Foundations of Conjectural Modelling some refinements
Huang
Consider two segments M and N which are constructed as follows:
N = a + b where a exists, b does not exist.
We can draw a picture of N as follows :
N = a + b = |-----------------| + | ~ ~ ~ |
M = a * b where a exists, b does not exist.
We can draw a picture of M as follows :
M = a * b = |-~-~-~-~-~-~-~-~-~-~-~|
We can think of this philosophically (in words) as follows. N is
constructed by juxtaposing an existent segment with a nonexistent one.
M is constructed by multiplying nonexistence into existence, because
the points which comprise M are each taken as existing with
probability p_k.
Algebraically, we can try to show that M and N have the same magnitude
and explore what that means.
If we want to multiply (a) by a scalar quantity to get (a+b), that
scalar would be (a+b) / a . Multiplying by (a+b) / a will have the
effect ot magnifying (a) to a magnitude of precisely (a+b).
So,
[(a+b) / a] * a = (a+b)
Restated in words, the magnitude M is equivalent to the magnitude N.
This is true for all (a) whenever b=0.
But the INTERESTING thing is that we got N by adding, and we got M by
multiplying.
And this is indeed interesting as we try to develop a kind of algebra
which is based on operators which are "indeterminately either addition
or multiplication". Technically, this statement was worded for the
layman, because we will not be doing algebra at all, nor even
mathematics. We are modelling conjecturally which, technically, is not
mathematics.
This simple relationship
[(a+b) / a] * a = (a+b)
shows that additional and multiplication are equivalent whenever b=0,
and our claim is that in Nature we can substitute for b any length
which is less than Plancklength.
My claim is that the relationship [(a+b) / a] * a = (a+b)
should hold true for all b s.t. 0 < b < Plancklength.
Uncle Al
[snip crap]
> shows that additional and multiplication are equivalent whenever b=0,
> and our claim is that in Nature we can substitute for b any length
> which is less than Plancklength.
[snip crap]
idiot
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2
Heliyummm
> Huang wrote:
>
> [snip crap]
>
> > shows that additional and multiplication are equivalent whenever b=0,
> > and our claim is that in Nature we can substitute for b any length
> > which is less than Plancklength.
>
> [snip crap]
>
> idiot
Put money where mouth is.
$100 says you cannot find an error in what I said - big mouth.
What's up Auntie Albert ? $100 would be kinda nice - would it not ?
FIND THE ERROR IN WHAT I SAY for $100 or you can be MY guest to just
shut up.
Mistress Helios
[(a+b) / a] * a = (a+b)
The above relationship is obviously true on inspection.
The interpretation of it, given above, is likewise obviously true on
inspection.
$100 says your scrotum is shriveled too tight to even read what I
said, much less find a mistake.
$100 says that the tightening of your sphincter is cutting off oxygen
to the brain.
$100, payable by PayPal is quite safe in my hands, you can make no
claim to the prize.
$100 yawns as if bored, unafraid, it giggles girlishly and rolls it's
eyes , grinning.
Mistress Helios
a = |-----------------|
b = | ~ ~ ~ |
a * b = |-~-~-~-~-~-~-~-~-~-~-~|
If we want to multiply a = |-----------------| by a scaling factor to
increase it's size so that it is equal in magnitude to a * b = |-~-~-~-
~-~-~-~-~-~-~-~| , we must multiply by (a+b)/a .
Hence, we have a relation ship [(a+b) / a] * a which is equal in
magnitude to (a+b).
The math is simple and stupid because b=0, and I dont care how stupid
it may sound. It is true.
In words, when b=0, we have that multiplication and addition become
interchangeable.
Multiplication and Addition become Interchangeable in this special
case, as demonstrated by the geometric illustrations above.
Heliyummm
This |-----------------|
added to this | ~ ~ ~ |
yields this |-----------------| + | ~ ~ ~ |
but...
This |-----------------|
multiplied by this ( |-----------------| + | ~ ~ ~ | ) /
|-----------------|
yields this |-~-~-~-~-~-~-~-~-~-~-~|
Clearly, [(a+b) / a] * a = (a+b)
In words, you have two magnitudes. One of them is a product, and the
other is a sum. They are equal in magnitude.
If someone handed you one of these magnitudes with no other
information, you would have no reason to believe that it was one or
the other.
NOWHERE ELSE do you have that a*b = a+b.
And this is obviously a statement about order and disorder because
multiplication implies a kind of uniformity whereas addition is much
more amorphous, items of any size can all be summed together but when
you multiply you are simply adding things which are all of a uniform
size.
It makes perfect sense, in this regard, to consider making
calculations using trivial magnitudes.
Heliyummm
Take my money. Please. $100. Come get it.
Just imagine all the Viagra you could buy with that.
Come take my money or I'll have to spend it all on strippers.
Mistress Helios
One glaringly obvious complaint that could be proposed is that you do
have some apparent problems, for example :
Rebuttal #1
"This makes no sense because if a exists and b does not exist,
then,
a + b1 = a + b2 even when b1 and b2 are not equal."
Response to Rebuttal #1
In fact it does make sense, and this is where the notion of
CONSERVATION comes in.
