WTF is up with the Darwin unit definitions?
John Vreeland
Darwin as [ln(x2) - ln(x1)] / dT, where x1 and x2 are the
characteristic sizes you are measuring and dT is the timespan between
them. This formula makes no sense mathematically. Even if you ignore
the units you are using (meters, feet, whatever) the value you get
will vary depending on what units it was initially measured in.
For example, if a flower increases in size from one centimeter to two
in one million years, then (ignoring centimeters) the result is an
infinite number of darwins. If you perform the same calculation in
meters you get a much smaller answer.
Clearly the formula should be ln(x2/x1) / dT, yet every Internet
reference I can find contains the bogus formula. I "corrected" the
wikipedia out of a sense of mathematical outrage, but am I missing
something here?
--
John Vreeland (IEEE.org)
"Will future ages believe that such stupid bigotry ever existed!" ---Ivanhoe
Perplexed in Peoria
"John Vreeland" <vree...@snotmail.com> wrote in message news:r83u03t8729teflv1...@4ax.com...
> I thought it was a stupid mistake in the Wikipedia when they defined a
> Darwin as [ln(x2) - ln(x1)] / dT, where x1 and x2 are the
> characteristic sizes you are measuring and dT is the timespan between
> them. This formula makes no sense mathematically. Even if you ignore
> the units you are using (meters, feet, whatever) the value you get
> will vary depending on what units it was initially measured in.
>
> For example, if a flower increases in size from one centimeter to two
> in one million years, then (ignoring centimeters) the result is an
> infinite number of darwins. If you perform the same calculation in
> meters you get a much smaller answer.
>
> Clearly the formula should be ln(x2/x1) / dT, yet every Internet
> reference I can find contains the bogus formula. I "corrected" the
> wikipedia out of a sense of mathematical outrage, but am I missing
> something here?
Yes. Several things. For one thing, ln(1) is zero, not negative infinity.
Second, the wiki formula gives the same result as your formula, as long as
the same units are used for both x1 and x2. But that is a requirement of
your formula, too.
For another thing, the formula does not define a darwin. It defines
a kind of evolutionary change rate which can be denominated in darwins.
http://en.wikipedia.org/wiki/Darwin_%28unit%29
FWIW, I prefer your version of the formula since I dislike the practice
of taking logarithms of anything that has dimensions. But you definitely
see it done in a lot of places.
John Vreeland
wrote:
> "John Vreeland" <vreej...@snotmail.com> wrote in messagenews:r83u03t8729teflv1...@4ax.com...
> > I thought it was a stupid mistake in the Wikipedia when they defined a
> > Darwin as [ln(x2) - ln(x1)] / dT, where x1 and x2 are the
> > characteristic sizes you are measuring and dT is the timespan between
> > them. This formula makes no sense mathematically. Even if you ignore
> > the units you are using (meters, feet, whatever) the value you get
> > will vary depending on what units it was initially measured in.
>
> > For example, if a flower increases in size from one centimeter to two
> > in one million years, then (ignoring centimeters) the result is an
> > infinite number of darwins. If you perform the same calculation in
> > meters you get a much smaller answer.
>
> > Clearly the formula should be ln(x2/x1) / dT, yet every Internet
> > reference I can find contains the bogus formula. I "corrected" the
> > wikipedia out of a sense of mathematical outrage, but am I missing
> > something here?
>
> Yes. Several things. For one thing, ln(1) is zero, not negative infinity.
>
> Second, the wiki formula gives the same result as your formula, as long as
> the same units are used for both x1 and x2. But that is a requirement of
> your formula, too.
>
> For another thing, the formula does not define a darwin. It defines
>
> FWIW, I prefer your version of the formula since I dislike the practice
> of taking logarithms of anything that has dimensions. But you definitely
> see it done in a lot of places.
Ah. I was trying to get to sleep and I realized that my example was
botched. Anyway, the formula as originally stated is correct IF you
are dealing with dimensionless units. However, what dimensionless
units are ever used in measurement? It looks like someone tried to
simplify the original formula, forgetting that you can not simplify
ln(x/y) into ln(x) - ln(y) if x and y have units. Assuming you even
consider that simplification! That was drilled into my head in high
school.
Yes, I have seen it done before, too, but it results in an ad-hoc law
that depends on the measurement system used with some kind of silly
compensation constants. Why would anyone want to do that? And yet
the formula was listed the wrong way every place I looked. Is this a
case of cut-and-paste ignorance?
