The answer, it turns out, is that at least in principle one can, although to do so requires a somewhat higher level of mathematical abstraction than has so far been necessary in this book. … But how does one give rules for the evolution of such a system?

And what this does is to make the sequence of colors taken on by any particular cell depend on the colors of cells progressively further and further to the right in the initial conditions. … And what this means is that there is a third possible mechanism for randomness, which this time does not rely in any way on randomness already being present outside the system one is looking at.

And the problem is that while practical devices may eventually relax to what is essentially the same state, they can do this only at a certain rate. … But even when the device used to sample the environment does no amplification and has no relevant internal structure, one may still not see

At the end of Chapter 5 I gave some examples of constraints, and I showed that constraints do exist that can force quite complex behavior to occur. … Yet if one only knows constraints then such constraints do not on their own immediately yield any specific procedure for working out what behavior will occur.

But countless times I have been asked how models based on simple programs can possibly be correct, since even though they may successfully reproduce the behavior of some system, one can plainly see that the system itself does not, for example, actually consist of discrete cells that, say, follow the rules of a cellular automaton. But the whole point is that all any model is supposed to do—whether it is a cellular automaton, a differential equation, or anything else—is to provide an abstract representation of effects that are important in determining the behavior of a system.

Presumably there do exist situations in which there is some kind of delicate balance—say of whether the first eddy is shed at the top or bottom of an object—and in which small changes in initial conditions can have a substantial effect. … But since changes in the configurations of such particles do not seem to have any discernible

Biological systems do appear to have some tricks for speeding up the search process. … And indeed one suspects that in fact the vast majority of features of biological organisms do not correspond to anything close to optimal solutions: rather, they represent solutions that were fairly easy to find, but are good enough not to cause fatal problems for the organism.

How does it pick out which programs to use? … But from the discoveries in this book we know that this will not in general be the case: above a fairly low threshold, adding complexity to an underlying program does not fundamentally change the kind of behavior that it can produce.

So to what extent does the actual history of biological evolution reflect the kinds of simple characteristics that I have argued one should expect from natural selection? … So how then does such diversity arise?

And indeed—much as in other areas of engineering—the typical experience in developing software is that to make a computer do something complicated requires setting up a program that is itself somehow correspondingly complicated. … And the only reasonable way to do this is to expose ourselves to a large number of examples.