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:
[Shannon's entropy] is a meaningful measure over any probability
distribution, while [Gibb's thermodynamic entropy] has meaning only if
the p_i are the probabilities of a system being in the i^th quantum
state when the system is at equilibrium, as rigorously defined for
thermodynamics....[Shannon's 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
VP, Product Development and Software Engineering
NuTech Solutions
404.427.4759
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