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SWENSON: THE DEVELOPMENT OF SPACE-TIME
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317
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| is readily falsified by simple physical experiments, such as the Benard experiment mentioned above. In this experiment dynamic order, or autocatakinetics, is seen to arise not infinitely improbably, but with probability one, that is, every time and as soon as it gets the chance. Rather than incommensurabilty, or anomaly, this suggests a universality to spontaneous ordering that would unify the two rivers. |
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BERTALANFFY, SCHROEDINGER, AND PRIGOGINE AND
THE BALANCE EQUATION OF THE SECOND LAW
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An important contribution was made toward this discourse in the middle of this century by Bertalanffy (16) who showed that "spontaneous order ... can appear" in systems with energy flowing through them; and Schrodinger (17), who, comparing living things to flames, pointed out that such systems (all autocatakinetic systems) do not violate the second law as long as they produce entropy (or minimize potentials) at sufficient rates to compensate for their ordering (their increase in space-time dimensions or internal entropy reduction) and, thereby, satisfy the balance equation of the second law. The idea was further popularized by Prigogine (18), under the rubric of "dissipative structures". Such systems were thus given "permission" to exist given the classical view of the second law, but according to Boltzmann's interpretation they were still infinitely improbable. The question of why order is seen to arise whenever it gets the chance, in simple physical systems, in the evolutionary record writ large, in the "fecundity principle"' on which Darwinian theory depends, and in the directedness towards, that characterizes the intentional content of epistemic activity in general remained. |
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THE LAW OF MAXIMUM ENTROPY PRODUCTION OR
WHY THE WORLD IS IN THE ORDER PRODUCTION BUSINESS
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The solution to the puzzle is found in two parts.(3,5,11,12). The first is the recognition of an important point found implicitly in the BertalanffySchroedinger-Prigogine contribution but not noted explicitly by them. In particular, since to come into being and persist, an autocatakinetic system must increase the rate of entropy production of the system plus environment at a sufficient rate to satisfy the balance equation of the second law, then ordered flow, according to the balance equation, must be more efficient at dissipating potentials that disorder flow. FIGURE 5 shows the dramatic increase in the rate at which the potential is minimized, for example, in the Benard cell experiment in the transition from the disordered to ordered regime, and the balance equation tells us that this is precisely what must happen.
Now this becomes important only with the second part of the solution, which is the answer to a question that was never addressed in the Bertalanffy-Schroedinger-Prigogine discourse. In particular, which path(s) out of all available paths will a system take to minimize potentials or maximize the entropy? The answer (the law of maximum entropy production) is the path or assembly of paths that minimizes the potential (maximizes the entropy) at the fastest rate given the constraints. Just like the second law, the law of maximum entropy production is intuitively easy
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