> weasel" as a template were each and every single character change that
> matches this template is selectable, evolution would proceed at
> lightning speed - relatively speaking. This is because the odds of
> "successful mutation" of each character position in a sequence are
> only 1 in 27 (including a spacing character).
Yes, you are right there. I did not explain myself well. You need to
add a space to the beginning and end of each string before you test it
against the template, otherwise, as you say, things like "Methi" will
be selected for, and that would indeed make things vastly too easy. I
am assuming that you would not be upset with a positive selection for
a string like " is like a " even though the thought is incomplete. If
that's OK with you, then it's easy enough to automate. Adding the
spaces before the selection will insure that you only get strings of
intact words. Going from " like a " all the way to " like a weasel "
should be adequately challenging, no?
Note that those added spaces are part of the selection process, not
part of the string itself. The random mutation process will have to
insert real spaces into the string on its own in order to make word
divisions. So the selection process will involve checking to see
whether the string contains an initial or final space as part of the
string. If it does not, then you add the needed space(s) before
running the selection; then, if the string is positively selected for,
you remove any space that had been added during the selection process
before releasing the string back into the pond.
>
<snip>
>
> If you wanted to limit selection to fully intact meaningful sections
> of Shakespeare, that would be perfectly fine, but extremely limiting
> to your evolutionary hopes. You would no doubt find your computer
> unable to evolve much at all from Shakespeare, as far as sequence
> length is concerned, with the limitation of meaningful selection in
> place.
OK. I just showed you how the selection could be modified to prevent
meaningless word fragments from being selected. I think that using
that rule, Zach could build a Shakespearator that would generate much
more than "Methinks it is like a weasel." In fact, it would be much
easier to select against a very large literary text, rather than a
single phrase.
Bill
>
>
> Sean
> www.naturalselection.0catch.com
Andrew Arensburger
> One final point about exponential increases. Again, Zach has mentioned
> this already. Both y=L^3 and z=26^L increase "exponentially."
Actually, L^3 increases geometrically as L increases. If you
plot the two (or even L^2 and 2^L), you'll see that the exponential
curve (2^L) grows much faster than the polynomial one (L^2).
--
Andrew Arensburger, Systems guy University of Maryland
arensb.no-...@umd.edu Office of Information Technology
The windmills are winning.
Sean Pitman
> In talk.origins Bill Rogers <bro...@noguchi.mimcom.net> wrote:
> > One final point about exponential increases. Again, Zach has mentioned
> > this already. Both y=L^3 and z=26^L increase "exponentially."
>
> Actually, L^3 increases geometrically as L increases. If you
> plot the two (or even L^2 and 2^L), you'll see that the exponential
> curve (2^L) grows much faster than the polynomial one (L^2).
Finally, someone who actually recognizes this! The relative increase
in L^3 actually approaches zero with each increase in L. This does
not happen with true exponential formulas, such as 2^L or my own use
of 26^L. Hopefully Zach and Bill will be able to grasp this and stop
referring to L^3 as growing "exponentially" with an increasing L since
it does nothing of the sort.
But, if this concept seems difficult for them to grasp, try getting
them to understand the L^3 says absolutely nothing about how the ratio
of meaningful vs. meaningless sequences changes with increasing L.
The fact of the matter is that Zach's own computer program simulations
showed a truly exponential decrease in the ratio of meaningful vs.
non-meaningful sequences with increasing L. But, although I've tried
to explain this concept and relevance of a true exponential increase
to Zach, he just doesn't get it. He doesn't seem to understand that
an exponential increase means that a certain linear change will result
in a doubling of a particular value every time that linear change is
realized.
For example, if every two steps I take on the X-axis, the Y-axis value
doubles, that is an exponential relationship. Every time I take
another two steps, the Y-axis value doubles again. That is what it
means for there to be an "exponential" increase over time. If it
takes a longer and longer walk down the X-axis to get this doubling
effect of the Y-axis, as it does with Zach's L^3 calculation, that is
a geometric increase, not an exponential increase.
Not understanding this, Zach has no concept about the power of truly
exponential relationships to create truly enormous numbers in very
short order. He doesn't see that even if my calculation of a neutral
gap was just 10 instead of 1,000,000 for a given level of complexity
that this matters little if this gap increases in a truly exponential
manner with each step up the ladder of complexity - as Zach's own
computer programs demonstrate happens with the average number of
mutations required to find meaningful words/sequences at higher and
higher levels of complexity.
For example, lets say that the average number of mutations it takes to
achieve success increased only by a factor of 10 for each level
instead of 26 as I have previously suggested . . . Zach still looses
"the war" very quickly. In just 100 steps up the ladder, the average
number of mutations needed to achieve success would have expanded to
10^100, far beyond Zach's L^3 search space. Of course, this is a very
far cry from what Zach would have you believe using his meaningless
L^3 calculation, but this is the reality of the situation for
evolutionists.
So, will Zach and Bill see the light? I'm not holding my breath . . .
In any case though, I'm very glad to see that there is at least
someone contributing to this forum who actually understands basic
mathematics.
Zachriel
> Andrew Arensburger <arensb.no-...@umd.edu> wrote in message
news:<c7o3qr$jf7$1...@grapevine.wam.umd.edu>...
>
> > In talk.origins Bill Rogers <bro...@noguchi.mimcom.net> wrote:
> > > One final point about exponential increases. Again, Zach has mentioned
> > > this already. Both y=L^3 and z=26^L increase "exponentially."
> >
> > Actually, L^3 increases geometrically as L increases. If you
> > plot the two (or even L^2 and 2^L), you'll see that the exponential
> > curve (2^L) grows much faster than the polynomial one (L^2).
>
> Finally, someone who actually recognizes this! The relative increase
> in L^3 actually approaches zero with each increase in L. This does
> not happen with true exponential formulas, such as 2^L or my own use
> of 26^L. Hopefully Zach and Bill will be able to grasp this and stop
> referring to L^3 as growing "exponentially" with an increasing L since
> it does nothing of the sort.
Thank you Andrew for pointing that out. Sean has been using the word
"exponential" rather loosely, in the sense of something growing really,
really fast. I didn't bother to point out the semantic distinction as it is
not directly relevant to the discussion, but L^3 is more properly referred
to as forming a geometric progression.
Please note that I have been putting "exponential" in quotes or brackets.
* Nonsense. Not all "exponential" equations are equal.
* There are limits, but they have nothing to do with your "exponential"
arguments
* <snip more Exponential Pitman>
* <snip exponential redux>
> But, if this concept seems difficult for them to grasp, try getting
> them to understand the L^3 says absolutely nothing about how the ratio
> of meaningful vs. meaningless sequences changes with increasing L.
How many times do I have to say that the Pitman Number does indeed represent
the "the ratio of meaningful vs. meaningless sequences", but that it doesn't
represent the "ratio of meaningful vs. non-meaningful mutations". You are
incorrectly trying to assert an equivalence between the two statements.
http://tinyurl.com/2sk3o
> The fact of the matter is that Zach's own computer program simulations
> showed a truly exponential decrease in the ratio of meaningful vs.
> non-meaningful sequences with increasing L. But, although I've tried
> to explain this concept and relevance of a true exponential increase
> to Zach, he just doesn't get it. He doesn't seem to understand that
> an exponential increase means that a certain linear change will result
> in a doubling of a particular value every time that linear change is
> realized.
I make no such inaccurate assumption. What I do state is that the "the ratio
of meaningful vs. meaningless SEQUENCES" is represented by the Pitman
Number, but that the "ratio of meaningful vs. non-meaningful MUTATIONS" is
not. Further, we can calculate the total number of mutations, but we can
only determine the number of meaningful strings by reference to a
"meaning-o-meter", in this case, a Dictionary.
> For example, if every two steps I take on the X-axis, the Y-axis value
> doubles, that is an exponential relationship. Every time I take
> another two steps, the Y-axis value doubles again. That is what it
> means for there to be an "exponential" increase over time. If it
> takes a longer and longer walk down the X-axis to get this doubling
> effect of the Y-axis, as it does with Zach's L^3 calculation, that is
> a geometric increase, not an exponential increase.
>
> Not understanding this, Zach has no concept about the power of truly
> exponential relationships to create truly enormous numbers in very
> short order.
I am apparently aware of the numbers involved as I have included them on my
Calcs.xls workbook. It is their application to the problem at hand that is
at issue.
http://www.zachriel.com/mutagenation/calcs.xls
<snip>
Bill Rogers
> > One final point about exponential increases. Again, Zach has mentioned
> > this already. Both y=L^3 and z=26^L increase "exponentially."
>
> Actually, L^3 increases geometrically as L increases. If you
> plot the two (or even L^2 and 2^L), you'll see that the exponential
> curve (2^L) grows much faster than the polynomial one (L^2).
Indeed, as I pointed out in the post you are responding to, the ratio
of L^3/26^L goes to zero as L goes to infinity. So Sean's calculation
of the size of the sequence space being searched gets "unboundedly"
wrong as string length increases.
Thanks for correcting the sloopiness wrt geometric progression.
Bill
Bill Rogers
> bro...@noguchi.mimcom.net (Bill Rogers) wrote in message news:<8984713a.04051...@posting.google.com>...
>
> > Sean, your claim is that the relevant ratio, for evolution of
> > meaningful words (or phrases). Is # of meaningful strings/# of all
> > possible strings. For words of length L, this would be # entries in a
> > complete English dictionary/26^L, I am sure you agree that that is the
> > ratio your have been talking about. Call that "Sean's Ratio." It would
> > give you the global average distance between meaningful strings.
>
> even the likelihood of islands or interconnecting bridges between
> meaningful sequences. In fact, at very low levels of complexity,
> these interconnecting bridges would be so common that all meaningful
> sequences in sequence space would be interconnected by single-step
> bridges. No isolated islands would exist. However, with each step up
> the ladder, the obvious exponential expansion of the "Sean Ratio"
> strongly suggests that these islands and interconnecting bridges
> become more and more strained, in an exponential manner, until they
> even start to break. Completely isolated islands quickly form at very
> low relative levels of meaningful complexity and this isolation shows
> an exponential increase with each step up the ladder. Even Zach's
> programs demonstrate this fact very nicely.
>
> > Zach's claim is that that ratio does not matter at all. Why not?
>
> always be clustered as you move up the ladder in the same way and
> ratio that they are clustered at low levels of complexity. In this
> all of you are very mistaken.
That's a matter for experiment, not assertion or back of the envelope
calculation. So far, it does not seem that the mutegenator has any
trouble identifying words by searching much, much less of sequence
space than Sean's ratio would suggest.
>
> > It
> > does not matter because evolution always starts from somewhere. In
> > this analogy it might start from a specific L letter word.
>
> Yes, everything starts somewhere.
>
> > The real
> > ratio that matters, in figuring out how hard it is to evolve new words
> > from that starting point, is # of meaningful words 1 mutation away
> > from the starting word/total number of possible mutants 1 mutational
> > step away from the starting word
>
> There are a couple of problems here. You have to know how many
> possible mutations, meaningful or not, are 1 mutation away from your
> starting point. Zach estimates this number with his L^3 calculation
> given certain mutation types used in his simulation. Now, you have to
> know the likelihood that of all these possible mutations, that one
> will be "meaningful". Let me ask you Bill, how can you estimate and
> then extrapolate, outside of direct experimentation, such a
> likelihood? Certainly, such an estimate cannot be made based on the
> L^3 number itself since the L^3 number says nothing, in itself, about
> the likelihood of coming across a meaningful sequence - Nothing at
> all. The L^3 number is not a ratio and therefore says nothing about
> the likelihood of anything.
>
> > the upper limit of the denominator is L^3 (the limit of all possible
> > point mutations, insertions and deletions, fragments).
> > The numerator depends on the particular starting word,
>
> Yes, a specific number does depend on the particular starting point,
> but there certainly are averages that could be calculated. Some
> islands and bridges will certainly be larger than others, but the
> important concept is one of average size and distance for a given
> level of complexity.
>
> > but can be
> > measured empirically with the Word Mutator.
>
> Yes, this can be done with Zach's "Word Mutator" although Zach has yet
> to put up any real number averages as far as actual ratios are
> concerned.
>
> > Let's call this "Zach's ratio."
>
> But Zach hasn't presented his findings of what the average ratio is
> for the various levels of complexity.
>
> > Do you dispute that Zach's ratio represents "how evolution searches
> > sequence space" ? You start with a meaningful sequence (a word, or a
> > functional protein) and you search the region of sequence space that
> > is 1 mutational step away from your starting point. You apply your
> > selection criterion, and then you move on from (a) new starting
> > point(s).
>
> I do dispute this in a limited degree since this setup says nothing
> about the limits of what a population can search in a given amount of
> time/generations. It does not take into account the mutation rate or
> reproductive rate or the steady state size of the population. Because
> of this, it really does not address the average time required for a
> given _population_ to realize a successful search.
No, of course not, these are words, not beetles. But it does enable
you to ask whether the volume of sequence space you have to search to
find a meaningful L-letter word is that predicted by Sean's ratio or
Zach's. So far, the word mutagenator has been finding words by
searching a tiny fraction of the volume that your approach suggests it
should have to search.
>
> > The word analogy is not perfect, in many ways, but it is
> > interesting as an illustration of how a random mutation/selection
> > algorithm searches sequence space.
>
> Actually, I would argue that the English word analogy is extremely
> realistic and very relevant to the problem of how random mutation
> combined with meaning-based selection searches a sequence space.
OK.
>
> > Furthermore, it is possible to measure Zach's ratio as a function of
> > L.
>
> This is where you make your big mistake. It is not possible to
> measure Zach's ratio as a function of L since L has absolutely nothing
> to say about the ratio of meaningful sequences and neither does L^3.
>
> > I do not think Zach has done it yet, but it is certainly doable
> > with his program.
>
> Oh really? How is this doable? Why don't you just explain how
> knowing the length of a sequence has anything whatsoever to do with
> its possible meaning or the meaning of the 1-step surrounding
> sequences? This notion is completely unfounded as I see it. There is
> no basis for it in any language system, much less the English language
> system.
Of course it's doable. And not even very hard. You start with a seven
letter word. You get word mutator to generate all the possible one
step mutants derived from that seven letter word (approximately 7*7*7,
but Zach has counted them exactly).That's your denominator. Then you
search all of the mutants against a digital dictionary and find out
how many of the mutants are meaningful words. That's your numerator.
So you find Zach's ratio for that particular starting word. Then you
pick another seven letter word and repeat it. On and on for as many
seven letter word starting points as you like. That will give you a
distribution of "Zach's ratio" for seven letter word starting points.
You could, pretty easily, even get the program to randomly choose your
starting point from the dictionary, so you couldn't be accused of
picking particularly "fruitful" starting points. Then you continue the
experiment by obtaining similar distributions from starting points of
L=1,2,3,4,5,6,7...N, for as long as you have patience. Then you will
have measured Zach's ratio as a function of L.
>
> The fact of the matter is that all or none of the sequences
> surrounding your initial starting point of a particular length could
> be meaningfully beneficial. Knowing the length says nothing about
> either extreme possibility or anything in between. The only way you
> can get even a rough idea about such a likelihood, without actual
> direct observation, is by knowing something about the number of
> meaningful sequences that actually exist in sequence space as well as
> how a potential for clustering changes with each level of complexity.
Actually, what you have to do is do the experiment described above.
>
> > One final point about exponential increases. Again, Zach has mentioned
> > this already. Both y=L^3 and z=26^L increase "exponentially."
>
> Consider the following sequence for L^3 with increasing L.
>
> 1^3 = 1
> 2^3 = 8 = increase of 8 fold
> 3^3 = 27 = increase of 3.38 fold
> 4^3 = 64 = increase of 2.37 fold
> 5^3 = 125 = increase of 1.95 fold
> 6^3 = 216 = increase of 1.72 fold
> 7^3 = 343 = increase of 1.59 fold
> 8^3 = 512 = increase of 1.49 fold
>
> Now, compare this to the following sequence for 26^L
>
> 26^1 = 26
> 26^2 = 676 = increase of 26 fold
> 26^3 = 17576 = increase of 26 fold
> 26^4 = 456976 = increase of 26 fold
> etc . . .