Mark VandeWettering
> I thought it was a stupid mistake in the Wikipedia when they defined a
> Darwin as [ln(x2) - ln(x1)] / dT, where x1 and x2 are the
> characteristic sizes you are measuring and dT is the timespan between
> them. This formula makes no sense mathematically. Even if you ignore
> the units you are using (meters, feet, whatever) the value you get
> will vary depending on what units it was initially measured in.
>
> For example, if a flower increases in size from one centimeter to two
> in one million years, then (ignoring centimeters) the result is an
> infinite number of darwins. If you perform the same calculation in
> meters you get a much smaller answer.
>
> Clearly the formula should be ln(x2/x1) / dT, yet every Internet
> reference I can find contains the bogus formula. I "corrected" the
> wikipedia out of a sense of mathematical outrage, but am I missing
> something here?
Perhaps that (ln(x2)-ln(x1))/dt is equal to ln(x2/x1) / dT?
Mark
Mark VandeWettering
Well, fine. Yes, your formula is probably clearer and more proper, but
saying that "you cannot simplify" the formula this way seems like an
odd claim as well, since they are equivalent (give the same answer).
Taking the difference of two "log feet" for instance may seem odd, but
it really is no different than taking the log of dimensionless quantity
formed by the ratio of the two feet.
> Yes, I have seen it done before, too, but it results in an ad-hoc law
> that depends on the measurement system used with some kind of silly
> compensation constants.
No, it doesn't.
> Why would anyone want to do that? And yet the formula was listed
> the wrong way every place I looked. Is this a case of cut-and-paste
> ignorance?
Mark
Ernest Major
<vree...@snotmail.com> writes
>I thought it was a stupid mistake in the Wikipedia when they defined a
>Darwin as [ln(x2) - ln(x1)] / dT, where x1 and x2 are the
>characteristic sizes you are measuring and dT is the timespan between
>them. This formula makes no sense mathematically. Even if you ignore
>the units you are using (meters, feet, whatever) the value you get
>will vary depending on what units it was initially measured in.
>
>For example, if a flower increases in size from one centimeter to two
>in one million years, then (ignoring centimeters) the result is an
>infinite number of darwins. If you perform the same calculation in
>meters you get a much smaller answer.
>
>Clearly the formula should be ln(x2/x1) / dT, yet every Internet
>reference I can find contains the bogus formula. I "corrected" the
>wikipedia out of a sense of mathematical outrage, but am I missing
>something here?
It's all very well committing an April Fool, but should you embed an
infactuality in WikePedia's edit log? If I'm not mistaken that' one
place that can't be corrected.
--
alias Ernest Major
John Vreeland
<wett...@attbi.com> opined:
Right. WTF was I doing? Don't work on stuff in the middle of the
night, you begin to see things.
Dunno what I was talking about actually, and find it hard to believe I
wrote that. If it's okay with y'all I'm gonna pretend I never wrote
that. It must have been noodle80.
--
Two Creation Scientists can hold an intelligent conversation, if one of them is a sock puppet.
---John Vreeland(IEEE.org)
Robert Carnegie
> I thought it was a stupid mistake in the Wikipedia when they defined a
> Darwin as [ln(x2) - ln(x1)] / dT, where x1 and x2 are the
> characteristic sizes you are measuring and dT is the timespan between
> them. This formula makes no sense mathematically.
You briefly did have me believing in this, at least that rsome twit
had put content into Wikipedia about a unit called the darwin. The
difficulty would be your believing it to be wrong, and then raising it
here instead of correcting it in WP.
John Vreeland
There really is a darwin unit, for anyone who wants to recognize it.
It's the e-fold (natural log) change in a characteristic per million
years. It's not a terribly useful unit of measure but it has its
place. I was trying to make a complicated joke out of it for the
day's festivities but completely botched it, making myself look even
stupider than normal. Don't dream up stuff at the last second in the
middle of the night while somebody else is mixing the drinks.
Mark VandeWettering
Ah. I like my humor to have a little more, well... humor in it.
The problem with trying to post something stupid on April Fool's day
in talk.origins is that it normally swamped by the natural background
levels. It's very hard to tell April Fools day from any other day
in talk.origins.
