Howard Pattee said [November 20, 2010 7:19 PM]:
This point is well-known in physics by the two models of a gas. Microscopically the dynamic model of an ideal box of atoms is reversible (time-symmetric) while the thermodynamic model is irreversible. Clearly these models are formally contradictory and therefore neither model can be derived from (or reduced to) the other. As Max Planck noted: “For it is clear to everybody that there must be an unfathomable gulf between a probability, however small, and an absolute impossibility . . . Thus dynamics and statistics cannot be regarded as interrelated.”
Thanks Howard for pointing this out. Although I've taught classical thermodynamics at the undergraduate level and statistical thermodynamics at the graduate level, there seems to be a gap between the two that is not really paid attention to in engineering programs. Although the Maxwell Demon paradox is mentioned, the logical implications are not explored. We simply teach that the microscopic and macroscopic are related by the formula for change in entropy equaI to Plancks constant times the natural log of the ratio of thermodynamic probabilities of the macrostates. I did some research after your post and days of hard thinking. My gut tells me that the assumption of sign reversal in the classical mechanics description being equivalent to reversibility has something wrong with it. One thing I find fascinating is that this paradox and its cousins are the stimulus for your semiotic approach to evolution. Like all other paradoxes, it doesn't seem to matter whether one actually finds the "true" answer. What matters is that the stimulation can lead to new ideas like your semiotic approach. Look at all the mathematical progress that has its roots in Zeno's Paradox.