>
> Certainly it is clear to see that although L^3 does show an
> exponential increase with increasing L, that this exponential increase
> becomes less and less "exponential" with every increase in L. What is
> also clear is that L^3 represents a hugely exponential decrease as a
> proportion of sequence space with increasing L. That means that my
> ratio becomes more and more significant while any correlation that
> might be had with L^3 at lower levels becomes rapidly less
> significant, in an exponential manner, as one moves up the ladder of
> meaningful sequence complexity.
>
> > But the
> > limit, as L goes to infinity, of y/z = 0. That is, the number you
> > think limits evolution in the word analogy, (26^L), becomes infinitely
> > greater than the number that actually describes the sequence space
> > that evolution searches (L^3).
>
> You fail to consider that the ratio of meaningful sequences within the
> L^3 search space surrounding an average starting point decreases in a
> very rapid exponential manner with increasing L, as Zach's own
> programs demonstrate very nicely. In fact, the decrease does not
> necessarily stop before reaching zero, as you and Zach evidently
> believe it does. Odds are very very good, that in relatively short
> order there will be no sequences with novel meanings at all within the
> L^3 strike zone. This very real possibility becomes exponentially more
> and more likely with increasing L - even within the English language
> system. In fact, Zach's own programs demonstrate this pattern quite
> nicely.
>
> > So as L gets larger, the "Pitman
> > number" overestimates the sequence space to be searched by an
> > exponentially increasing factor.
>
> Not at all. In fact, this number becomes more and more reliable with
> increasing L while the "Zach number" (L^3) becomes less and less
> reliable, in an exponential fashion.
Please read what I just wrote. The Pitman number overestimates the
sequence space to be searched by an exponentially increasing factor.
You do NOT disagree with that. Think about it. What you disagree with
is that there will be anything interesting to be found within one
mutational step (a Zach number of mutants) immediately around a given
starting point. The Zach number is the correct upper bound for the
number of possible one step mutations (according to your list of
acceptable mutations) starting from a given word of length L. It is
perfectly reliable.
>
> >You are wrong about 2-3 letter words,
> > very wrong about 7 letter words, astronomically wrong about 12 letter
> > words, and unboundedly wrong about still longer words.
>
> Actually, it is more like I was fairly right about 2-3 letter
> sequences, more right about 7-letter sequences, and even more right
> about 12-letter sequences. If you keep going up the ladder, you will
> find that my predictions become exponentially more and more reliable
> relative to Zach's predictions.
OK, please make a prediction. Starting from "abnormally" how many
total mutants would have to be explored before you could expect to
come upon another meaningful 10 letter word? You can calculate that
trivially, right? Using the Pitman number and a digital dictionary.
Then let Zach run the word mutator and see what happens.
Well, here's another way to think about why 26^L is irrelevant. There
are vast regions of sequence space that never, ever need to be
searched and will never get searched. They are included in 26^L but a
real word mutator will never, ever in a zillion years search them. For
example, consider qzxxxzq, qzxzxqx, qqqstxxx, etc. Around many, many
strings there is a space one mutational step wide (or two or three
even) in which no meaningful word is found. That means that starting
from a meaningful word, the word mutator will never ever take you into
those regions of sequence space. So they are pretty irrelevant. There
aren't any meaningful words in them and your random mutation/selection
search will never take you into them. The only situation in which they
would be relevant would be if you found that most words were
surrounded by "walls" of xxygzzwz-like strings and that there was no
possible pathway to another word. You've yet to propose an example of
any such isolated word.
>
> > Bill
>
> Sean
> www.naturalselection.0catch.com
Sean Pitman
> > > You are referring to the Pitman Number, the ratio of total permutations
> > > of 26 letters, to the permutations that actually exist in the Dictionary.
> >
> > No. What I am referring to here is the average number of mutations
> > that _your_ computer program(s) required to find new meaningful
> > sequences at a given level or higher. What was the actual ratio that
> > your computer simulation found?
>
> It depends on the word. That's why I built a simulator. However, in all
> cases it was less, usually much less, than the Pitman Number.
What was it Zach? I keep asking you over and over again to present
this ratio and you keep stalling. Sure it depends on the word. So,
take 10 or so very different words for each level and calculate the
average number of mutations required to find a new word from those 10
starting points within that level or higher. Do this for levels 1
through 20.
> We do know
> that if there is a path to another word, that the maximum number of
> mutations required is less than L^3 per generation.
You do NOT know that L^3 is the maximum number of mutations needed to
find a certain number of, say 100 or so, meaningful character
sequences at higher and higher levels. In fact, your computer
programs have indicated just the opposite. They show an exponentially
rapidly decreasing ratio of meaningful _mutations_ vs. non-meaningful
_mutations_ at higher and higher levels. Of course, you still don't
seem to understand how exponential formulas work so you probably will
continue to fail to grasp this concept.
> > The ratios give
> > you the _average_ number of mutations it would take to find a new
> > meaningful sequence (an English word in this case) at a minimum
> > sequence length.
>
> This is incorrect. It gives you the ratio of all permutations to valid
> words. This is not the same as the number of mutations. We don't have to
> search randomly. We can use mutation and selection.
I'm talking about the number of meaningful _mutations_ Zach. The
number of meaningful mutations vs. the number of non-meaningful
mutations used by your computer programs to find a certain number of
meaningful words in each level of complexity from L = 1 to 20. I am
talking about a ratio here, a ratio that your own computer discovered.
Tell us Zach, what average ratio did your computer discover exists
for each level of complexity that it investigated?
> > Again, what was the ratio that your computer found
> > for level 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 . . . ect.? I've asked you
> > to list this several times and you keep stalling. Don't list what you
> > think my ratios are. List what your ratios are.
>
> Everybody knows that I have provided the answer.
But you haven't Zach. You haven't told us what you think the average
ratio of meaningful vs. meaningless _mutations_ is at each level, for
L = 1 to 20. List this ratio for each level.
> The problem isn't the
> simplistic calculation of the Pitman Number, but the fact that you assert
> incorrectly that only random means will find the path to other words.
The odds of finding "other words" involves a ratio that is based on
average meaningful vs. meaningless _mutations_ for a given level.
This ratio does in fact involve a purely "random means" that cannot be
guided until a new meaningful sequence is found since all
non-meaningful sequences are equally non-selectable. Selecting
between non-meaningful sequences is therefore a neutral process and
results in a truly "random walk" until, by sheer luck of the odds
ratio, the random walk happens upon a new meaningful sequence.
> > Again, this exponentially growing average ratio of meaningful vs.
> > meaningless that you will find means exactly what I said it does. It
> > tells you the average number of mutations it takes to get from your
> > starting island to any other word within that island. Obviously, the
> > difficulty of finding a new meaningful word/sequence expands
> > exponentially with each step up the ladder even within islands of
> > words. According to your own observed ratios, even within your
> > clusters of islands with higher relative ratios than the surrounding
> > sequence space, this expansion is exponential and thus devastating to
> > your position.
>
> Except that Word Mutator can find new words in much less than a Pitman
> Number of attempts. This directly contradicts your assertion.
Actually, this does not contradict my assertion, as I have pointed out
to you time and again. My assertion was one of averages, which did
not rule out islands or common bridges between large islands at lower
levels of complexity. In fact I said many times that all meaningful
3-letter sequences were probably connected by single letter-change
bridges. Certainly this would also clearly be true of 6- and
7-character sequences as well. Large islands and interconnecting
bridges would still be present, though much less common and much
thinner, exponentially so, than they were at lower levels. Even at
very high levels such islands will exist, though they will be very
rare and very isolated, relatively speaking, from the other islands in
that level.
Again, you have badly misinterpreted my statements and my intent,
which is not surprising coming from someone who thinks that L^3 show
"exponential" expansion with increasing L.
> What is really disappointing, Sean, is that we can't even begin to
> understand the process if you keep pretending you can't see it happening
> before your eyes. There really are limits to our analogous word-game, but
> they are completely unavailable to your present understanding.
I see what is happening just fine Zach. What is happening is nothing
significantly beyond what my own predictions said would happen. Do I
even seem remotely surprised by your findings Zach? Not at all. In
fact, I have predicted such evolutionary progression as your computers
achieved in this forum and on my own website many times. I have
predicted that evolution would proceed very easily (with reasonable
population sizes, reproductive rates, and mutation rates) well beyond
the 30 or 40 genetic character level before significant stalling would
start to be a seriously recognizable problem. I then predicted that
"impossible" lines for the evolution of anything new would occur for
those functions requiring a minimum of only a couple thousand fairly
specified amino acid "characters" working together at the same time.
I predicted all of this well before you came on the scene, and yet you
got none of it and you don't even seem to understand the rather
obvious implications of your model. You don't recognize the
exponential, not geometric, decrease in the meaningful vs. meaningless
_mutation_ ratio with each step up the ladder. Therefore, you
extrapolate a meaningless L^3 formula which tells you absolutely
nothing about ratios at very low levels, so how on Earth do you think
it can tell you anything about ratios at higher levels? All of your
assertions are based on nonsensical assumptions and a lack of
knowledge about basic mathematics and genetics.
> > Even here though, you have a significant
> > problem. Even your ratios that you have calculated yourself expand
> > exponentially so that you reach walls of impossibility very quickly by
> > extrapolation of even your numbers.
>
> There is an upper-limit of L^3. For a string of a hundred letters, we must
> sort through at most a million mutations per generation.
Again, your problem is that although 100^3 = 1,000,000 . . . this says
absolutely nothing about how many of the 1 million possible mutations
will be meaningfully selectable - nothing! At least try and
understand this concept. At one point it seemed that you at least
recognized the truth of this statement, but it seems that you have
regressed into complete blindness to this reality again. The L^3
calculation says absolutely nothing about the average ratio of
meaningful vs. meaningless mutations at any level, much less the
100-character level in the English language system. In fact, based on
the exponential decline in this ratio with increasing levels, it is my
26^L number that actually becomes more and more valuable, in an
exponential manner, it determining the likelihood that a random
mutation will in fact be selectably meaningful. Again, this position
is strongly supported by your own computer models which do in fact
show an exponential, not geometric, decline in the average ratio of
meaningful vs. meaningless _mutations_ with increasing sequence length
in the English language system.
> > > You were wrong. We don't have to walk through all that space randomly.
> >
> > Yes, you do.
>
> Apparently not. This is the crux of your blindness.
LOL - Apparently so since I cannot see what is obviously false as
true. Even your computer programs experienced an exponentially
expanding random walk in the form of a decreasing ratio of meaningful
vs. meaningless mutations. Apparently you don't understand the
concept of "random walk" either. Why am I not surprised?
> > The fact of the matter is
> > that random walk exists even in your computer simulations.
>
> Random mutation plus selection.
Random mutation is random walk Zach. It is random UNTIL positive
selection takes place. Don't you get that Zach?
> > This
> > random walk also expands at an exponential rate in your computer
> > simulations. If it wasn't for your enormous reproductive rates and
> > mutation rates, your relatively small population would have to "swim
> > for it" much sooner than it currently does.
>
> As I have mentioned, if you don't want to compute every possible mutation
> per generation, you can use the Word Mutagenator, which takes one random
> mutation at a time.
And how many of these random mutations are required, on average, to
find a new meaningful sequence within a given level or higher? Does
this average number increase, decrease, or stay the same with
increasing character length? Please, list these average random walk
distances for levels 1 through 20.
> > But, even with your parameters as your currently have them set, the
> > exponentially expanding random walk averages will quickly stall out
> > even your computer programs well shy of the 1,000-character level and
> > probably shy of the 100-character level.
>
> We have no well-defined validation method for strings longer than words. If
> you have one, let us know.
I've already agreed to a validation method that you have already
proposed. Have you forgotten so fast?
> It clearly demonstrates you were wrong. You claim the compuational
> difficulty of the problem increases with the Pitman Number. It does not. It
> increase with (at most) L^3. They are very, very different numbers.
Again, your L^3 calculation says absolutely nothing about the odds
that a random mutation will be meaningful at any level. In fact, the
evidence shows that the ratio decreases exponentially with increasing
L. This means that my suggested ratio of C^L is in fact very much in
line with the odds ratio for predicting the likelihood of a meaningful
mutation at higher and higher levels. In fact, C^L gets more and more
accurate with increasing L, just like I've always said. On the other
hand, any correlation there may be at a given level with your L^3
calculation becomes less and less strong, in an exponential manner,
with increasing L. Do you understand that this creates a very serious
problem with your extrapolation attempts?
> > You repeatedly warn me to
> > In fact, your own programs support my own contentions far more
> > than they support yours.
>
> Nonsense. Not all "exponential" equations are equal.
That's for sure, especially since L^3 is not an exponential equation
at all.
> > You place your focus on relative minutia and
> > end up loosing the war. In fact, you effectively destroy your own
> > main position. You outflank yourself.
>
> Being off by a factor of, well, zillions, is not "relative minutia".
Being off in understanding the concept of "exponential expansion" is
actually worse. Even if I were off by trillions upon trillions at a
given level, the exponential expansion would make it look like nothing
in relatively short order. You just don't get this fact because you
aren't recognizing the concept of exponential expansion vs. your L^3
expansion.
> > That is in fact why I am spending so much time with you. You actually
> > did something that supports my position, not yours. It is you who
> > have come up with faulty conclusions based on erroneous assumptions
> > and meaningless extrapolations of worthless calculations (i.e., your
> > L^3 calculation for example). Even you admitted yourself that the L^3
> > calculation says nothing about the likelihood of finding a meaningful
> > sequence, and yet you continue to use it in extrapolations that assume
> > this very thing. Does that really make much sense to you?
>
> The L^3 is the upper-limit of how many possible point mutations and
> recombinations of a string of length L, or a collection of strings with a
> combined length of L are available per generation.
Again, knowing the number of possible mutations from the perspective
of a single individual undergoing a single mutation event says nothing
about the likelihood that this random mutation will be "meaningful" -
nothing. Do you understand this Zach? Because, it seems to me that
this is your main problem.
David Dalle
> "Sean Pitman" <seanpi...@naturalselection.0catch.com> wrote in message
> news:80d0c26f.04051...@posting.google.com...
Wow, I have followed this thread a bit, and visited Zach's website:
> http://www.zachriel.com/mutagenation/calcs.xls
I would not enter in a war of words with Zach!
I have also visited the poetic subject's website:
> > www.naturalselection.0catch.com
It is very good too, I am absolutely convinced by it...convinced that
Sean is an IDiot! (I assume that was its intended goal?)
David
Sean Pitman
> Thank you Andrew for pointing that out. Sean has been using the word
> "exponential" rather loosely, in the sense of something growing really,
> really fast.
LOL - Great back peddle! My use of the word "exponential" means just
that "exponential". When I say that my calculations show an
exponential pattern, they do. This is very much unlike your L^3
calculation which does not show an exponential increase, but rather a
decreasing relative increase with increasing L. That means that there
is a very very big difference between my use of truly exponential
formulas, such as 3^L and your use of non-exponential formulas such as
L^3. If you had understood the difference, why didn't you point this
difference out instead of referring to L^3 as showing an "exponential"
increase with increasing L - even on your website?
> I didn't bother to point out the semantic distinction as it is
> not directly relevant to the discussion, but L^3 is more properly referred
> to as forming a geometric progression.
The distinction is much more than one of mere semantics and the proper
understanding of this distinction is vital to this discussion.
> Please note that I have been putting "exponential" in quotes or brackets.
Oh, whatever! That's like former President Clinton asking for the
definition of "is". You also used the term "exponential" on your
website to refer to your L^3 calculation as well as several other
places in this thread. Certainly Bill thought that is what you meant
anyway, as well as Andrew.
> > But, if this concept seems difficult for them to grasp, try getting
> > them to understand the L^3 says absolutely nothing about how the ratio
> > of meaningful vs. meaningless sequences changes with increasing L.
>
> How many times do I have to say that the Pitman Number does indeed represent
> the "the ratio of meaningful vs. meaningless sequences", but that it doesn't
> represent the "ratio of meaningful vs. non-meaningful mutations". You are
> incorrectly trying to assert an equivalence between the two statements.
> http://tinyurl.com/2sk3o
The "equivalence" becomes more and more pronounced with increasing L.
