an attempt to generalize the arrow of time: from entropic equalization, to biomorphic reproduction, to cognitive exploration.
7.09.2012
Entropy growth as an *increase* of order
The only universal trend in physical world is the growth of entropy, toward some kind of equilibrium.
Entropy is usually considered to be a measure of disorder, antithetical to reproduction & prediction.
It is well known that physical entropy growth increases complexity of the exact description of micro-states in all interacting systems. But that complexity is irrelevant for overall behavior of these systems because it is random: the differences between micro-states cancel-out on a macro-level. What matters for whole-system prediction is macro-gradients, which don’t cancel out. Such gradients are reduced in interactions, increasing effective order or predictability of the system. This interpretation is my own.
Physical disorder appears to increase in interactions because Information Theory measures it by the number of bits in the description, which is compressed, rather than by the difference in physical values, which is not. Variation within contiguous objects is lower than that between them because interactions follow S-T continuum. Interaction between the objects will reduce overall differences, but increase those within each. Total variation will be reduced in magnitude, but increased in the number of smaller differences, representation of which is less compressible. So, the description of closed system may require more bits as a result. But physics study empirical values, not their descriptions.
The above describes effects of repulsive interactions. For attractive interactions (gravity) the disparity in concentration across Space is increasing, but so does stability of the results, - the change over Time is decreasing (down to a “timeless” black hole). The distinction of Time from Space is its irreversible direction. Any reversal can be defined only in terms of a higher-dimensional coordinate. For a top dimension, there is no higher coordinate, so a reversal is inconceivable. Irreversibility of Time means that it is a top dimension, thus equalization predominates for both repulsive & attractive interactions. However, Plank scale is a limit for any continuous interaction, thus also for resulting entropy growth.
So, both the growth of entropy & that of reproduction represent increasing stability over time & similarity across space. The difference between them is in scope: entropy increases in all interacting systems (no spatially distinct adaptive interface), while reproduction is restricted to a genotype or an equivalent. Obviously, the growth of entropy drives all biological processes. Still, simple averaging is infinitely inferior to biological evolution, & most would never consider it as a form of meta evolution.
On the opposite, the "heat death" seems be life's worst nightmare. But evolution is just as inferior to technological progress driven by cognition, considering its speed & potential. And reproduction at its ultimate extreme, "the gray goo" scenario, seems just as abhorrent as the heat death. Some rational version of “Omega point” would be a final state for representation, - as depressing as anything final.
Indefinite transition to higher core types is possible only if the universe is open, - meta evolution in a closed universe will eventually run out of variation & die a heat death. The universe is closed if it can be fully described by a fixed number of patterns / physical constants. In that sense, a known universe is always closed, it just seems to get larger all the time.
A real question is whether unknown universe is empty, - will there ever be any new information / external impact? Bayesian take on the unknown is that all possibilities should be assigned equal probability. Since empty is one distinct possibility, & not empty is an infinite number of them, a priori chances that the universe is open are infinity-to-one.
Of course, any ecosystem can be effectively closed, - evolution may be reversed by entropy (lack| excess of free energy) or reproduction (food chain exhaustion or predators & parasites). Any given system has only an infinitesimal chance of evolving forever, but meta evolution should prevail overall.
From within the known universe, it does appear to be "closed” in terms of GR & QM constants, - no limits or exceptions were found in a hundred years of intense research. But, however fundamental, these cover only a tiny part of our knowledge. All other known patterns do decay/terminate with distance, in the frame of reference used to define them (smaller patterns are normally stronger/ more evolved, as larger systems evolve out of them later).
This negative meta-pattern of decay can't be interrupted by any known law, - there can never be an evidence of infinite range for any pattern. So, this decay meta-pattern blocks projection of GR & QM into infinity, although from outside of their frame of reference. Cosmological predictions are theoretically interesting, - that’s how things should develop without intelligent intervention. But such intervention will be armed by science of the future. Modern science is only ~300 years old, in a hundred years it should be as relevant as medieval alchemy is today.
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Best to think of physical entropy as information-theoretic entropy being applied to matter.
ReplyDeleteI think we already discussed this, ~10 years ago on usenet :).
DeleteI agree that it's the same concept, only the sign somehow got inverted in translation :).