Mark
rmj
"John Vreeland" <vree...@yahoo.com> wrote in message
news:1175454734....@q75g2000hsh.googlegroups.com...
change? It can't be whatever someone wants, but must be universally
specified.
Perplexed in Peoria
"Mark VandeWettering" <wett...@attbi.com> wrote in message news:slrnf102ak.2...@fishtank.brainwagon.org...
Especially when the posting is done (apparently) from the Eastern hemisphere
and arrives here in the American Midwest sometime in March.
The best prank I've ever seen took place several years back on the CBS
nightly newscast. As is often the case, they needed to fill in the last
few minutes with a human-interest story, and this one was about the
Swiss spaghetti harvest. Great news-footage of Swiss peasants using their
army knives to cut the spaghetti from the trees and laying it out to dry.
And the voice-over explaining that while the Swiss crop is less well known
than the Italian, connoisseurs rate it as slightly higher in quality. But,
alas, this traditional way of life in the Alps is on its way out due to EU
agricultural policies. And then we return to Walter Cronkite, saying "And
that's the way it is, April 1, 19..".
Tiny Bulcher
>
> The best prank I've ever seen took place several years back on the CBS
> nightly newscast. As is often the case, they needed to fill in the
> last
> few minutes with a human-interest story, and this one was about the
> Swiss spaghetti harvest. Great news-footage of Swiss peasants using
> their
> army knives to cut the spaghetti from the trees and laying it out to
> dry.
> And the voice-over explaining that while the Swiss crop is less well
> known
> than the Italian, connoisseurs rate it as slightly higher in quality.
> But,
> alas, this traditional way of life in the Alps is on its way out due
> to EU
> agricultural policies. And then we return to Walter Cronkite, saying
> "And
> that's the way it is, April 1, 19..".
And that was robbed off the BBC; Richard Dimbleby did the original story on
"Panorama" on April 1 1957.
http://news.bbc.co.uk/onthisday/hi/witness/april/1/newsid_4362000/4362667.stm
Perplexed in Peoria
"Tiny Bulcher" <RSGD...@aol.com> wrote in message news:yrSdnRB399D...@bt.com...
> þus cwæð Perplexed in Peoria:
It wasn't Cronkite? You are joking, right?
Ernest Major
<gle...@jps.net> writes
The change part of the definition of the darwin is the ratio of the
initial and final values of a quantifiable trait. Because it is a ratio
it is a dimensionless number, i.e. has no units.
--
alias Ernest Major
Ernest Major
Peoria <jimme...@sbcglobal.net> writes>> žus cwęš Perplexed in Peoria:
http://en.wikipedia.org/wiki/Spaghetti_tree
http://www.museumofhoaxes.com/spaghetti.html
--
alias Ernest Major
Tiny Bulcher
Oh, I'm sure the studio bits were Cronkite all right, but the film insert in
between was good old Auntie Beeb.
John Wilkins
> "Mark VandeWettering" <wett...@attbi.com> wrote...
The BBC did it. CBS just lifted it.
--
John S. Wilkins, Postdoctoral Research Fellow, Biohumanities Project
University of Queensland - Blog: scienceblogs.com/evolvingthoughts
"He used... sarcasm. He knew all the tricks, dramatic irony, metaphor,
bathos, puns, parody, litotes and... satire. He was vicious."
rmj
"Ernest Major" <{$to$}@meden.demon.co.uk> wrote in message
news:z2mLV8Y$SBEG...@meden.invalid...
Some traits can be quantified in multiple ways. For example, bone strength;
do you choose the width of the bone, the percentage of calcium or some other
element or molecule, the pressure to crack the bone (and at what angle and
distance is the pressure applied), the pressure to crush the bone, etc. It
would seem that each of these would give a different Darwin, and so the
Darwin is a worthless unit.
> --
> alias Ernest Major
>
Perplexed in Peoria
"rmj" <gle...@jps.net> wrote in message news:cg0Qh.17445$PL....@newsread4.news.pas.earthlink.net...
>
> "Ernest Major" <{$to$}@meden.demon.co.uk> wrote in message
> news:z2mLV8Y$SBEG...@meden.invalid...
> > initial and final values of a quantifiable trait. Because it is a ratio it
> > is a dimensionless number, i.e. has no units.
Actually, the dimensions of the darwin is time^(-1). More specifically,
per-million-years.