This is not the case with your L^3 formula in which the "equivalence"
becomes exponentially less and less pronounced with increasing L. The
ratio of meaningful vs. meaningless MUTATIONS does in fact decrease in
an exponential fashion with increasing L. In other words, with each
step along the X-axis, the Y-change increases in the same exponential
increment or greater as compared to the previous X-axis increase.
With your L^3 calculation, each increase in the X-axis direction
results in a decreased Y-axis increase as compared to the previous
X-axis increase of the same quantity. Do you see the difference?
> > The fact of the matter is that Zach's own computer program simulations
> > showed a truly exponential decrease in the ratio of meaningful vs.
> > non-meaningful sequences with increasing L. But, although I've tried
> > to explain this concept and relevance of a true exponential increase
> > to Zach, he just doesn't get it. He doesn't seem to understand that
> > an exponential increase means that a certain linear change will result
> > in a doubling of a particular value every time that linear change is
> > realized.
>
> I make no such inaccurate assumption. What I do state is that the "the ratio
> of meaningful vs. meaningless SEQUENCES" is represented by the Pitman
> Number, but that the "ratio of meaningful vs. non-meaningful MUTATIONS" is
> not. Further, we can calculate the total number of mutations, but we can
> only determine the number of meaningful strings by reference to a
> "meaning-o-meter", in this case, a Dictionary.
Again, using your observed ratio of "meaningful vs. non-meaningful
MUTATIONS", what happens with increasing L? What happens to this very
ratio Zach? It decreases in an exponential fashion or a geometrically
exponential fashion (i.e., more than the exponential decrease of the
previous Y-axis decrease with the same X-axis increase).
> > For example, if every two steps I take on the X-axis, the Y-axis value
> > doubles, that is an exponential relationship. Every time I take
> > another two steps, the Y-axis value doubles again. That is what it
> > means for there to be an "exponential" increase over time. If it
> > takes a longer and longer walk down the X-axis to get this doubling
> > effect of the Y-axis, as it does with Zach's L^3 calculation, that is
> > a geometric increase, not an exponential increase.
> >
> > Not understanding this, Zach has no concept about the power of truly
> > exponential relationships to create truly enormous numbers in very
> > short order.
>
> I am apparently aware of the numbers involved as I have included them on my
> Calcs.xls workbook. It is their application to the problem at hand that is
> at issue.
> http://www.zachriel.com/mutagenation/calcs.xls
You are aware of the numbers involved, but are evidently clueless
about their meaning or their application to this issue. Your inane
extrapolations of your L^3 calculations are completely baseless and
yet you continue on your merry way evidently oblivious to the
disconnect between the calculations and numbers involved and what they
really mean.
Sean
www.naturalselection.0catch.com
Zachriel
"Bill Rogers" <bro...@noguchi.mimcom.net> wrote in message
news:8984713a.04051...@posting.google.com...
> seanpi...@naturalselection.0catch.com (Sean Pitman) wrote in message
news:<80d0c26f.04051...@posting.google.com>...
> >
> > Actually, it is more like I was fairly right about 2-3 letter
> > sequences, more right about 7-letter sequences, and even more right
> > about 12-letter sequences. If you keep going up the ladder, you will
> > find that my predictions become exponentially more and more reliable
> > relative to Zach's predictions.
>
> OK, please make a prediction. Starting from "abnormally" how many
> total mutants would have to be explored before you could expect to
> come upon another meaningful 10 letter word? You can calculate that
> trivially, right? Using the Pitman number and a digital dictionary.
> Then let Zach run the word mutator and see what happens.
I saw Sean post a couple since this was posted, but he hasn't yet answered.
So let me do my part.
Your reference to "total mutants" might indicate that we are not to use
selection. Without selection, it takes 4 generations consisting of 46
million mutations to discover the new 10-letter words "dillydally",
"informally" and "immortally".
However, with Pond = 50 and selecting for length, after 6 generations
consisting of 2 million mutations, we discovered the 11-letter word,
"volleyballs".
Sean's Ratio(10) = 14,460,878,473
Sean's Ratio(11) = 516,949,927,745
Sean, your Ratio seems a bit high.
Zachriel
"Sean Pitman" <seanpi...@naturalselection.0catch.com> wrote in message
news:80d0c26f.04051...@posting.google.com...
news:<h7udncuYlpk...@adelphia.com>...
>
> > Thank you Andrew for pointing that out. Sean has been using the word
> > "exponential" rather loosely, in the sense of something growing really,
> > really fast.
>
> LOL - Great back peddle! My use of the word "exponential" means just
> that "exponential". When I say that my calculations show an
> exponential pattern, they do. This is very much unlike your L^3
> calculation which does not show an exponential increase, but rather a
> decreasing relative increase with increasing L. That means that there
> is a very very big difference between my use of truly exponential
> formulas, such as 3^L and your use of non-exponential formulas such as
> L^3. If you had understood the difference, why didn't you point this
> difference out instead of referring to L^3 as showing an "exponential"
> increase with increasing L - even on your website?
Um. Where? If I did, I would be happy to correct it, but a global seach
doesn't show the word "exponential" on my domain.
Google search of www.zachriel.com for "exponential".
http://tinyurl.com/3d7qs
But does it really matter? It doesn't change the nature of your argument.
> > I didn't bother to point out the semantic distinction as it is
> > not directly relevant to the discussion,
This answers your question as to why I didn't make it an issue. Indeed, the
word "exponential" has more than one definition, though in mathematics it is
usually reserved for functions of the form b^x (or in banking $^T).
Please note you are asking a question to which I have already provided an
answer.
> > but L^3 is more properly referred
> > to as forming a geometric progression.
>
> The distinction is much more than one of mere semantics and the proper
> understanding of this distinction is vital to this discussion.
We can call your assertion the "Pitman Number", the "Sean Ratio", or simply
"Fred", but it doesn't make it a measure of the "ratio of meaningful vs.
non-meaningful mutations" as you assert.
> > Please note that I have been putting "exponential" in quotes or
brackets.
>
> Oh, whatever! That's like former President Clinton asking for the
> definition of "is". You also used the term "exponential" on your
> website to refer to your L^3 calculation as well as several other
> places in this thread. Certainly Bill thought that is what you meant
> anyway, as well as Andrew.
If I was unclear, I apologize. However, I can't find such a reference on my
website--and neither can Google. Meanwhile, semantics don't change the false
nature of your assertion.
> > > But, if this concept seems difficult for them to grasp, try getting
> > > them to understand the L^3 says absolutely nothing about how the ratio
> > > of meaningful vs. meaningless sequences changes with increasing L.
> >
> > How many times do I have to say that the Pitman Number does indeed
represent
> > the "the ratio of meaningful vs. meaningless sequences", but that it
doesn't
> > represent the "ratio of meaningful vs. non-meaningful mutations". You
are
> > incorrectly trying to assert an equivalence between the two statements.
> > http://tinyurl.com/2sk3o
>
> The "equivalence" becomes more and more pronounced with increasing L.
> This is not the case with your L^3 formula in which the "equivalence"
> becomes exponentially less and less pronounced with increasing L. The
> ratio of meaningful vs. meaningless MUTATIONS does in fact decrease in
> an exponential fashion with increasing L.
So you say. Can you provide evidence of this. What are the total number of
first-generation mutations, using the rules of point-mutation and
recombination, that are available to a clonal population of a ten-letter
word? How did you determine this? Please show your math.
The number of possible first-generation mutations is bound by L^3. The
number of possible mutations continues to climb at a faster rate with
increase in L.
Sean, whether or not this process of mutation and selection will result in
new words must be determined empirically. It could have been that some words
or even all words were distributed in such a way that only a "random walk"
would lead from one word to another. However, it is quite clear that this is
not the case.
> > > For example, if every two steps I take on the X-axis, the Y-axis value
> > > doubles, that is an exponential relationship. Every time I take
> > > another two steps, the Y-axis value doubles again. That is what it
> > > means for there to be an "exponential" increase over time. If it
> > > takes a longer and longer walk down the X-axis to get this doubling
> > > effect of the Y-axis, as it does with Zach's L^3 calculation, that is
> > > a geometric increase, not an exponential increase.
> > >
> > > Not understanding this, Zach has no concept about the power of truly
> > > exponential relationships to create truly enormous numbers in very
> > > short order.
> >
> > I am apparently aware of the numbers involved as I have included them on
my
> > Calcs.xls workbook. It is their application to the problem at hand that
is
> > at issue.
> > http://www.zachriel.com/mutagenation/calcs.xls
>
> You are aware of the numbers involved, but are evidently clueless
> about their meaning or their application to this issue. Your inane
> extrapolations of your L^3 calculations are completely baseless and
> yet you continue on your merry way evidently oblivious to the
> disconnect between the calculations and numbers involved and what they
> really mean.
Actually, I counted the number of possible mutations in several different
ways.
Zachriel
> "Zachriel" <sp...@zachriel.com> wrote in message
news:<RKSdnTW6upc...@adelphia.com>...
>
> > > > You are referring to the Pitman Number, the ratio of total
permutations
> > > > of 26 letters, to the permutations that actually exist in the
Dictionary.
> > >
> > > No. What I am referring to here is the average number of mutations
> > > that _your_ computer program(s) required to find new meaningful
> > > sequences at a given level or higher. What was the actual ratio that
> > > your computer simulation found?
> >
> > It depends on the word. That's why I built a simulator. However, in all
> > cases it was less, usually much less, than the Pitman Number.
>
> What was it Zach? I keep asking you over and over again to present
> this ratio and you keep stalling. Sure it depends on the word. So,
> take 10 or so very different words for each level and calculate the
> average number of mutations required to find a new word from those 10
> starting points within that level or higher. Do this for levels 1
> through 20.
I provided you the method. Why don't you even try? Oh, well. Let me do the
21-letter words. There are only eight of them, and there are 6682
first-generation mutations of these words. The number of neighboring words
is as follows:
antiauthoritarianisms, 23
psychopharmacological, 20
psychotherapeutically, 26
electroencephalograms, 17
electroencephalograph, 13
unconstitutionalities, 19
incomprehensibilities, 17
internationalizations, 27
Keep in mind that this data is empirical in nature. The number of neighbors
varies even though they each have the same length. The average is 20.25
neighbors per word. Here are the immediate neighbors of
"electroencephalograph":
electroencephalographs, length 22!
electrograph, graph, elect, halo, rap, log, roe, ha, lo, a, o
> > We do know
> > that if there is a path to another word, that the maximum number of
> > mutations required is less than L^3 per generation.
>
> You do NOT know that L^3 is the maximum number of mutations needed to
> find a certain number of, say 100 or so, meaningful character
> sequences at higher and higher levels.
Never made that claim. The claim is (an upper-bound of) L^3 *per
generation*. The number of generations required is empirical and depends on
the method of selection. It is conceivable that words are distributed in
such a way that there is no evolutionary path available, or only an
extremely long one. However, this is apparently not the case for the vast
majority of words, at least when choosing for length or Scrabble score.
> In fact, your computer
> programs have indicated just the opposite. They show an exponentially
> rapidly decreasing ratio of meaningful _mutations_ vs. non-meaningful
> _mutations_ at higher and higher levels. Of course, you still don't
> seem to understand how exponential formulas work so you probably will
> continue to fail to grasp this concept.
>
> > > The ratios give
> > > you the _average_ number of mutations it would take to find a new
> > > meaningful sequence (an English word in this case) at a minimum
> > > sequence length.
> >
> > This is incorrect. It gives you the ratio of all permutations to valid
> > words. This is not the same as the number of mutations. We don't have to
> > search randomly. We can use mutation and selection.
>
> I'm talking about the number of meaningful _mutations_ Zach. The
> number of meaningful mutations vs. the number of non-meaningful
> mutations used by your computer programs to find a certain number of
> meaningful words in each level of complexity from L = 1 to 20. I am
> talking about a ratio here, a ratio that your own computer discovered.
> Tell us Zach, what average ratio did your computer discover exists
> for each level of complexity that it investigated?
From my investigations there are usually several such neighbors for just
about every word in the Dictionary. You have yet to find even one without
neighbors. We know the number of possible mutations. It is the sum of the
point-mutations and recombinations.
> > > Again, what was the ratio that your computer found
> > > for level 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 . . . ect.? I've asked you
> > > to list this several times and you keep stalling. Don't list what you
> > > think my ratios are. List what your ratios are.
> >
> > Everybody knows that I have provided the answer.
>
> But you haven't Zach. You haven't told us what you think the average
> ratio of meaningful vs. meaningless _mutations_ is at each level, for
> L = 1 to 20. List this ratio for each level.
I did it for length 21. I leave the others as an exercise for the reader.
> > The problem isn't the
> > simplistic calculation of the Pitman Number, but the fact that you
assert
> > incorrectly that only random means will find the path to other words.
>
> The odds of finding "other words" involves a ratio that is based on
> average meaningful vs. meaningless _mutations_ for a given level.
> This ratio does in fact involve a purely "random means" that cannot be
> guided until a new meaningful sequence is found since all
> non-meaningful sequences are equally non-selectable. Selecting
> between non-meaningful sequences is therefore a neutral process and
> results in a truly "random walk" until, by sheer luck of the odds
> ratio, the random walk happens upon a new meaningful sequence.
Turns out that every word I've ever tried (hundreds) has such neighbors. We
know that number of possible mutations are the sum of point-mutations and
recombinations. For the eight 21-letter words in our dictionary there are an
average of 20.25 valid neighbors. There are 6682 available mutations, the
ratio therefore being 1/330.
> > > Again, this exponentially growing average ratio of meaningful vs.
> > > meaningless that you will find means exactly what I said it does. It
> > > tells you the average number of mutations it takes to get from your
> > > starting island to any other word within that island. Obviously, the
> > > difficulty of finding a new meaningful word/sequence expands
> > > exponentially with each step up the ladder even within islands of
> > > words. According to your own observed ratios, even within your
> > > clusters of islands with higher relative ratios than the surrounding
> > > sequence space, this expansion is exponential and thus devastating to
> > > your position.
> >
> > Except that Word Mutator can find new words in much less than a Pitman
> > Number of attempts. This directly contradicts your assertion.
>
> Actually, this does not contradict my assertion, as I have pointed out
> to you time and again. My assertion was one of averages, which did
> not rule out islands or common bridges between large islands at lower
> levels of complexity. In fact I said many times that all meaningful
> 3-letter sequences were probably connected by single letter-change
> bridges. Certainly this would also clearly be true of 6- and
> 7-character sequences as well. Large islands and interconnecting
> bridges would still be present, though much less common and much
> thinner, exponentially so, than they were at lower levels. Even at
> very high levels such islands will exist, though they will be very
> rare and very isolated, relatively speaking, from the other islands in
> that level.
Funny. There seems to a bridge from "electroencephalograph" straight to
"electroencephalographs" and to "graph" for that matter. Could it be a
result of the fact that "electroencephalograph" is a complex structure
composed of smaller sub-units that accreted over time?
> Again, you have badly misinterpreted my statements and my intent,
> which is not surprising coming from someone who thinks that L^3 show
> "exponential" expansion with increasing L.
>
> > What is really disappointing, Sean, is that we can't even begin to
> > understand the process if you keep pretending you can't see it happening
> > before your eyes. There really are limits to our analogous word-game,
but
> > they are completely unavailable to your present understanding.
>
> I see what is happening just fine Zach. What is happening is nothing
> significantly beyond what my own predictions said would happen. Do I
> even seem remotely surprised by your findings Zach? Not at all. In
> fact, I have predicted such evolutionary progression as your computers
> achieved in this forum and on my own website many times. I have
> predicted that evolution would proceed very easily (with reasonable
> population sizes, reproductive rates, and mutation rates) well beyond
> the 30 or 40 genetic character level before significant stalling would
> start to be a seriously recognizable problem. I then predicted that
> "impossible" lines for the evolution of anything new would occur for
> those functions requiring a minimum of only a couple thousand fairly
> specified amino acid "characters" working together at the same time.
No. You predicted that to find a seven-letter word would take a "random
walk" through hundreds-of-thousands of permutations. Don't make me quote you
again. Argh!