Without elaborating much further on this, is saddens me that Auntie
Albert missed his opportunity to even attempt to take my money.
It is still sitting there, a nice neat stack of crisp freshly printed
notes, one atop the other with a little paper band around it.
Heliyummm
> One glaringly obvious complaint that could be proposed is that you do
> have some apparent problems, for example :
>
> Rebuttal #1
> "This makes no sense because if a exists and b does not exist,
> then,
> a + b1 = a + b2 even when b1 and b2 are not equal."
>
> Response to Rebuttal #1
> In fact it does make sense, and this is where the notion of
> CONSERVATION comes in.
A very interesting idea Mistress Helios.
So, what you are saying is that an interval of length is conjectured
to contain a certain amount of nonexistence, and that no matter how
you subdivide that interval into subintervals the total amount of
trivial magnitude must be conserved, is that correct ?
That's very interesting. Ive never seen conservation applied in
algebra like that. Usually, conservation itself is conjectured as a
law of physics by silly bearded men in tall buildings with tiny
reading glasses and goatees. Are you seriously saying that
conservation is a mathematical process, and not simply some silly old
law in some dusty old physics book ?
Is that what you are saying ? Well - is it ?
Heliyummm
Basically, yes. That is exactly right.
We dont have proofs in conjectural modelling because nothing can
possibly be proved when you are working with existentially
indeterminate things. We cannot create proofs. But we can create
axioms. Axioms are not proved in math, nor are they proved in
conjectural modelling. But they are extremely important in conjectural
modelling for defining the fundamental operations of addition,
multiplication, uniqueness, etc.
We use axioms to force our "conjectural algebra" to coform to a
behaviour which exhibits conservation, essentially the same kind of
conservation which is discussed in physics. What we are conserving is
the trivially nonexistent part "b".
We have no theorems in conjectural modelling, but we can have axioms.
The most important axiom now known as Harris' Axiom was discussed
elsewhere, that "existential forms are self referential"
I am not sure about the exact wording of this next Axiom, or if it
just an incarnation of the other one mentioned above. But, we can
describe what it does.
Given an existent a1 and nonexistent b1, we have the conjectured
magnitude a1+b1.
Regardless of how we subdivide a1+b1 into subintervals, all of the a's
must add up to a1 and all of the b's must add up to b1
Likewise, if we have an a+b and c+d, and we add them together, the
result must be [a+c]+[b+d] where the [a+c] exists, and the [b+d] is
trivially nonexistent.
The main thing is that whenever b > 0, we _cannot_ simply write a+b =
a, despite the fact that b is trivially nonexistent.
Heliyummm
>
$100 USD awaits anyone who can tell me why this is wrong.
$100 USD awaits anyone who can tell me why this is wrong.
$100 USD awaits anyone who can tell me why this is wrong.
Speak your mind and claim your prize.
Speak your mind and claim your prize.
Speak your mind and claim your prize.
-OR- bend over and concede that I am correct !!
Tim Little
> $100 USD awaits anyone who can tell me why this is wrong.
> $100 USD awaits anyone who can tell me why this is wrong.
> $100 USD awaits anyone who can tell me why this is wrong.
> Speak your mind and claim your prize.
> Speak your mind and claim your prize.
> Speak your mind and claim your prize.
Strich, is that you?
- Tim
Sam Wormley
Just a copy cat.
Heliyummm
So, we will try to construct a kind of algebra where conservation is
imposed Axiomatically.
The operator of such an algebra may not be defineable. We already
stated that we dont know if it is addition or multiplication, or even
some kind of distribution. So, we may need to go forward _without_
defining an operator, and simply defining what it does.
At first, thinking about an algebra with an undefined operator may
seem ridiculous. However, random variables behave very much the same
and so it's really not such a crazy idea.
Some researchers are exploring the relationship between indeterminacy
and defineability. Something which has no order whatsoever may be
undefineable. My reference to that area of study is probably a bit
lacking, but there is certainly a conection between these two areas,
defineability and indeterminacy. So, without going to far in the
direction of establishing that relationship......we can say the
following with what we have thus far:
If we try to construct an algebra where the operator is undefined, or
perhaps it is defined with a certain amount of deliberate ambiguity,
then you are manufacturing indeterminacy.
The really elegant thing in all of this is the relationship between
indeterminacy and defineability. Some genuine elegance I think.
To recap how strange this thing will look:
- The elements ( "numbers" ) are existentially indeterminate
- The operator is defined with ambiguity built into it
- Conservation of existence and nonexistence is enforced by Axiom
- Expected values are given as the existent part of a number because
nonexist magnitudes are unobserveable
- The whole theory simply vanishes as trivial if one assumes the
universe is causal/deterministic and of course it is indeterminate
whether one or the other is more or less applicable in any modelling
situation.
Lastly, nothing is proveable. There are no proofs in this area, unless
they are very special kinds of proofs which allow a certain amount of
ambiguity. The primary issue is understanding how to transform back
and forth from conjectural modelling to mathematics, this seems more
important to me than whether one is capable of constructing "partially
ambiguous proofs".