Excerpt

What is the proper measure of intrinsic complexity to apply to states of a physical system?

What role does thermodynamic irreversibility play in enabling systems to evolve spontaneously toward states of high complexity?

A fundamental problem for statistical mechanics is to explain why dissipative systems (those in which entropy is continually being produced and removed to the surroundings) tend to undergo “self-organization,” a spontaneous increase of structural complexity, of which the most extreme example is the origin and evolution of life. The converse principle, namely that nothing very interesting is likely to happen in a system at thermal equilibrium, is reflected in the term “heat death.” In the modern worldview, thermodynamic driving forces, such as the temperature difference between the hot sun and the cold night sky, have taken over one of the functions of God: they make matter transcend its clod-like nature and behave instead in dramatic and unforeseen ways, for example, molding itself into thunderstorms, people, and umbrellas.

The notion that dissipation begets self-organization has remained informal and not susceptible to rigorous proof or refutation, largely through lack of an adequate mathematical definition of organization. The next section, after reviewing alternative definitions, proposes that organization be defined as “logical depth,” a notion based on algorithmic information and computational time complexity. Informally, logical depth is the number of steps in the deductive or causal path connecting a thing with its plausible origin. The theory of computation is invoked to formalize this notion as the time required by a universal computer to compute the object in question from a program that could not itself have been computed from a more concise program.

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