> "Getting from one meaningful 7-letter phrase to a different meaningful
> 7-letter phrase requires, on average, a fairly long random walk through
> 250,000 meaningless options."
> http://tinyurl.com/ypos7
I have tried many seven-letter words and it takes no where near that long a
walk. I asked for a counterexample, even provided you software, but you have
yet to provide one, not one.
> I predicted all of this well before you came on the scene, and yet you
> got none of it and you don't even seem to understand the rather
> obvious implications of your model. You don't recognize the
> exponential, not geometric, decrease in the meaningful vs. meaningless
> _mutation_ ratio with each step up the ladder. Therefore, you
> extrapolate a meaningless L^3 formula which tells you absolutely
> nothing about ratios at very low levels, so how on Earth do you think
> it can tell you anything about ratios at higher levels? All of your
> assertions are based on nonsensical assumptions and a lack of
> knowledge about basic mathematics and genetics.
>
> > > Even here though, you have a significant
> > > problem. Even your ratios that you have calculated yourself expand
> > > exponentially so that you reach walls of impossibility very quickly by
> > > extrapolation of even your numbers.
> >
> > There is an upper-limit of L^3. For a string of a hundred letters, we
must
> > sort through at most a million mutations per generation.
>
> Again, your problem is that although 100^3 = 1,000,000 . . . this says
> absolutely nothing about how many of the 1 million possible mutations
> will be meaningfully selectable
We don't know how many of these mutations will be meaningful. You are
certainly correct! However, if even one of them is meaningful, then the odds
are certainly less than the Sean Ratio. Our Word Mutator doesn't handle
phrases, so we must use other means.
We know that "Beware a war of words ere you err" (length 33) has no more
than ~36000 possible first-generation mutations. You are right that we have
no way to know from this calculation whether a valid mutation exists. This
number just represents the denominator of the final result. If there is no
valid mutation, let us call the string "sterile". So let's take a look!
"Beware a wad of words ere you err" (note that this mutant string is also
length 33). Well, we found at least one. So the odds of finding a valid
mutation is no worse than 1 in 36000.
<snip more of exponential Pitman>
Bennett Standeven
>
> > > > You are referring to the Pitman Number, the ratio of total permutations
> > > > of 26 letters, to the permutations that actually exist in the Dictionary.
> > >
> > > No. What I am referring to here is the average number of mutations
> > > that _your_ computer program(s) required to find new meaningful
> > > sequences at a given level or higher. What was the actual ratio that
> > > your computer simulation found?
> >
> > It depends on the word. That's why I built a simulator. However, in all
> > cases it was less, usually much less, than the Pitman Number.
>
> What was it Zach? I keep asking you over and over again to present
> this ratio and you keep stalling. Sure it depends on the word. So,
> take 10 or so very different words for each level and calculate the
> average number of mutations required to find a new word from those 10
> starting points within that level or higher. Do this for levels 1
> through 20.
>
my program, I got the following:
All trials used four bracket types and pop.size 300, max length equal
to 500
at 1,000 gens: 11, 66%
at 2,000 gens: 14, 62%
at 3,000 gens: 17, 59%
at 4,000 gens: 21, 57%
at 5,000 gens: 24, 55%
at 6,000 gens: 25, 54%
at 7,000 gens: 28, 52%
at 8,000 gens: 31, 51%
at 9,000 gens: 33, 50%
at 10,000 gens: 35, 50%
at 15,000 gens: 47, 46%
at 20,000 gens: 58, 42.5%
at 30,000 gens: 85, 38%
at 40,000 gens: 101, 36%
at 50,000 gens: 125, 34%
at 100,000 gens: 253, 28.5%
Here, the first number is the average of the maximal lengths across
all runs, and the second, percentile, number is the average success
rate of all mutations that occurred during all the runs. (A mutation
is deemed sucessful if it produces a valid string, without regard to
length.)
The version of the program I used was this:
#include <stdio.h>
#include <string.h>
#include <random.h>
#include <time.h>
#define MAXLEN 500
#define POPVAL 300
char Mutation[2*MAXLEN + 2];
char * Pop[POPVAL];
int reCombine = 100, debug;
char chararr[8] = "()[]{}<>";
long int totmut = 0, succmut = 0;
int Validate(void);
// Return a random number between a and b, inclusive.
int Random(int a, int b) {
unsigned int c;
if(b < a) { c = b; b = a; a = c; }
c = random();
c %= b-a+1;
c += a;
return c;
}
void debug_print(char err[])
{
if(debug == 1) puts(err);
}
/* ------------------------
* MUTAGENATOR
* for a random Word in population
* Random for Mutation or Recombination
* return 1 if mutation is valid, 0 otherwise.
*/
int Mutagenator(const char * Word)
{
int c, lengthWord, i, j, q;
lengthWord = strlen(Word);
if((random() % 128) < reCombine) {
// MUTATIONS
// Random type of Mutation
c = Random(1, 5);
switch(c) {
case 1: //Delete Mutation
i = Random(0, lengthWord - 2);
strncpy(Mutation, Word, i);
strcat(Mutation, Word + i+2);
break;
case 2: //Two Point Mutation
i = Random(0, lengthWord - 1);
j = Random(0, 7);
strcpy(Mutation, Word);
Mutation[i] = chararr[j];
i = Random(0, lengthWord - 1);
j = Random(0, 7);
Mutation[i] = chararr[j];
break;
case 3: //Insert Mutation
i = Random(0, lengthWord);
j = Random(0, 3);
strncpy(Mutation, Word, i);
strcat(Mutation, Word + i - 2);
break;
case 4: //Remainders
i = Random(0, lengthWord-2);
j = Random(2, lengthWord - i);
j -= j%2; // j should be even.
strncpy(Mutation, Word, i);
strcat(Mutation, Word + j + i);
break;
case 5: //Snippets
i = Random(0, lengthWord-2);
j = Random(2, lengthWord - i);
j -= j%2; // j should be even.
strncpy(Mutation, Word + i, j);
Mutation[j] = 0; // Mutation must be null-terminated.
break;
}
}
else {
char Snippet[MAXLEN+2], Snippet2[MAXLEN+2];
int lengthInsert;
// RECOMBINATIONS
i = Random(0, lengthWord-2);
j = Random(2, lengthWord - i);
j -= j%2; // j should be even.
strncpy(Snippet, Word + i, j); // Take a snippet from Word
Snippet[j] = 0; // ensure Snippet is null-terminated.
// Take a snippet from another word from existing population
i = Random(0, POPVAL-1);
lengthInsert = strlen(Pop[i]);
j = Random(0, lengthInsert-2);
q = Random(2, lengthInsert - j);
q -= q%2; // q should be even.
strncpy(Snippet2, Pop[i] + j, q);
Snippet2[q] = 0; // ensure Snippet2 is null-terminated.
// Pick a random point in this subject snippet
q = Random(0, strlen(Snippet2));
strncpy(Mutation, Pop[i], q);
strcat(Mutation, Snippet);
strcat(Mutation, Pop[i] + q);
}
if(strlen(Mutation) < 2) return 0; // don't allow empty strings.
if(strlen(Mutation) >= MAXLEN) return 0; // Mutation is too long.
totmut++;
if(Validate()) {
succmut++;
return 1; // check Mutation against chosen language.
}
return 0;
} // End of Mutagenator.
int test(char *Temp)
{
int i;
signed int j = 0;
char seekchar, startchar;
startchar = Temp[0];
switch(Temp[0]) {
case '(': seekchar = ')'; break;
case '[': seekchar = ']'; break;
case '{': seekchar = '}'; break;
case '<': seekchar = '>'; break;
case 0: return 1; // null string is automatically valid.
default: return 0; // close bracket at beginning
}
for(i=0; i < strlen(Temp); i++)
{
if(Temp[i] == startchar) j++; // openparen
if(Temp[i] == seekchar) j--; // closeparen
if(j < 0) return 0; // too many close brackets
if(j == 0) break; // found end of first bracket sequence
}
if (j > 0) return 0; // too many open brackets
Temp[i] = 0;
if(!(test(Temp+1))) return 0; // check first sequence for validity.
if(!(test(Temp+i+1))) return 0; // check remainder of string.
return 1; // if both substrings are valid, Temp was valid.
}
int Validate(void)
{
char Temp[MAXLEN];
strcpy(Temp, Mutation);
return test(Temp);
}
int main()
{
int i, k, m;
long int j, mutats, numtrials, totlen;
char mutatst[15], numtrst[15];
double succrat;
i=rawclock();
srandom(i);
printf("Please enter number of generations: ");
gets(mutatst);
mutats = atol(mutatst);
printf("Number of trials: ");
gets(numtrst);
numtrials = atol(numtrst);
for(i = 0; i < POPVAL; i++) {
Pop[i] = malloc(MAXLEN);
if(Pop[i] == NULL) return 1; // Out of memory
}
totlen = 0;
for(m = 0; m < numtrials; m++) {
for(i = 0; i < POPVAL; i++) {
switch(i%4) {
case 0: strcpy (Pop[i], "()"); break;
case 1: strcpy (Pop[i], "[]"); break;
case 2: strcpy (Pop[i], "{}"); break;
case 3: strcpy (Pop[i], "<>"); break;
}
}
for(j = 0; j < mutats; j++) {
i = Random(0, POPVAL-1);
if(Mutagenator(Pop[i])) strcpy(Pop[i], Mutation);
for(k=0; k<MAXLEN; k++) {
Mutation[k] = 0;
}
}
k = 0;
for(i = 0; i < POPVAL; i++)
if (strlen(Pop[k]) < strlen(Pop[i])) k = i;
printf("%ld ", strlen(Pop[k])); totlen += strlen(Pop[k]);
}
succrat = (double) succmut / (double) totmut;
printf("\n%ld, %f", totlen/numtrials, succrat);
return 0;
}
// End of program.
The most important difference from my original program is that this
version will recombine two snippets, instead of recombining a string
with a snippet as the original program did. I have also introduced a
different validity testing function, but it doesn't seem noticably
more efficient than the old one.
Sean Pitman
> I saw Sean post a couple since this was posted, but he hasn't yet answered.
> So let me do my part.
>
> Your reference to "total mutants" might indicate that we are not to use
> selection. Without selection, it takes 4 generations consisting of 46
> million mutations to discover the new 10-letter words "dillydally",
> "informally" and "immortally".
>
> However, with Pond = 50 and selecting for length, after 6 generations
> consisting of 2 million mutations, we discovered the 11-letter word,
> "volleyballs".
>
> Sean's Ratio(10) = 14,460,878,473
> Sean's Ratio(11) = 516,949,927,745
>
> Sean, your Ratio seems a bit high.
Finally, I think you are starting to provide the actual ratios found
by your simulations that I've been asking for for some time now. What
you need to do now is show this ratio for each level from L= 1 to 20
like I previously asked. If you do that, you will no doubt discover
something very interesting, like an exponential decrease in your ratio
with each increase in L.
Another point I would like to bring up here is that my question about
the "total mutants" required to find a "meaningful" mutant within a
given level of L or higher does indeed involve "selection" since only
meaning is selectable with survivability points given to increased
sequence "length" in this case.
As far as my predictions are concerned, I repeat myself yet again.
Islands and archipelagoes of islands do in fact exist in sequence
space at all levels of complexity. For very low levels of
informational complexity such as Zach is working with, these islands
are relatively large, many may be fairly close together, and the
interconnecting bridges are relatively common. However, with each
increase in minimum sequence length (L), the islands become smaller,
more widely separated, and the bridges become much more strained and
start to break away completely.
For example, imagine an ocean where the land is very sticky and
stretchy. An attempt to separate the land into islands by adding more
and more water is like trying to pull bubble gum apart. As the land
stretches, holes are formed, but initially there are very wide bridges
between all major landmasses. Getting from one island to any other is
only a matter of walking across these very wide bridges. Now,
consider what would happen in this scenario if 26^L amounts of water
and L^2 amounts of land were added for every increase in L. What
would happen to the bridges and size of the larger landmasses?
Obviously, in very short order, these bridges and landmasses would
become stretched to the breaking point - right? Soon the appearance
of sequence space would be one of a huge amount of "water" with tiny
islands of "land" having tiny threads of "bridges" connecting some of
the islands. Very quickly though the vast majority of these
thread-like bridges would also break and the islands would become more
and more isolated, in an exponential manner, with every increase in L.
At this point, the only way to get from one island to the next would
be to swim blindly through the ocean until by sheer luck one happened
upon a new island within that level of sequence space or greater.
Given this scenario as a "true" reflection of language systems, as is
my position, how could one calculate a rough estimate of the average
number of random-walk steps it would take to come across a new
beneficial character sequence with a given L? Well, Zach has directly
observed that starting with some meaningful 10-letter sequences the
random walk is in fact over 2 million steps/tries since he calculated
the ratio of meaningful to meaningless from one starting point as
being at least 1 in 2 million. I accept this number as useful even
though it is not an average number even from the starting single point
that Zach used in this case. It would be more meaningful if Zach
would see how long it took to find 10 or 100 new meaningful sequences
from a given starting point at each L. Beyond this, it would nice to
have analysis of at least 10 or even 100 widely diverse starting
points at each L. But, at least you have pushed Zach to do what I was
having difficulties getting him to do. He has finally started to
actual present his own observed ratio that was found by his computer
simulations.
So, why am I not at all surprised by Zach's ratio of 1 in 2 million
for L = 10? After all, the average distance between meaningful
sequences at this level is easy to calculate at 26^10, or a bit over
141 trillion steps. How on earth then did Zach's computers find new
meaningful sequences at this level in just over 2 million tries? The
reason is because the L = 10 level is still a very low level,
relatively speaking, and the bubble gum bridges still keep the islands
reasonably reachable at this level.
Now, compare the average random walk at the L = 7 level to the average
random walk at the L = 3 level. What ratio would Zach's computer
programs find? For argument's sake, lets say that Zach's L = 1 ratio
is no more than 1 in 40. What about Zach's L = 5 ratio? Lets say
that this ratio turns out to be around 1 in 1,600. And, of course, we
know that Zach's L = 10 ratio is around 1 in 2.5 million. Are we
starting to see a pattern here that looks very much like my described
scenario about what happens to sequence space with increasing L? If
my little hypothetical scenario turns out to be even remotely
accurate, Zach looses the war. Now why is this again?
Well, it is clear that with every doubling of L, the ratio meaningless
to meaningful _mutations_ in Zach's illustration shows an exponential
increase (by a factor of 2). So, how many mutations will Zach's
computers have to sort through randomly at the L = 20 level to find a
new meaningful sequence on _average_? Well, a good rough estimate
would be 2 million^2 or about 4 trillion. What about at the L = 40
level? Oh, about 16 trillion trillion (1.6 x 10^25) mutations on
average using Zach's own observed rate of ratio expansion.
Are we starting to see the problem? Is my use of the word "zillions"
taking on a whole new meaning for you now?
Zachriel
>
> Are we starting to see the problem? Is my use of the word "zillions"
> taking on a whole new meaning for you now?
>
No.
Traklman
>From: "Zachriel" sp...@zachriel.com
>Date: 5/11/2004 7:20 PM Central Standard Time
>Message-id: <keGdnaV4mt3...@adelphia.com>
>We know that "Beware a war of words ere you err" (length 33) has no more
>than ~36000 possible first-generation mutations. You are right that we have
>no way to know from this calculation whether a valid mutation exists. This
>number just represents the denominator of the final result. If there is no
>valid mutation, let us call the string "sterile". So let's take a look!
>
>"Beware a wad of words ere you err" (note that this mutant string is also
>length 33). Well, we found at least one. So the odds of finding a valid
>mutation is no worse than 1 in 36000.
>
Or, even better: "Beware a war of swords ere you err"
Zachriel
> "Zachriel" <sp...@zachriel.com> wrote in message
news:<YJCdnVrVdte...@adelphia.com>...
>
> > I saw Sean post a couple since this was posted, but he hasn't yet
answered.
> > So let me do my part.
> >
> > Your reference to "total mutants" might indicate that we are not to use
> > selection. Without selection, it takes 4 generations consisting of 46
> > million mutations to discover the new 10-letter words "dillydally",
> > "informally" and "immortally".
