Yes! YES! THANKYOU Grant!!!!!! I keep forgetting that crucial point.
OK, all you wise guys out there. What do you say to that?
Nick
Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University ([email protected])
http://home.earthlink.net/~nickthompson/naturaldesigns/
http://www.cusf.org [City University of Santa Fe]
----- Original Message -----
From: Grant Holland
To: The Friday Morning Applied Complexity Coffee Group
Sent: 7/14/2010 7:38:45 AM
Subject: Re: [FRIAM] Gravity as an emergent phenomenon
Verlinde makes the same unfortunate argument that is made by scores of
scientists - even noted thermodynamicsists - about so-called "disorder": namely
that certain permutations are "disordered", while other permutations are not.
To wit:
"Think of the universe as a box of scrabble letters. There is only one way to
have the letters arranged to spell out the Gettysburg Address, but an
astronomical number of ways to have them spell nonsense. Shake the box and it
will tend toward nonsense, disorder will increase and information will be lost
as the letters shuffle toward their most probable configurations. Could this be
gravity?"
I find this argument specious.
Just because, from an anthropomorphic, English-speaking bias, he finds the
Gettysburg address "more ordered" than any other permutation of the same length
- it is not. They are all permutation of the same number of letters. Each is as
well-defined, and well-ordered, as the other.
Anyway, "order" is an ill-defined, conflated term within the discussion of
thermodynamics. It enjoys two distinct usages that get oft-conflated in the
conversation regarding entropy. One usage is that it means "disorganization",
"absence of arrangement", "dispersed", etc. This is approximately the meaning
had originally by R. Clausius. The other usage is that of "uncertainty" or
"unpredictability". This is the meaning had by Shannon. "Disorganized" and
"uncertain" do not mean the same thing. I can prove this because they can vary
independently - and, the same phenomenon can exhibit one without the other -
the Organized state can sometimes be Uncertain...
In between the meanings of Clausius and Shannon are the meanings of entropy put
forth by Boltzmann and Gibbs. Those meanings are often taken to be about
"disorganization", but they are actually about "uncertainty". They involve
probabilities. So, there is much confusion within statistical thermodynamics
about "entropy", because the conversation often assumes that "disorder" is
about "disorganization", when it is actually about "unpredictability".
Certainly, it is confusing since Clausius was all about "dispersion",
"disorganization", while these other two physicists, Boltzmann and Gibbs, were
actually about "uncertainty".
On the other hand, Shannon was not behaving as a physicist, when he "borrowed"
the word "entropy" (upon the insistence of von Neumann) for his measure of
uncertainty. Indeed, he even "borrowed" most of his formula from Gibbs.
However, with his definition of entropy, Gibbs ( and Boltzmann before him) was
doing physics - he was describing a specific physical phenomenon.
On the other hand, Shannon was not doing physics. Rather he was doing
mathematical statistics. His definition of entropy is a mathematical function
whose domain space is probability distributions (to use the term loosely). With
Shannon's entropy, any probability distribution now has a "measure of
unpredictability". Some PDFs have more unpredictability built into them than
others, and he measures it.
Harold Morowitz also makes this point:
[Shannons entropy] is a meaningful measure over any probability distribution,
while [Gibbs thermodynamic entropy] has meaning only if the pi are the
probabilities of a system being in the ith quantum state when the system is at
equilibrium, as rigorously defined for thermodynamics
.[Shannons entropy] is a
measure on a probability distribution; it is not a physical quantity.
[Morowitz 1992]
This is obviously a pet peeve of mine. Welcome any comments!
Grant
Pamela McCorduck wrote:
Great food for thought. Gravity might be no more than an emergent phenomenon:
http://www.nytimes.com/2010/07/13/science/13gravity.html?_r=1&partner=rss&emc=rss
"God keep me from ever completing anything. This whole book is but a
draft--nay, but the draft of a draft. Oh, Time, Strength, Cash, and Patience!"
Melville, "Moby Dick"
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Grant Holland
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