In the end the Principle of Computational Equivalence encapsulates both the ultimate power and the ultimate weakness of science. For it implies that all the wonders of our universe can in effect be captured by simple rules, yet it shows that there can be no way to know all the consequences of these rules, except in effect just to watch and see how they unfold.
Free Will: What makes us think there is freedom in what a system does? In practice the main criterion seems to be that we cannot readily make predictions about the behavior of the system. It seems likely that the individual steps in each train of thought follow quite definite underlying rules. And the crucial point is then that I suspect that the computation performed by applying these rule is often sophisticated enough to be computationally irreducible -- with the result that it must intrinsically produce behavior that seems to us free of obvious laws.
Second Law of Thermodynamics: No reasonable experiment can ever involve setting up the kind of initial conditions that will lead to decreases in randomness, and that therefore all practical experiments will tend to show only increases in randomness. But it may not be universally valid, some celluar automata can exhibit self organization.
Ultimate mode of universe: I strongly suspect that the vast majority of physical laws discovered so far are not truly fundamental, but are instead merely emergent features of the large-scale behavior of some ultimate underlying rule. Could it be that underneath all the complex phenomena we see in physics there lies some simple program which , if run long enough, would reproduce our universe in every detail?
Data compression: all the compression methods can be thought of as corresponding to fairly simple programs.
Cryptography: using celluar automaton to generate encryption key.
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