> >
> > However, with Pond = 50 and selecting for length, after 6 generations
> > consisting of 2 million mutations, we discovered the 11-letter word,
> > "volleyballs".
> >
> > Sean's Ratio(10) = 14,460,878,473
> > Sean's Ratio(11) = 516,949,927,745
> >
> > Sean, your Ratio seems a bit high.
>
> Finally, I think you are starting to provide the actual ratios found
> by your simulations that I've been asking for for some time now.
Ok, Sean. I'm going to explain this one more time before I have to take a
hiatus from this "Thread-of-the-Year" for a few days. (Thanks Bill Rogers
for the nomination!)
> What
> you need to do now is show this ratio for each level from L= 1 to 20
> like I previously asked.
I provided you what I believe are very useful tools to answer many of these
types of questions yourself.
> If you do that, you will no doubt discover
> something very interesting, like an exponential decrease in your ratio
> with each increase in L.
Why exponential? Why not some other relationship?
> Another point I would like to bring up here is that my question about
> the "total mutants" required to find a "meaningful" mutant within a
> given level of L or higher does indeed involve "selection" since only
> meaning is selectable with survivability points given to increased
> sequence "length" in this case.
Yes, selection for meaning is a type of selection, one which was discussed
on my website. However, as nearly all words connect to all other words, if
we don't limit our Pond Size, we end up with a vast collection of strings to
sort through. Here are some results for the first few generations:
"sean pitman"
Mutations and Snippets
Pond = unlimited (set to empty)
Selection for any word
seaman, 13 words
shaman, 123 words
seminal, 1128 words
bitmapping, 8399 words
fingerprinting, 26000+ words
After over a billion mutants considered, Word Mutation had discovered more
than 26000 words, a third of our entire dictionary!
Proof is in the Pudding
http://www.zachriel.com/mutagenation/Pudding.asp
A reasonable limiting of the Pond Size for the length of words under
consideration results in much more rapid results. This is also part of the
original conditions, by the way.
> As far as my predictions are concerned, I repeat myself yet again.
> Islands and archipelagoes of islands do in fact exist in sequence
> space at all levels of complexity.
We know exactly what you predicted, a random walk through
hundreds-of-thousands of permutations for length-7 words, and billions for
length-14 words. Please don't make me quote you again.
> For very low levels of
> informational complexity such as Zach is working with, these islands
> are relatively large, many may be fairly close together, and the
> interconnecting bridges are relatively common. However, with each
> increase in minimum sequence length (L), the islands become smaller,
> more widely separated, and the bridges become much more strained and
> start to break away completely.
You have not demonstrated this, but merely asserted it.
> For example, imagine an ocean where the land is very sticky and
> stretchy. An attempt to separate the land into islands by adding more
> and more water is like trying to pull bubble gum apart. As the land
> stretches, holes are formed, but initially there are very wide bridges
> between all major landmasses. Getting from one island to any other is
> only a matter of walking across these very wide bridges. Now,
> consider what would happen in this scenario if 26^L amounts of water
> and L^2 amounts of land were added for every increase in L. What
> would happen to the bridges and size of the larger landmasses?
Your analogy may or may not be applicable. Consider a map of the roads
connecting cities across North America. These roads represent only a tiny
fraction of the surface of the map. Let's blow the map up to the size of the
Solar System, but leave the width of the roads the same. Yet, they can still
connect the cities.
Analogies are good for explaining things, or for making hypotheses, but do
not represent proof and can easily mislead us. "If the world is round, then
the Chinese must stand on their heads."
> Obviously, in very short order, these bridges and landmasses would
> become stretched to the breaking point - right?
This has not been demonstrated. Indeed I offered a contrary analogy.
> Soon the appearance
> of sequence space would be one of a huge amount of "water" with tiny
> islands of "land" having tiny threads of "bridges" connecting some of
> the islands. Very quickly though the vast majority of these
> thread-like bridges would also break and the islands would become more
> and more isolated, in an exponential manner, with every increase in L.
> At this point, the only way to get from one island to the next would
> be to swim blindly through the ocean until by sheer luck one happened
> upon a new island within that level of sequence space or greater.
They used to think that the Pacific Ocean couldn't be crossed by ancient
peoples in open boats. They were wrong.
http://www.samoa.co.uk/q-and-a/3849.html
> Given this scenario as a "true" reflection of language systems, as is
> my position, how could one calculate a rough estimate of the average
> number of random-walk steps it would take to come across a new
> beneficial character sequence with a given L? Well, Zach has directly
> observed that starting with some meaningful 10-letter sequences the
> random walk is in fact over 2 million steps/tries since he calculated
> the ratio of meaningful to meaningless from one starting point as
> being at least 1 in 2 million. I accept this number as useful even
> though it is not an average number even from the starting single point
> that Zach used in this case.
Then you admit you were originally wrong when you predited that it would
require a random walk through a Pitman Number(10) or 14,460,878,473 number
of permutations. It's about time. (You can retract your admission now. ;-)
> It would be more meaningful if Zach
> would see how long it took to find 10 or 100 new meaningful sequences
> from a given starting point at each L.
Well, why don't you. My only intention was to demonstrate that you were
wrong concerning how many permutations it would take to find a new 7- or
14-letter word starting from another 7- or 14-letter word. This has been
done. Everything else has been a diversion.
> Beyond this, it would nice to
> have analysis of at least 10 or even 100 widely diverse starting
> points at each L.
Go for it. Maybe you can learn something about how words are distributed in
sequence space. By the way, we haven't even included valid *phrases* that
also inhabit that space. What percentage of that space is inhabited by valid
phrases and how are they connected? We already know that the entire poem "O
Sean Pitman" is connected with the single-letter word "O".
> But, at least you have pushed Zach to do what I was
> having difficulties getting him to do. He has finally started to
> actual present his own observed ratio that was found by his computer
> simulations.
>
> So, why am I not at all surprised by Zach's ratio of 1 in 2 million
> for L = 10? After all, the average distance between meaningful
> sequences at this level is easy to calculate at 26^10, or a bit over
> 141 trillion steps. How on earth then did Zach's computers find new
> meaningful sequences at this level in just over 2 million tries?
That's is good question. Hopefully the cognitive dissonance will jar your
mind free of its preconceptions.
> The
> reason is because the L = 10 level is still a very low level,
> relatively speaking, and the bubble gum bridges still keep the islands
> reasonably reachable at this level.
This was not your previous claim. Should I quote you again?
Sean, if you are merely conjecturing, please say so. I can respect that. But
you state these assertions with such certainty that you mislead yourself and
you mislead others.
> Now, compare the average random walk at the L = 7 level to the average
> random walk at the L = 3 level. What ratio would Zach's computer
> programs find? For argument's sake, lets say that Zach's L = 1 ratio
> is no more than 1 in 40. What about Zach's L = 5 ratio? Lets say
> that this ratio turns out to be around 1 in 1,600. And, of course, we
> know that Zach's L = 10 ratio is around 1 in 2.5 million. Are we
> starting to see a pattern here that looks very much like my described
> scenario about what happens to sequence space with increasing L? If
> my little hypothetical scenario turns out to be even remotely
> accurate, Zach looses the war. Now why is this again?
No, Sean. I've already proven the only point I ever intended to address. You
have now changed your calculations to a new assertion, one you hope is out
of reach of my little Mutagenation experiments.
> Well, it is clear that with every doubling of L, the ratio meaningless
> to meaningful _mutations_ in Zach's illustration shows an exponential
> increase (by a factor of 2).
This is not clear so. It could very easily be some other relationship. Have
you included meaningful phrases in your sequence space? No.
> So, how many mutations will Zach's
> computers have to sort through randomly at the L = 20 level to find a
> new meaningful sequence on _average_? Well, a good rough estimate
> would be 2 million^2 or about 4 trillion. What about at the L = 40
> level? Oh, about 16 trillion trillion (1.6 x 10^25) mutations on
> average using Zach's own observed rate of ratio expansion.
This is the actual problem. We know what the number of mutations are
available for each generation (G), a number which is bound by L^3 for large
L. The actual computation is on the Calcs.xls spreadsheet, but let's just
call it "L^3". We do not know how many G are required to find a particular
result. Perhaps it might be one G, perhaps it might be infinite G. We can
determine this empirically a number of different ways including with the
Word Mutator.
However, we do know that "Beware a war of words ere you err" has a mutant in
"Beware a war of swords ere you err" (thanks Traklman!), which is actually
one letter longer. We know that this is one of only 36K mutants--and there
are still others. We also know many other such phrases and constructions
that have obvious rules of selection so that we can say that the total
permutations required is on the order of G*(L^3).
pitman
pit, man
put, pan, wit
jut, plan, wig
just, plain, wing
just plain, wring
just plain, wrong
just plain wrong
If we don't specify a particular result, then we know for a fact that words
can mutate into other words of various forms--regardless of length--and that
some of these words might have value in certain settings--the very
definition of meaning. We can put "pitman" into the Word Mutator and in
short order we have "pinpricking", Scrabble score 22. With "sean" we end up
with "chuckled" among other words. If you wanted to make this a mechanical
process, you could assign a "humor score" to each word and see what happens.
Word Mutator can be used for this by simply changing the Scrabble scores to
anything you want for any *meaningful* purpose you want, then selecting for
Scrabble score.
In a Sea swimming with trillions of "Pitman", some just might evolve into
new and different forms.
>
> Are we starting to see the problem? Is my use of the word "zillions"
> taking on a whole new meaning for you now?
No, Sean. You are still confusing millions and zillions.
http://www.zachriel.com/mutagenation/
Sean Pitman
No? - That's it? Not even an attempt to explain the obvious
exponential expansion of the number of mutations required by your
computer programs with every doubling of L?
You don't seem to understand that your own computer programs show an
_exponentially_ decreasing ratio of meaningful vs. meaningless
MUTATIONS that, if extrapolated accordingly, quickly reaches practical
impossibility in very short order. In order to keep up with such an
exponentially declining ratio, a population would have to increase in
size and/or reproductive rate and/or mutation rate by the same
magnitude. But there are relatively low constraining maximum limits
for each of these changes. Very quickly there is nothing a population
can do to keep up with the exponentially expanding neutral gap and
evolution simply stalls out this side of a practical eternity of time.
I bet that even Bill is able to recognize the significance of this
problem - maybe. What about you Zach? What do you have to say about
this?
Sean Pitman
> > I'm talking about the number of meaningful _mutations_ Zach. The
> > number of meaningful mutations vs. the number of non-meaningful
> > mutations used by your computer programs to find a certain number of
> > meaningful words in each level of complexity from L = 1 to 20. I am
> > talking about a ratio here, a ratio that your own computer discovered.
> > Tell us Zach, what average ratio did your computer discover exists
> > for each level of complexity that it investigated?
>
> From my investigations there are usually several such neighbors for just
> about every word in the Dictionary.
That is why you need to provide the _average_ number of mutations for
a given level. You cannot simply find two words that are very similar
in spelling, such a vocation and vacation, and then simply ignore the
possibility that such clustered islands may be widely separated from
every other island cluster by significant neutral gaps. This is
demonstrated nicely by your own computer programs which, by your own
assertion, showed an increase, by a factor of 2, in the number of
mutations required to find a meaningful sequence, on average, with
every doubling of L.
> You have yet to find even one without neighbors.
Your own computer programs show you that island clusters become more
and more widely separated so that it requires an exponentially
increasing number of mutations to find a meaningful sequence with
every increase in L. Finding the existence of a little island cluster
here and there does not mean that these clusters are interconnected
with passable bridges. Sure, you might be able to make your way
around a relatively tiny island at very high levels of L, but you
won't be able to get off this island and onto any other island this
side of a practical eternity of time.
For example, say that at L = 100 you are able to find an island that
consists of 100 fairly easily evolvable meaningful sequences of equal
length or greater. But, what is 100 compared to the total number of
possible meaningful sequences in sequence space at this level of L?
Your colony is basically stuck on that island and can't get off
without swimming a very significant distance to find another island at
that level or greater. This island is very very isolated and
relatively tiny relative to the sequence space.
> > > > Again, what was the ratio that your computer found
> > > > for level 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 . . . ect.? I've asked you
> > > > to list this several times and you keep stalling. Don't list what you
> > > > think my ratios are. List what your ratios are.
> > >
> > > Everybody knows that I have provided the answer.
> >
> > But you haven't Zach. You haven't told us what you think the average
> > ratio of meaningful vs. meaningless _mutations_ is at each level, for
> > L = 1 to 20. List this ratio for each level.
>
> I did it for length 21. I leave the others as an exercise for the reader.
Actually you didn't. You didn't list a ratio that your _computers_
found at all for level 21 since your computers never evolved anything
at L = 21 nor did they find an average ratio of meaningful vs.
meaningless mutations for this level or greater. However, you did
actually list a ratio for L = 10 that was actually found by your own
computer programs. I thought you would never do this, but you actually
did. Your ratio for meaningful vs. meaningless mutations at level L =
10 was probably greater than 1 in 2,500,000 - right?
Now that is a "ratio" Zach. That is the type of _average_ ratio that
I want you to show for each level of L = 1 to 20 where meaningful
sequences are at the same level or greater. And, to find a more
accurate _average_, you need to evolve at least 100 meaningful
sequences at each level for each of 10 widely separated starting
points.
> > The odds of finding "other words" involves a ratio that is based on
> > average meaningful vs. meaningless _mutations_ for a given level.
> > This ratio does in fact involve a purely "random means" that cannot be
> > guided until a new meaningful sequence is found since all
> > non-meaningful sequences are equally non-selectable. Selecting
> > between non-meaningful sequences is therefore a neutral process and
> > results in a truly "random walk" until, by sheer luck of the odds
> > ratio, the random walk happens upon a new meaningful sequence.
>
> Turns out that every word I've ever tried (hundreds) has such neighbors. We
> know that number of possible mutations are the sum of point-mutations and
> recombinations. For the eight 21-letter words in our dictionary there are an
> average of 20.25 valid neighbors. There are 6682 available mutations, the
> ratio therefore being 1/330.
Plug a 21-letter word into your computer program and see how many
mutations it takes your computer program, on average, to find a new
meaningful 21-letter sequence or greater. Do this for all eight of
your 21-letter words. That result will be your "ratio". It certainly
will be far less than 1/330. Trust me! After all, you yourself
recognized that at L = 10 the ratio of meaningful to meaningless
mutations was less than 1 in 2 million! Do you think that this ratio
is going to dramatically improve to only 1 in 330 by increasing L to
20? Please Zach, you're loosing it!
> > Actually, this does not contradict my assertion, as I have pointed out
> > to you time and again. My assertion was one of averages, which did
> > not rule out islands or common bridges between large islands at lower
> > levels of complexity. In fact I said many times that all meaningful
> > 3-letter sequences were probably connected by single letter-change
> > bridges. Certainly this would also clearly be true of 6- and
> > 7-character sequences as well. Large islands and interconnecting
> > bridges would still be present, though much less common and much
> > thinner, exponentially so, than they were at lower levels. Even at
> > very high levels such islands will exist, though they will be very
> > rare and very isolated, relatively speaking, from the other islands in
> > that level.
>
> Funny. There seems to a bridge from "electroencephalograph" straight to
> "electroencephalographs" and to "graph" for that matter. Could it be a
> result of the fact that "electroencephalograph" is a complex structure
> composed of smaller sub-units that accreted over time?
Plug either "electroencephalographs" or "electroencephalograph" into
your computer programs and see how many other words or islands
clusters of words of this length or greater can be evolved and what
the average ratio is of meaningful vs. meaningless mutations. Also,
plug "graph" into your simulation and see how long it takes your
computer to evolve "electroencephalograph" *without your help* and
what the overall ratio of meaningless vs. meaningful mutations it took
at each level up the ladder.
Again, showing little tiny islands like this says very little about
the overall appearance of sequence space at a given level. Also, it is
much easier to devolve than it is to evolve. It is relatively each to
go from a bigger meaningful sequence to a smaller meaningful sequence,
but it is much much harder to go from a smaller meaningful sequence to
a larger meaningful sequence.