> Some traits can be quantified in multiple ways. For example, bone strength;
> do you choose the width of the bone, the percentage of calcium or some other
> element or molecule, the pressure to crack the bone (and at what angle and
> distance is the pressure applied), the pressure to crush the bone, etc. It
> would seem that each of these would give a different Darwin, and so the
> Darwin is a worthless unit.
No more so than the inch is. Length of femur can be measured in inches, and
so can length of tibia. It might be that from A. afarensis to H. sapiens, the
cranial capacity increased at a rate of 1.2 darwins, whereas femur length
grew at a mere 0.3 darwin rate, femur cross-section at 0.4 darwins, and femur
volume at 0.7 darwins. Where is the problem?
Cory Albrecht
> Some traits can be quantified in multiple ways. For example, bone strength;
> do you choose the width of the bone, the percentage of calcium or some other
> element or molecule, the pressure to crack the bone (and at what angle and
> distance is the pressure applied), the pressure to crush the bone, etc. It
> would seem that each of these would give a different Darwin, and so the
> Darwin is a worthless unit.
I'm thinking you'ld have to have to have _all_ of those measurement -
plus a gazillion more - and scatter-plot the results and draw in a trend
line. Assuming, of course, that your results don't Boyle's Law all over
your graph and make a trend line worthless.
Ernest Major
in Peoria <jimme...@sbcglobal.net> writes
>
>"rmj" <gle...@jps.net> wrote in message
>news:cg0Qh.17445$PL....@newsread4.news.pas.earthlink.net...
>>
>> "Ernest Major" <{$to$}@meden.demon.co.uk> wrote in message
>> news:z2mLV8Y$SBEG...@meden.invalid...
>> > The change part of the definition of the darwin is the ratio of the
>> > initial and final values of a quantifiable trait. Because it is a ratio it
>> > is a dimensionless number, i.e. has no units.
>
>Actually, the dimensions of the darwin is time^(-1). More specifically,
>per-million-years.
Yep. I carefully specified the "change part of the definition".
>
>> Some traits can be quantified in multiple ways. For example, bone strength;
>> do you choose the width of the bone, the percentage of calcium or some other
>> element or molecule, the pressure to crack the bone (and at what angle and
>> distance is the pressure applied), the pressure to crush the bone, etc. It
>> would seem that each of these would give a different Darwin, and so the
>> Darwin is a worthless unit.
>
>No more so than the inch is. Length of femur can be measured in inches, and
>so can length of tibia. It might be that from A. afarensis to H. sapiens, the
>cranial capacity increased at a rate of 1.2 darwins, whereas femur length
>grew at a mere 0.3 darwin rate, femur cross-section at 0.4 darwins, and femur
>volume at 0.7 darwins. Where is the problem?
>
Perhaps confusing a darwin with the rate of evolution of a lineage,
rather than of a trait.
--
alias Ernest Major
Ernest Major
<coryalbr...@hotmail.com> writes
The darwin is the rate of evolution of a trait, not a lineage. (And he
gives four different, but somewhat correlated, traits above. In practice
the only one we can measure with any degree of precision over geological
time would be the thickness of the bone.)
--
alias Ernest Major
bi...@juno.com
> For example, if a flower increases in size from one centimeter to two
> in one million years, then (ignoring centimeters) the result is an
> infinite number of darwins. If you perform the same calculation in
> meters you get a much smaller answer.
"Infinite?" Nyet. Dividing something by one million does not lead to
an infinite answer.
This may be an attempted joke, but it highlights an important fact:
the lack of mathematically precise predictions within evolutionary
theory. This lack is a major cause of the un-falsifiability of the
theory as a whole.
You can only falsify very minor parts of evolution; there is no
potential way to falsify the non-predictive theory as a whole. Ergo,
'tis not a hard science. Whereas, if evolution actually DID make
mathematically precise predictions, 'twould be in the realm of hard
falsifiable science.
>
> Clearly the formula should be ln(x2/x1) / dT, yet every Internet
> reference I can find contains the bogus formula. I "corrected" the
> wikipedia out of a sense of mathematical outrage, but am I missing
> something here?
You are missing the fact that all the hard sciences make
mathematically precise predictions, and to do this they don't have to
resort to unitless ratios. Nor do they have to dress up their theory
in a formula ripped off from freshman Calculus with unit-less terms.
That is because their mathematical equations actually predict
something precise enough to be tested.
Joke or not, this topic is sort of funny to me, but probably not in
the way you had hoped.