Date: Mon, 11 May 1992 10:22:13 -0400
From: "David H. Porush"
Subject: Re: Re-posted for Jeff Achter
To: Multiple recipients of list TNC
Thanks for the poem, Jeff.
The correspondence Course, correspondences also work. Take for example that great correspodence theory Information Theory. I don't know why the same mathematical formula for measuring entropy in a closed system, also works for measuring the amount of noise in a channel connecting messenger and receiver. It just does.
Information theory is a cool subject. Part of the reason the formulas for entropy work the same is precisely so that info-theory could get a leg up by looking like physics. There are some deep reasons why the systems work the same way. But the particular formulation of information entropy we use is just because it looks like something we've seen elsewhere; there's a way in which it's not necessarily canonical. Indeed, Von Neumann was urged to adopt the use of the word "entropy" in his arguments, as it would confuse and intimidate his opponents... ]<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
As regards the above:
Yes, though all the early cyberneticists took some pains to disguise the fact, the orginal formulations of entropy as a measure of the noise in a system (negentropy as information) were built on an analogy with the Second Law of Thermodynamics with the hoep of borrowing some of classical mechanics' certainty and authority. There are several issues here worth noting briefly:
(1) Norbert Wiener and John von Neumann (along with Einstein) simply could not accept, on an intellectual and on an emotional level, the intrusion of uncertainty onto the scene of phsyics represented by the Hesienberg Uncertainty Principle. Both also abhorred Godel's Theorem for similar reason, especially von Neumann who traced his intellectual roots to Russel's and Whitehead's set theory. Godel s theorem represented a refutation of set theory and upset te the rationalist applecart. (An interesting footnote is that Alan Turing was also a student of RUssel and a proponent of set theory. If you trace the evolution of his idea of a computer and the now famous Turing test, you can see it derives from his original attempt to find a way "around" Godel's Theorem.)
Wiener calls Heisenberg's Uncertainty Theorem "an AUgustinaina Devil" (excuse bad typing on the fly) "An Augustinian devil" and portrays his own formulation of the formula for entropy as a measure of information as anattempt to exorcise that demon. The thought which gives rise to cybernetics, then, is a rationalist's fantasy: if we can quantify the amount of information held in the brain of the observer, then then heisenberg scenario disappears.
(2) WHile it is true that the formula -k log p is built upon an analogy to classical mechanics (with k = Boltzmann's constant or Planck's constant, can't remember which now), it is also true that Wiener imagined there was an essential connection via the Maxwell Demon scenario. If the demon sitting astride the two chambers effectively sorts the hot molecues and cold molecules, then he disobeys the Second Law of Thermodynamics. But if he has a certain amount of information equal to the amount of energy (enthalpy) he creates then the ledger balances out. In other words, as Wiener notes, the Demon has to "know" which molecules are hot and whcih cold, requiring a certain amount of information. As Shannon proved every bit of information implies a physiucal channel to transmit it. ConsequentlWiener imagined that positing an essential equivalencebetween thermodynamic entorpy and informational entropywould somehow kill two demons with one stone and one-up rationality over what he saw were the intrusionsof irrationality.
NOTE TO JEFF ACHTER: The word "irrationality" is not to be taken as a metaphor here. Wiener was very concerned with irrationals. Take a look at Wiener numbers and why he was motated to invent them!
-- David Porush