> > Again, your problem is that although 100^3 = 1,000,000 . . . this says
> > absolutely nothing about how many of the 1 million possible mutations
> > will be meaningfully selectable
>
> We don't know how many of these mutations will be meaningful. You are
> certainly correct! However, if even one of them is meaningful, then the odds
> are certainly less than the Sean Ratio. Our Word Mutator doesn't handle
> phrases, so we must use other means.
You're wrong Zach. The finding of just one meaningful sequence next
to your starting point says nothing about the odds that you will find
another sequence after that and after that. You might even find a
small cluster of sequences, but what are the odds that you will find
another cluster? You see, you completely ignore this possibility in
your L^3 calculation. You simply assume that the ratio will not
significant change as L increases even though your own computer
programs show an _exponential_ decrease in the ratio of meaningful vs.
meaningless _mutations_ with increasing L.
> We know that "Beware a war of words ere you err" (length 33) has no more
> than ~36000 possible first-generation mutations. You are right that we have
> no way to know from this calculation whether a valid mutation exists. This
> number just represents the denominator of the final result. If there is no
> valid mutation, let us call the string "sterile". So let's take a look!
Ok . . .
> "Beware a wad of words ere you err" (note that this mutant string is also
> length 33). Well, we found at least one. So the odds of finding a valid
> mutation is no worse than 1 in 36000.
Keep going . . . How big is your island? How many single letter
character changes can you make before you run into walls? As someone
else has already suggested, you could get to several other phrases,
such as:
"Beware a war of swords ere you ere"
"Beware a wad of swords ere you ere"
"Beware a war of works ere you ere"
It seems though that very quickly one realizes that this island
starting point is quite small. There just aren't too many meaningful
much less "beneficial" sequences of this length or greater that are
only one character different from each other. Very quickly walls are
reached that require multiple character changes to be meaningful in
the English language system.
You see, the average ratio or average distance between meaningful
islands at this level of sequence space is not 1 in 3,600 as you full
well know. In fact, your own observed ratio for L = 10 was less than 1
in 2 million. Do you see the problem?
Mujin
objection:
On Thu, 13 May 2004 14:17:44 +0000 (UTC),
seanpi...@naturalselection.0catch.com (Sean Pitman) wrote:
>"Zachriel" <sp...@zachriel.com> wrote in message news:<keGdnaV4mt3...@adelphia.com>...
>
>
>> > I'm talking about the number of meaningful _mutations_ Zach. The
>> > number of meaningful mutations vs. the number of non-meaningful
>> > mutations used by your computer programs to find a certain number of
>> > meaningful words in each level of complexity from L = 1 to 20. I am
>> > talking about a ratio here, a ratio that your own computer discovered.
>> > Tell us Zach, what average ratio did your computer discover exists
>> > for each level of complexity that it investigated?
>>
>> From my investigations there are usually several such neighbors for just
>> about every word in the Dictionary.
>
>That is why you need to provide the _average_ number of mutations for
>a given level.
[snip]
[snip]
>For example, say that at L = 100 you are able to find an island that
>consists of 100 fairly easily evolvable meaningful sequences of equal
>length or greater. But, what is 100 compared to the total number of
>possible meaningful sequences in sequence space at this level of L?
>Your colony is basically stuck on that island and can't get off
>without swimming a very significant distance to find another island at
>that level or greater. This island is very very isolated and
>relatively tiny relative to the sequence space.
[snip]
>Now that is a "ratio" Zach. That is the type of _average_ ratio that
>I want you to show for each level of L = 1 to 20 where meaningful
>sequences are at the same level or greater. And, to find a more
>accurate _average_, you need to evolve at least 100 meaningful
>sequences at each level for each of 10 widely separated starting
>points.
[snip]
>Plug a 21-letter word into your computer program and see how many
>mutations it takes your computer program, on average, to find a new
>meaningful 21-letter sequence or greater. Do this for all eight of
>your 21-letter words. That result will be your "ratio". It certainly
>will be far less than 1/330.
[snip]
>Plug either "electroencephalographs" or "electroencephalograph" into
>your computer programs and see how many other words or islands
>clusters of words of this length or greater can be evolved and what
>the average ratio is of meaningful vs. meaningless mutations. Also,
>plug "graph" into your simulation and see how long it takes your
>computer to evolve "electroencephalograph" *without your help* and
>what the overall ratio of meaningless vs. meaningful mutations it took
>at each level up the ladder.
[snip]
My objection is simply this: Zachriel is not your student, Sean - he's
debating you as an equal - yet you constantly give him "assignments"
which to my mind is an incredibly arrogant and condescending approach
to this debate.
He has not only gone to some effort to write a program to simulate the
kind of empirical examination of probability space you are theorising
about, but has also provided you access to this program - he even
provided you with the source code so that you could make changes if
you object to any of the assumptions which went into the simulation.
I'm so amazed that he has been patient enough to continue the
discussion with you that I feel obligated to say bluntly something he
has been politely skirting around:
Do the bloody experiment yourself.
You seem certain that your theories regarding the nature and dynamics
of the probability space under discussion are correct, but for some
reason you are reluctant to support these theories with empirical
data. Run the simulations you think demonstrate your point, then post
the data with an analysis explaining why the data supports you. Until
then, you're blowing smoke leaving Zachriel with nothing to do but
rest on his laurels. Seriously, the discussion can't progress any
further until *you* start treating Zachriel as an equal instead of an
underling.
--
K
"Properly read, the Bible is the most potent force for atheism ever
conceived."
-- Asimov
Sean Pitman
> >Plug either "electroencephalographs" or "electroencephalograph" into
> >your computer programs and see how many other words or islands
> >clusters of words of this length or greater can be evolved and what
> >the average ratio is of meaningful vs. meaningless mutations. Also,
> >plug "graph" into your simulation and see how long it takes your
> >computer to evolve "electroencephalograph" *without your help* and
> >what the overall ratio of meaningless vs. meaningful mutations it took
> >at each level up the ladder.
>
> [snip]
>
> My objection is simply this: Zachriel is not your student, Sean - he's
> debating you as an equal - yet you constantly give him "assignments"
> which to my mind is an incredibly arrogant and condescending approach
> to this debate.
They aren't "assignments". They are challenges. The fact is that Zach
has already told us that the ratio of meaningful to meaningless
mutations for L = 10 is less than 1 in 2 million. But, since he made
that statement he has tried to back peddle to argue that since
"electroencephalograph" and "electroencephalographs" are only one
character change different that the ratio for L = 21 is just 1 in
9,200 or so. This is simply wrong and Zach knows it. All anyone has
to do to prove Zach's notion wrong here is to plug
"electroencephalograph" into Zach's own computer program and see how
many mutations it takes to find just 3 other meaningful English
language words/sequences of equal length or greater. You will see that
it is far greater than 9,200.
I myself plugged "electroencephalograph" into Zach's "Word Mutator".
After 2 million mutations, guess how many other words of 21 letters or
greater were "evolved"? Only 1 and this 1 was
"electroencephalographs", which was rapidly evolved, but then nothing
else of equivalent length or greater evolved thereafter.
What does that tell you about Zach's assertions? Trust me, I'm not
giving Zach challenges to which I don't already think I know the
answer. I just want Zach to see for himself that his own programs
work according to my predictions, not his. They do in fact show an
exponential expansion in the average number of _mutations_ needed to
achieve success with increasing sequence length, just like I
predicted. Zach, on the other hand, predicted a geometric expansion,
which is proved false by his own computer simulations. What does in
fact happen is that for every doubling of L, the average number of
mutations required to achieve success increases by a factor of at
least 2. This is a far cry from Zach's L^3 calculation. Check it out
yourself and see if I am not correct . . .
Zachriel
"Sean Pitman" <seanpi...@naturalselection.0catch.com> wrote in message
news:80d0c26f.04051...@posting.google.com...
news:<8c47a09ir1laeu4u4...@4ax.com>...
>
> > >Plug either "electroencephalographs" or "electroencephalograph" into
> > >your computer programs and see how many other words or islands
> > >clusters of words of this length or greater can be evolved and what
> > >the average ratio is of meaningful vs. meaningless mutations. Also,
> > >plug "graph" into your simulation and see how long it takes your
> > >computer to evolve "electroencephalograph" *without your help* and
> > >what the overall ratio of meaningless vs. meaningful mutations it took
> > >at each level up the ladder.
> >
> > [snip]
> >
> > My objection is simply this: Zachriel is not your student, Sean - he's
> > debating you as an equal - yet you constantly give him "assignments"
> > which to my mind is an incredibly arrogant and condescending approach
> > to this debate.
>
> They aren't "assignments". They are challenges. The fact is that Zach
> has already told us that the ratio of meaningful to meaningless
> mutations for L = 10 is less than 1 in 2 million.
No I didn't. A *particular* ten-letter word took that many mutations to find
another word of equal of longer size. Other ten-letter words only take a
single generation. No doubt, some take longer. On the other hand, I have
already pointed out that some words may be completely inaccessible to our
process of evolution. For instance, "Zachriel" has never appeared in any
trial I have made, even when setting the Scrabble score = 99.
I have no idea what the average is. The problem can't be solved by the use
of simplistic Pitmanian Exponents. Let me note that if even a single word is
inaccessible, then the "average" is infinite (or more properly undefined).
You made a specific and verifiable claim, Sean. You claimed it would take a
Pitman Number of steps (26^L / N) to find words in sequence space because
they were randomly distributed. Both aspects of your claim were falsified.
That's it. Please be intellectually honest enough to admit this simple and
well-demonstrated fact. We aren't even including the "zillions" of valid
phrases that inhabit the same sequence space.
In the spirit of your "challenges", please provide us a dictionary of all
valid phrases up to length 100 so we can calculate the Sean Ratio.
david ford
There's no need to [SP]"Check it out" for one's self, since evolution is a fact.
> Sean
> www.naturalselection.0catch.com
Sean Pitman
take, on average, to find at least 10 meaningful words at the same
level of sequence length (L) or greater using 5 widely diverse
starting points? The following are my own observations while playing
around with your program:
LEVEL 1:
"A" = 12 in 81 mutations (average of 1 in 6.75)
"I" = 11 in 81 mutations (average of 1 in 7.36)
"O" = 15 in 81 mutations (average of 1 in 5.4)
Given only 3 possible starting points at this level, the average ratio
of meaningless to meaningful at L = 1 or greater is 1 meaningful in
6.5 meaningless mutations.
Average ratio = 1 in 6.5
LEVEL 2:
"AH" = 12 in 146 (1 in 12.2)
"IS" = 11 in 146 (1 in 13.3)
"OR" = 12 in 146 (1 in 12.2)
"BE" = 12 in 146 (1 in 12.2)
"PI" = 12 in 146 (1 in 12.2)
Average ratio = 1 in 12.4
LEVEL 4:
"PIGS" = 15 in 307 (1 in 20)
"CART" = 21 in 307 (1 in 15)
"QUIT" = 10 in 307 (1 in 31)
"GOOD" = 13 in 307 (1 in 24)
"NODE" = 12 in 307 (1 in 26)
Average ratio = 1 in 23
LEVEL 8:
"CONCEDED" = 13 in 248,387 (1 in 19,100)
"BANKBOOK" = 12 in 655,237 (1 in 54,600)
"MARKETED" = 10 in 133,696 (1 in 13,400)
"DEFINITE" = 19 in 300,337 (1 in 15,800)
"SHACKLES" = 13 in 167,560 (1 in 12,900)
Average ratio = 1 in 23,200
LEVEL 16:
"UNCONVENTIONALLY" = only 2 in over 1,076,480,000 mutations
Average ratio = 1 in over 500 million mutations . . .
I don't think that you can argue much since your own observation ratio
for L = 10 was less than 1 in 2 million. But, if you think other
starting points would result in significantly higher _average_ ratios
at any of these levels then please do try your luck. Until then,
please do notice that a most interesting pattern seems to be emerging.
Notice that the average number of required mutations to achieve
success is not a function of L^3 with increasing L like you suggest.
Quite the contrary. The expansion of the average number of
_mutations_ it takes to achieve success occurs very much like I
suggested to you in the very beginning of our discussion. And, this
expansion would occur with multiword sequences as well as it does with
single words. Your future "Phrasenator" program would run into
exactly the same problem. Why? Because, the expansion of the
meaningless sequences (denominator - D) with increasing L is always
exponentially greater than the expansion of meaningful sequences
(numerator - N) with increasing L. What happens in such a situation
is that that N/D rapidly approaches zero - in an exponential fashion.
Even if like your "map" with very thin interlinking "roads", the roads
would rapidly break with increasing map size since not enough road is
made per increase relative to the non-road areas of the map to keep
the roads linked together in an unbroken chain.
For example, lets say, for arguments sake, that selectably
"beneficial" sequences increase in sequence space by an average of a
factor of 2 with every doubling of L but neutral and/or harmful
mutations increase by a factor of 20. What happens to the ratio of
meaningful vs. meaningless mutations with each doubling of L? Well,
say that in a particular sequence space of 20 total sequences there
were 10 potentially beneficial mutations and 10 potentially
detrimental mutations. What happens if we double the L? Well, at 2L
there will be only 100 potentially beneficial mutations relative to
the 10^20 potentially detrimental mutations. If this happens with
every doubling of L, you can see why existing bridges between islands
of meaningful sequences would quickly become stretched to the breaking
point and rapidly snap completely leaving smaller and smaller islands
to drift on an exponentially expanding vast ocean of emptiness with
only a relatively few faithful and closely tied neighbors as
companions. It is all very much like my "bubblegum island" scenario
that you simply tried to ignore out of hand. And yet, this is exactly
what happens, even with the use of your own computer simulation
programs.
Now it may take a very long time, but I think that eventually you will
actually join my side. You're a hard worker and very persistent.
Those are very good traits to have in a serious search for the truth
about anything. And, I do appreciate all the effort that you have put
into this particular discussion with me. Hopefully, we both continue
to approach truth knowing that neither one of us will ever fully
"arrive" as we both evolve in knowledge and understanding.
Zachriel
"Sean Pitman" <seanpi...@naturalselection.0catch.com> wrote in message
news:80d0c26f.04051...@posting.google.com...
Glad you're actually looking at the data finally. You will find that data
changes one's outlook completely.
You made a slight error in your calculations. You forgot to tell us what
Pond Size you chose. I set it at 25 and this is the results from
"unconventionally":
Pond Size = 25 (default)
5 generations
1,468,658 mutants
"interconnections"
"intercontinental"
(Usually I would recommend a larger Pond for growing longer words. You
don't grow mice in Petri dishes. I ran the simulation twice due to a
programming glitch and forgot to reset the Pond size to the larger value.
For Pond = 100, the results are the same but with 12 million mutants.)
Funny how selecting for length changes everything.
In any case, you're only off by a few of orders of magnitude; however, if we
are talking exponential expansion, over time that can be the difference
between millions and zillions. So instead of evolution taking "zillions" of
years as you have indicated, perhaps it only takes millions of years due to
a slight problem with your "zillionatious exponents".
> I don't think that you can argue much since your own observation ratio
> for L = 10 was less than 1 in 2 million. But, if you think other
> starting points would result in significantly higher _average_ ratios
> at any of these levels then please do try your luck. Until then,
> please do notice that a most interesting pattern seems to be emerging.
>
> Notice that the average number of required mutations to achieve
> success is not a function of L^3 with increasing L like you suggest.
I suggested no such thing. That's an upper-limit of L^3 *per generation*,
with each generation determined by how long the combined length of all the
strings involved takes to achieve whatever result is desired. Indeed, L^3 is
a very wide upper-limit depending on the number and length of strings
involved. Normally it is much less. On the other hand, the number of G
required needs to be determined empirically (or by means not yet suggested
on this thread) as it appears to vary widely between words. However, it
certainly does tend to increase with L, and it certainly does increase
precipitously when we start to run out of words, and increases without limit
when L>23.
> Quite the contrary. The expansion of the average number of
> _mutations_ it takes to achieve success occurs very much like I
> suggested to you in the very beginning of our discussion.
No, it doesn't. You specifically stated it was Sean's Ratio = 26^L / N. This
is incorrect for every word I've tried. If you wish to posit a different
exponential equation, have at it. But please don't state it with certainty
unless you have some evidence other than your "zillionatious" argument from
handwaving extrapolation due to ignorance.
