This kind of self-organization is quite opposite to what one would expect from the Second Law. And at first it also seems inconsistent with the reversibility of the system. For if all that is left at the end are a few simple structures, how can there be enough information to go backwards and reconstruct the initial conditions?

The answer is that one has to consider not only the stationary structures that stay in the middle of the system, but also all various small structures that were emitted in the course of the evolution. To go backwards one would need to set things up so that one absorbs exactly the sequence of structures that were emitted going forwards.

If, however, one just lets the emitted structures escape, and never absorbs any other structures, then one is effectively losing information. The result is that the evolution one sees can be intrinsically not reversible, so that all of the various forms of self-organization that we saw earlier in this book in cellular automata that do not have reversible rules can potentially occur.

If we look at the universe on a large scale, then it turns out that in a certain sense there is more radiation emitted than absorbed. Indeed, this is related to the fact that the night sky appears dark, rather than having bright starlight coming from every direction. But ultimately the asymmetry between emission and absorption is a consequence of the fact that the universe is expanding, rather than contracting, with time.

The result is that it is possible for regions of the universe to become progressively more organized, despite the Second Law, and despite the reversibility of their underlying rules. And this is a large part of the reason that organized galaxies, stars and planets can form.

Allowing information to escape is a rather straightforward way to evade the Second Law. But what the pictures on the facing page demonstrate is that even in a completely closed system, where no information at all is allowed to escape, a system like rule 37R still does not follow the uniform trend towards increasing randomness that is suggested by the Second Law.

What instead happens is that kinds of membranes form between different regions of the system, and within each region orderly behavior can then occur, at least while the membrane survives.

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From Stephen Wolfram: A New Kind of Science [citation]