You have a conjecture, nothing else.
> And, this
> expansion would occur with multiword sequences as well as it does with
> single words.
There is a different relationship with phrases due to the fact that my
dictionary starts running out of words at 10 letters and runs out completely
above 23 letters. When you provide me a dictionary of all valid English
phrases, I will modify the program accordingly.
> Your future "Phrasenator" program would run into
> exactly the same problem.
Still waiting for that list of valid phrases up to length 100 or so. After
all data trumps--every time.
Are you delaying because there are "zillions" of such valid phrases? If so,
how many zillions?
> Why? Because, the expansion of the
> meaningless sequences (denominator - D) with increasing L is always
> exponentially greater than the expansion of meaningful sequences
> (numerator - N) with increasing L. What happens in such a situation
> is that that N/D rapidly approaches zero - in an exponential fashion.
You assert an exponential expansion. But which exponential expansion are you
asserting? Perhaps you are right, but not all exponential equations are
equal. It depends on the base and exponent. (In banking, for instance, the
base is usually on the order of 1.000164.) We have already determined it is
not Sean's Ratio = 26^L / N. You just don't seem to want to admit this.
That single assertion is the only reason I started this thread, and the only
purpose I have ever intended. Without you admitting that you were wrong, and
then explicitly modifying your conjecture, no one will take your conjectures
seriously--and any of your bald assertions will probably be discarded
without a second look.
> Even if like your "map" with very thin interlinking "roads", the roads
> would rapidly break with increasing map size since not enough road is
> made per increase relative to the non-road areas of the map to keep
> the roads linked together in an unbroken chain.
What? Certainly an imaginary mapmaker could still connect the different
points on the map, using the exact same pen.
> For example, lets say, for arguments sake, that selectably
> "beneficial" sequences increase in sequence space by an average of a
> factor of 2 with every doubling of L but neutral and/or harmful
> mutations increase by a factor of 20. What happens to the ratio of
> meaningful vs. meaningless mutations with each doubling of L? Well,
> say that in a particular sequence space of 20 total sequences there
> were 10 potentially beneficial mutations and 10 potentially
> detrimental mutations. What happens if we double the L? Well, at 2L
> there will be only 100 potentially beneficial mutations relative to
> the 10^20 potentially detrimental mutations. If this happens with
> every doubling of L, you can see why existing bridges between islands
> of meaningful sequences would quickly become stretched to the breaking
> point and rapidly snap completely leaving smaller and smaller islands
> to drift on an exponentially expanding vast ocean of emptiness with
> only a relatively few faithful and closely tied neighbors as
> companions. It is all very much like my "bubblegum island" scenario
> that you simply tried to ignore out of hand. And yet, this is exactly
> what happens, even with the use of your own computer simulation
> programs.
Um. Do you then admit that the expansion you refer to is not set by Sean's
Ratio? That it is not 26^L / N? You did assert this previously, and used it
as the root of your zillionatious arguments against biological evolution. If
you can be so far off on your mathematics, doesn't that prode you to rethink
your position?
> Now it may take a very long time, but I think that eventually you will
> actually join my side.
<snip>
Please state exactly which exponential equation you are currently asserting
bounds the evolution of words and phrases?
Sean Pitman
> > > My objection is simply this: Zachriel is not your student, Sean - he's
> > > debating you as an equal - yet you constantly give him "assignments"
> > > which to my mind is an incredibly arrogant and condescending approach
> > > to this debate.
> >
> > They aren't "assignments". They are challenges. The fact is that Zach
> > has already told us that the ratio of meaningful to meaningless
> > mutations for L = 10 is less than 1 in 2 million.
> <snip>
>
> No I didn't. A *particular* ten-letter word took that many mutations to find
> another word of equal of longer size. Other ten-letter words only take a
> single generation. No doubt, some take longer.
No doubt. That is why it is best to do an _average_ time. The simple
finding of two 10-letter words that are just one letter different from
each other does not help you out of your predicament. All it shows is
that tiny islands exist in 10-letter sequence space, but it does not
show that this tiny island has any sort of L^3 bridge to cross to any
other island. I did the averages myself Zach and you are not too far
off in your 1 in 2 million ratio of meaningful vs. meaningless for L =
10. If you want to argue this point, and I'm sure you do, then, like
I suggested to you before, you should do your own observations. Do
like I suggested and take 10 or so widely spaced starting points and
see how long it takes those starting points to find 10 other
meaningful sequences at that level or greater. You cannot include
shorter sequences in this figure. Only sequences of the same length
or greater can be included.
The reason for excluding shorter sequences in the overall count is
that it is extremely easy to go down the ladder of complexity, but it
is quite another thing to go up this ladder. We want to know if a
given population can gain some meaningful sequence that they do not
already have at the same or higher levels of their current maximum
meaningful sequence complexity. A meaningful component of a larger
meaningful sequence is both fully formed already and therefore already
potentially independently functional and it is less complex than the
larger meaningful sequence. Deleting the larger sequence without
harming the smaller sequence is therefore quite easy to do. However,
starting with the smaller sequence it is much harder to evolve
anything in higher and higher levels. That is the challenge however.
> On the other hand, I have
> already pointed out that some words may be completely inaccessible to our
> process of evolution. For instance, "Zachriel" has never appeared in any
> trial I have made, even when setting the Scrabble score = 99.
Yes, and this becomes more and more of a problem, in an exponential
fashion with each step up the ladder of meaningful fairly specified
sequence length (L). For example, if you give "Zac" or "Zach" a high
selectability score you will no doubt find such sequences because of
the much higher average density of meaningful sequences in sequence
space at the 3- and 4-letter level (ratio of around 1 in 20). The
sequence "Zachriel" is 2L higher which makes it exponentially harder
to find anyway. My own numbers for L = 8, using your own computer
program, provide an average ratio of around 1 in 20,000 mutations.
With such an average ratio, why would one be surprised that quite a
few islands are already completely isolated from the rest of the
rapidly thinning web of interconnected sequences? Moving up from L =
8 to L = 10, the change in ratio from 1 in 20,000 to 1 in 2,000,000 is
obviously exponential in nature. Even you must admit this since a
ratio of 1 in 2 million isn't anywhere near your much trumpeted L^3
"ratio" which would be no more than 1 in 1,000 (a bit shy of 2 million
I'd say).
Extrapolating the graph, each doubling of L should result in at least
a factor of 2 decrease in the ratio of meaningful to meaningless
mutations. So, going from L = 8 to L = 16, a rough estimate suggests
that the ratio should go from 1 in 20,000 to over 1 in 400,000,000.
Your own estimate of 1 in 2 million for L = 10 is right in line with
this exponential progression. Extrapolating a bit more, at level L =
32, the ratio should drop exponentially to 1 in
160,000,000,000,000,000. Again, this is just a touch more than your
estimate of 1 in L^3 for this level or 32^3 (~30,000).
Do you see what a truly exponential growth does to the numbers now?
Who is it again who is having the problem understanding the difference
between "millions" and "zillions"?
> I have no idea what the average is. The problem can't be solved by the use
> of simplistic Pitmanian Exponents. Let me note that if even a single word is
> inaccessible, then the "average" is infinite (or more properly undefined).
Actually it isn't since there is a concept of "neutral evolution"
available to you - which you haven't included in your simulation.
With the use of neutral strings of characters tagging along with
beneficial strings, every possible beneficial sequence at a given
level is in fact technically "accessible". Of course, the random walk
my take a gazillion years to come across such a meaningful sequence at
higher levels of complexity, but it is still quite possible.
> You made a specific and verifiable claim, Sean. You claimed it would take a
> Pitman Number of steps (26^L / N) to find words in sequence space because
> they were randomly distributed. Both aspects of your claim were falsified.
Not at all. You actually demonstrated that my claim was true quite
nicely. My claim was that the distribution of all meaningful
sequences in the sequence spaces of all language systems are in fact
fairly spread out in that space and that with increasing minimum
sequence length at a given degree of specificity, these clusters and
islands of meaningful sequences start to separate from each other at a
truly exponential rate that is at least close to the 26^L figure.
This observation becomes more and more true, in an exponential
fashion, at higher and higher levels of complexity.
Your computer programs have illustrated as much and yet you still
continue to be blinded to the reality of the situation. The ratio
declines exponentially Zach. There is no way around that fact. Your
L^3 calculation is a gross error of thinking and does not mirror the
true changing ratio of meaningful vs. meaningless mutations at all.
In fact, it becomes exponentially more and more wrong with each
increase of L, as shown above until it looks downright silly for you
to continue using this formula in your arguments. It is erroneous and
the only reason that your program is able to continue to evolve at all
in less than millions of "generations" of average time at levels like
L = 10 is because of your program's enormous reproductive rates and
mutation rates. However, even with such generous search speed as your
population has, it will not be able to do very well for very much
longer because of the exponential expansion of the meaningless
sequences that it must search through with each increase in L. The
exponentially declining ratio thing just kills you Zach - and you
loose the war. But don't feel bad. You aren't the first one and you
won't be the last.
> That's it. Please be intellectually honest enough to admit this simple and
> well-demonstrated fact. We aren't even including the "zillions" of valid
> phrases that inhabit the same sequence space.
I agree. But, even if we did include all potentially
meaningful/beneficial sequences, it wouldn't help you much for one
simple reason. The reason is that the addition of non-beneficial
possibilities with each increase in L is exponential relative to the
addition of beneficial possibilities. As I've pointed out before,
this results in the same problem as you have with "single word only"
possibilities. The expansion of meaningful vs. meaningless mutations
will follow the same exponential pattern.
To use an example that I have already used, say that we start with 10
meaningful and 10 meaningless sequences in a sequence space totaling
20 sequences. Say that with every doubling of L the meaningful
sequences increase by a factor of 2 while the meaningless sequences
increase by a factor of 20. What happens to the ratio? The
meaningful sequences go from 10 to 100 while the meaningless sequences
go from 10 to 10^20. If this keeps happening with every doubling of
L, you can see that it becomes rather unbelievable to think that the
meaningful sequences could remain all clustered together or
interconnected in one tiny spot of sequence space. Even if they
formed a perfectly linear line like a single winding thin road on a
map, it would obviously take intelligent design to keep that road from
breaking up with the exponential addition of map relative to road -
wouldn't you say?
> In the spirit of your "challenges", please provide us a dictionary of all
> valid phrases up to length 100 so we can calculate the Sean Ratio.
You will find that at L = 100 that the "Sean Ratio" or another such
exponentially determined ratio will be much closer to reality than the
geometric "Zach Ratio" of 1 in L^3.
In any case, I've already agreed to your proposal of how meaningful
English language sentences and paragraphs could be defined. If you
follow Standard English language structure and grammar with each
sentence referring to the same idea, then that will be acceptable as
"meaningful". As previously discussed, this obviously excludes
"laundry lists" of words since they have very low specificity.
Seppo Pietikainen
> "Sean Pitman" <seanpi...@naturalselection.0catch.com> wrote in message
<snipping everything>
I think that Sean visualizes a totally different landscape than what Zachriel proposes.
Please correct me if I'm wrong, but from the above discussions I feel that Sean Pitman sees a "fixed
landscape" separated by a rising or settling "sea of fitness" that *all* mutations face, having to
cross ever narrowing "bridges" of survivability, depending on how "fit" they are.
My understanding of Zachriel's thesis is that he proposes a model by which each
mutant lives on its own virtual landscape, creating in effect a new set of hills, valleys
and deadly gorges the new organism lives in.
(while simultaneously competing with other organisms with a different set of hills, valleys and
deadly falls, but that's another story...).
I'm not at all sure I was able to convey my thoughts, but I can live with it...
To summarize, I think that Sean and Zachriel are talking past each other. I'm *far* more
ready to accept Zachriel's model than Sean's "model".
Seppo P.
Sean Pitman
> fact.
Oh, that's right . . . If you already know your theory is "a fact",
what point is ther in testing it?! LOL - You guys are starting to
sound more and more religiously fundamental every day.
John Harshman
Sean Pitman wrote:
>>There's no need to [SP]"Check it out" for one's self, since evolution is a
>>fact.
>>
>
> Oh, that's right . . . If you already know your theory is "a fact",
> what point is ther in testing it?! LOL - You guys are starting to
> sound more and more religiously fundamental every day.
As it happens, David is religiously fundamental. He's a creationist
trying to be sarcastic.
Sean Pitman
> > LEVEL 16:
> >
> > "UNCONVENTIONALLY" = only 2 in over 1,076,480,000 mutations
> >
> > Average ratio = 1 in over 500 million mutations . . .
>
> Glad you're actually looking at the data finally. You will find that data
> changes one's outlook completely.
>
> You made a slight error in your calculations.
Not at all. You evidently didn't get the part were at least 10 new
words must be evolved at each level or greater (not lesser as you like
to do) to determine the average.
>You forgot to tell us what
> Pond Size you chose.
Pardon me, but the results were practically identical even though I
tried the same thing with "pond sizes" ranging from 25 to 1,000.
> I set it at 25 and this is the results from
> "unconventionally":
>
> Pond Size = 25 (default)
> 5 generations
> 1,468,658 mutants
> "interconnections"
> "intercontinental"
That is exactly the same result that I got. The problem is that these
are the only 2 words that will evolve at this level or greater and the
goal was to evolve at least 10 words at each level to get a better
idea of the average distribution the islands in sequence space at
various levels. I gave up trying to get to 10 after a few hundred
million mutations were analyzed by your program and still all I had
was 2 new words. The average distance is therefore clearly well over
1 in 1.4 million mutations. Even you must see that this is certainly
true. In fact the actual average ratio is probably well over 1 in 500
million mutations for your "population" if the experiment were
actually carried out long enough and with a large enough population to
actually find 10 new 16-character words or larger with each of 5
different starting points.
> (Usually I would recommend a larger Pond for growing longer words. You
> don't grow mice in Petri dishes. I ran the simulation twice due to a
> programming glitch and forgot to reset the Pond size to the larger value.
> For Pond = 100, the results are the same but with 12 million mutants.)
Exactly. And if you kept running your program with your pond size at
100 until you found at least 10 new words at that level or greater,
your program wouldn't find them until well after the ratio of 1 in 500
million had been long gone.
> Funny how selecting for length changes everything.
Funny how it limits evolution to very low levels of complexity isn't
it?
> In any case, you're only off by a few of orders of magnitude;
Again you are confused Zach. It is you who are off by a few orders of
magnitude. Go back and re-read the part about getting 10 new words in
each level or greater. Just because you find a small cluster of 2 or
3 words doesn't mean that evolution can find any other words with this
group of higher than average ratio. The average ratio for L = 16 is
certainly over 1 in 500 million mutations. Your own program clearly
shows that this is true. The exponential decline of the meaningful
vs. meaningless ratio is so obvious that I can't for the life of me
see how you are still so blind to this fact and to its significance.
> however, if we
> are talking exponential expansion, over time that can be the difference
> between millions and zillions. So instead of evolution taking "zillions" of
> years as you have indicated, perhaps it only takes millions of years due to
> a slight problem with your "zillionatious exponents".
Not at all. Exponential expansion, even if I am off by many orders of
initial magnitude, quickly translates into "zillions" of years at
relatively low levels of complexity (i.e., character sequences no more
than 1,000 or so fairly specified characters long as I've said
before).
> > I don't think that you can argue much since your own observation ratio
> > for L = 10 was less than 1 in 2 million. But, if you think other
> > starting points would result in significantly higher _average_ ratios
> > at any of these levels then please do try your luck. Until then,
> > please do notice that a most interesting pattern seems to be emerging.
> >
> > Notice that the average number of required mutations to achieve
> > success is not a function of L^3 with increasing L like you suggest.
>
> I suggested no such thing. That's an upper-limit of L^3 *per generation*,
> with each generation determined by how long the combined length of all the
> strings involved takes to achieve whatever result is desired. Indeed, L^3 is
> a very wide upper-limit depending on the number and length of strings
> involved. Normally it is much less. On the other hand, the number of G
> required needs to be determined empirically (or by means not yet suggested
> on this thread) as it appears to vary widely between words. However, it
> certainly does tend to increase with L, and it certainly does increase
> precipitously when we start to run out of words, and increases without limit
> when L>23.
The number of generations (G) needed is dependent upon the population
size, mutation rate, reproductive rate per generation as well as the
RATIO of meaningful vs. meaningless mutations. How many
non-meaningful mutations must be searched through by the population
before a meaningful mutation will be found, on average, at a given
level or greater? Depending upon how many mutations a given population
can search in a given span of time, you can find a "winning" sequence
more or less quickly. It all depends upon how fast that population
can search through the junk to find the treasure. The more junk, the
more time is required for a given population with a steady state size,
mutation rate, and reproductive rate.
Your problem is that your L^3 calculation has absolutely no relevance
to determining the rate of evolution in the population - none at all.
And yet, you try very hard to assert that the L^3 calculation does
have something to do with the average time involved. You claim that on
average a new meaningful 100-character sequence could be evolved every
1 million mutations or so using your L^3 extrapolation. I claim, on
the other hand, that it would take more like 10^100 mutations, on
average, to find a new 100-character sequence.
Which prediction does the evidence best support? Your computer model
supports my position, not yours. Obviously, the _average_ time needed
by your computer to evolve even 10-letter words, according to your own
observations, is on the order of 1 in 2 million mutations. This is far
above what you have suggested on your website and in this forum as an
extrapolation of the L^3 calculation for L = 10. Why don't you say on
your website that the actual average number of mutations it takes to
evolve 10-letter words is not L^3 or 1000 mutations for L = 10, but
rather 2 million mutations?
I mean, this is in fact what it looks like you are saying on your
website is it not? You write, "For a thousand letters, the total
possible mutations is 10^9, which is many orders of magnitude less
than 'zillions'". Of course, this makes people think that you think
that new meaningful 1000-character sequences will evolve in less than
10^9 mutations on average - right? Of course now you know that this
idea is completely bogus. Even according to your own observations new
10-letter sequences require an average of well over 2 million
mutations each, relative to an average starting point. But, by your
L^3 calculation, the average number of mutations needed is only 1,000
("M = L^3"). Now whose thinking is way off here?
Oh, and by the way, I see that you quickly changed this part of your
website:
"This makes I = S * L = L^3, a nice round figure. Gee whiz. Maybe Sean
Pitman is right, after all. That number does increase geometrically!"
The last word in this phrased used to read "exponentially" just a week
or so ago. You won't admit it of course since you have already
basically denied it, but you did in fact change "exponentially" to
read "geometrically" in this passage.
> > Quite the contrary. The expansion of the average number of
> > _mutations_ it takes to achieve success occurs very much like I
> > suggested to you in the very beginning of our discussion.
>
> No, it doesn't. You specifically stated it was Sean's Ratio = 26^L / N. This
> is incorrect for every word I've tried.
I specifically stated that this ratio was a good rule of thumb that
gets more and more reliable with higher levels of complexity. I
specifically stated that with low levels of complexity there exist
islands that are relatively close together with many interconnecting
bridges in between, but that these islands rapidly separate and the
bridges rapidly narrow and break, in an exponential fashion, with each
increase in L. I also specifically stated that once you know what the
actual ratio is for meaningful vs. non-meaningful mutations that this
ratio would increase in an exponential manner with each increase in L.
That is exactly what happened with your own program as I have already
pointed out to you. With increasing L, the ratio of meaningful vs.
non-meaningful mutations decreases by a factor of at least 2. So,
again, say you start with a ratio of 1 in 1,500 for L = 5. What ratio
would you expect to see for L = 10? Well, with just a factor of 2
increase with every doubling of L we would expect so see a ratio of 1
in 2,250,000. This, of course, is right about at what you and I
observed as the actual ratio - is it not? Clearly then, we are
talking a true exponential expansion here. What then is the only
logical assumption one can make about increases of L beyond level 10?
That they will also show roughly the same exponentially decreasing
ratio - right? This obviously means that the ratio for L = 20 would
be around 1 in 5 trillion. L = 40 would have a ratio of about 1 in 25
trillion trillion. L = 80 would be running about 1 in 6.25e50
mutations.
Are you starting to see how this observed exponential progression is
far far more consistent with my position and predictions than to
yours? In fact, the exponential nature of this declining ratio simply
kills your position in no uncertain terms. You flat out loose the war
in very short order.
> If you wish to posit a different
> exponential equation, have at it. But please don't state it with certainty
> unless you have some evidence other than your "zillionatious" argument from
> handwaving extrapolation due to ignorance.
Your own programs show this exponential expansion just the way that I
have described it here. What more evidence do you want than that
given to you by your own computer programs? You don't seem to
understand that any truly exponential process of expanding neutral
gaps would just do your theory in completely. Certainly the one that
matches reality, as discovered by your computer programs, is simply
devastating to your position.
> You have a conjecture, nothing else.
Not at all Zach. I have very good evidence both before and now after
you have come along with your computer programs. You only helped my
position is all. Your computer programs showed exactly what I
expected them to show. They showed a dramatic exponential expansion
of average neutral gaps (i.e., the ratio of meaningful to
non-meaningful mutations) between meaningful sequences with increasing
length. That alone is enough to sink your position without any
lifeboats.
> > Your future "Phrasenator" program would run into
> > exactly the same problem.
>
> Still waiting for that list of valid phrases up to length 100 or so. After
> all data trumps--every time.
>
> Are you delaying because there are "zillions" of such valid phrases? If so,
> how many zillions?
But there aren't. That is your problem. With each increase in L, the
number of new "beneficial" sequences does not increase nearly as fast
as the number of new non-beneficial sequences increases. In fact, the
difference is an exponential difference. That is why, even at very
low levels of complexity, such as the difference between 4-letter and
8-letter words, the ratio of meaningful vs. non-meaningful mutations
decreases exponentially (far more than the actual difference between
the absolute number of 4- and 8-letter words in the dictionary).
> > Why? Because, the expansion of the
> > meaningless sequences (denominator - D) with increasing L is always
> > exponentially greater than the expansion of meaningful sequences
> > (numerator - N) with increasing L. What happens in such a situation
> > is that that N/D rapidly approaches zero - in an exponential fashion.
>
> You assert an exponential expansion. But which exponential expansion are you
> asserting? Perhaps you are right, but not all exponential equations are
> equal. It depends on the base and exponent. (In banking, for instance, the
> base is usually on the order of 1.000164.) We have already determined it is
> not Sean's Ratio = 26^L / N. You just don't seem to want to admit this.
Try this little experiment Zach and see if it doesn't tell you
something. Take the number 1.000164 and increase it by a factor of 2.
How many times can you keep increasing each result by a factor of 2
until your computer calculator cannot calculate any more because the
number is too big? My calculator stalled out at 29 with 1e38235. Do
you see how this relates to your position?
> That single assertion is the only reason I started this thread, and the only
> purpose I have ever intended. Without you admitting that you were wrong, and
> then explicitly modifying your conjecture, no one will take your conjectures
> seriously--and any of your bald assertions will probably be discarded
> without a second look.
Anyone who takes the time to read what I wrote in the original posts
to this thread and on my website will know what my true position
actually was and is - that it is far more than a simple "bald"
assertion - like your L^3 assertion. You have attempted to build a
strawman representation of my position, which is not and never was
even remotely reflective of my actual position. In doing so however,
you have only succeeded in demonstrating the validity of my position.
Also, the fact of the matter is that many, even among the most
prominent and intelligent members of this forum, actually do take my
"conjectures" seriously. You yourself have spent a great deal of time
responding to my "conjectures" and have even devoted an entire website
to opposing my ideas in particular. How can I be more honored and
feel that I am truly being "taken seriously" than this?
> > Even if like your "map" with very thin interlinking "roads", the roads
> > would rapidly break with increasing map size since not enough road is
> > made per increase relative to the non-road areas of the map to keep
> > the roads linked together in an unbroken chain.
>
> What? Certainly an imaginary mapmaker could still connect the different
> points on the map, using the exact same pen.
Not if his ink was more limited than the distance between the dots on
the map that he had to connect.
> > For example, lets say, for arguments sake, that selectably
> > "beneficial" sequences increase in sequence space by an average of a
> > factor of 2 with every doubling of L but neutral and/or harmful
> > mutations increase by a factor of 20. What happens to the ratio of
> > meaningful vs. meaningless mutations with each doubling of L? Well,
> > say that in a particular sequence space of 20 total sequences there
> > were 10 potentially beneficial mutations and 10 potentially
> > detrimental mutations. What happens if we double the L? Well, at 2L
> > there will be only 100 potentially beneficial mutations relative to
> > the 10^20 potentially detrimental mutations. If this happens with
> > every doubling of L, you can see why existing bridges between islands
> > of meaningful sequences would quickly become stretched to the breaking
> > point and rapidly snap completely leaving smaller and smaller islands
> > to drift on an exponentially expanding vast ocean of emptiness with
> > only a relatively few faithful and closely tied neighbors as
> > companions. It is all very much like my "bubblegum island" scenario
> > that you simply tried to ignore out of hand. And yet, this is exactly
> > what happens, even with the use of your own computer simulation
> > programs.
>
> Um. Do you then admit that the expansion you refer to is not set by Sean's
> Ratio? That it is not 26^L / N? You did assert this previously, and used it
> as the root of your zillionatious arguments against biological evolution. If
> you can be so far off on your mathematics, doesn't that prode you to rethink
> your position?
The 26^L/N calculation was meant to be a rough estimate demonstrating
the exponential nature of sequence space expansion relative to the
increase in meaningful sequences within sequence space. It is also
gets more and more accurate with increasing minimum sequence length as
rough predictor of the average number of mutations it would take, on
average, to find new meaningful sequences within a certain level of
complexity or greater. You yourself showed that at L = 10 that the
average ratio was around 1 in 2 million or so. This is right in line
with my predictions of very rapid exponential expansion of neutral
gaps, which rapidly stall out evolutionary progression of a give
population with set size, mutation rate and reproduction rate - just
like I have always said.
In view of this, it is your predictions of significant evolution that
have come up significantly wanting. As I said in the beginning of
this thread, you simply cannot evolve anything equivalent to your "O
Sean Pitman" poem this side of a practical eternity of time (i.e.,
zillions of years). That was the initial challenge and that is
exactly what your own computer programs have shown to be impossible -
just like I said.
> > Now it may take a very long time, but I think that eventually you will
> > actually join my side.
> <snip>
>
> Please state exactly which exponential equation you are currently asserting
> bounds the evolution of words and phrases?
I have detailed it extensively above and in previous threads. Look at
what happens every time L is doubled. Very quickly the ratio of
meaningful to meaningless mutations decreases by a FACTOR of 2. That
is the exponential equation that your own programs produced. It simply
demolishes your own argument. I don't know how my repeating this over
and over again is going to help you understand any better since it is
already so obvious. What more do you need Zach?
Sean Pitman
Ah, well that makes more sense then ; )
david ford
Evolution is a well-proven fact. Dobzhansky, Mayr, Wilson, Gould,
Futuyma, Dawkins, Sagan, and Simpson are extremely knowledgeable
scientists, and I appeal to their expert opinion as support for my
assertion that evolution is a _fact_.
Once theories become as well-supported as evolution, there's really no
longer any more need to try to produce additional evidence for that
fact-hood. It's really a dead issue as to whether the fact of
evolution is correct or not. It is so well supported that if some
IDiot comes along claiming that he or she has located some "flaw" with
the fact of evolution, we already know we needn't bother with
investigating his or her totally erroneous claim.
Feynman on giving all the information; Dobzhansky, Mayr, Wilson,
Gould, Futuyma, Dawkins, Sagan, Simpson
http://www.google.com/groups?selm=Pine.SGI.3.95.970912002214.12893C-100000%40umbc8.umbc.edu
Zachriel
"Sean Pitman" <seanpi...@naturalselection.0catch.com> wrote in message
news:80d0c26f.04051...@posting.google.com...
>
> In any case, I've already agreed to your proposal of how meaningful
> English language sentences and paragraphs could be defined. If you
> follow Standard English language structure and grammar with each
> sentence referring to the same idea,
How do I tell my computer what an "idea" is? Do you really sit around and
dream up new ways to make phantasmagorical goal-posts?
Zachriel
"Sean Pitman" <seanpi...@naturalselection.0catch.com> wrote in message
news:80d0c26f.04051...@posting.google.com...
news:<T-idnUKSqNA...@adelphia.com>...
>
> > > LEVEL 16:
> > >
> > > "UNCONVENTIONALLY" = only 2 in over 1,076,480,000 mutations
> > >
> > > Average ratio = 1 in over 500 million mutations . . .
> >
> > Glad you're actually looking at the data finally. You will find that
data
> > changes one's outlook completely.
> >
> > You made a slight error in your calculations.
>
> Not at all. You evidently didn't get the part were at least 10 new
> words must be evolved at each level or greater (not lesser as you like
> to do) to determine the average.
You do realize that 10 words of 16 length is a specialized string of 160 in
combined length. Why are you moving the goal-posts, Sean, especially in such
a transparent fashion?
Let's do this again. Please answer each point.
*****************
* Point #1
* Sean's Assertion
*
*****************
This was your assertion. This was your claim:
> > "Getting from one meaningful 7-letter phrase to a different meaningful
> > 7-letter phrase requires, on average, a fairly long random walk through
> > 250,000 meaningless options."
> > http://tinyurl.com/ypos7
or to rephrase for L,
> > "Getting from ONE meaningful L-letter phrase to a different meaningful
> > L-letter phrase requires, on average, a fairly long random walk through
> > Pitman Number = 26^L / N meaningless options."
> > http://tinyurl.com/ypos7
This is false and has been demonstrated, yet you have never admitted this.
This entire thread is dedicated to the refutation of this assertion. When
you have repudiated this assertion, then we can perhaps continue on to other
subjects. Please do not go past this point until you have satisfactorily
answered this objection. Please withdraw this false assertion.
****************
*
* Point #2
* Sean's revised assertion
*
****************
I will attempt to restate your position. If you disagree with this
restatement, please clearly state your assertion. And please show your math.
You now assert that the number of permutations to evolve X number of words
at a given length of L is an unnamed and undefined function, but you are
convinced it is some exponential. Yet, even though you haven't given any
specifics, you claim that this exponential will quickly reach "zillions".
Please show your math or withdraw your assertion, or in the light of your
false assertion in Point #1, rephrase it as a conjecture. But please show
your math, and quit with the handwaving.
**************
* Point #3
* Zachriel's non-assertions
*
**************
Please be careful not to misstate my position. At no time have I indicated
that all results are available in L^3 mutations. Rather L^3 is the number of
mutants available for each generation. The number of generations depends on
many factors (including the seed words, Pond size, method of selection,
results desired, etc.), and some results may not be available at all to our
evolutionary algorithm.
Also, I have never stated that the number of mutations to evolve long words
is not some exponential function of L, nor have I asserted the contrary.
Rather I have stated that the function is not the Sean Ratio, and have
demonstrated that to a great deal of certainty.
I do assert the demonstrated truth that many results are available to our
evolutionary algorithm, and of these, many are of the form described in your
original assertion and are evolvable in much less than a Pitman Zillion.
Zachriel
"Sean Pitman" <seanpi...@naturalselection.0catch.com> wrote in message
news:80d0c26f.04051...@posting.google.com...
>
> "UNCONVENTIONALLY" = only 2 in over 1,076,480,000 mutations
>
> Average ratio = 1 in over 500 million mutations . . .
>
Pop=500
"unconventionally"
~6 generations (Q'd out)
mutants 244,462,096
length 16
"conventionalisms"
"interdependently"
"collaborationism"
"collaborationist"
"interconnections"
"interventionists"
"intercontinental"
"representational"
length 18
"noninterventionist"
length 19
"nonrepresentational"
The Pitman Number(16) = 100,946,164,119,048,000,000
The Pitman Number(19) = 19,653,006,800,009,300,000,000,000
Using Sean's own chosen word, with his *brand-new* requirement of TEN words,
we have evolved a word of L+3, another word of L+2, and eight other words of
length L.
and did it in less than 0.000000000242170763132416% of Sean's originally
predicted value for L=16.
*****
Just in! Sean has adjusted his predictions. (More on this later. I may not
be able to post for the next few days.)
*****