even though the underlying laws for this system are perfectly definite, its overall behavior ends up being sufficiently complicated that many aspects of it seem to follow no obvious laws at all.

And indeed if one were to talk about how the cellular automaton seems to behave one might well say that it just decides to do this or that—thereby effectively attributing to it some sort of free will.

But can this possibly be reasonable? For if one looks at the individual cells in the cellular automaton one can plainly see that they just follow definite rules, with absolutely no freedom at all.

But at some level the same is probably true of the individual nerve cells in our brains. Yet somehow as a whole our brains still manage to behave with a certain apparent freedom.

Traditional science has made it very difficult to understand how this can possibly happen. For normally it has assumed that if one can only find the underlying rules for the components of a system then in a sense these tell one everything important about the system.

But what we have seen over and over again in this book is that this is not even close to correct, and that in fact there can be vastly more to the behavior of a system than one could ever foresee just by looking at its underlying rules. And fundamentally this is a consequence of the phenomenon of computational irreducibility.

For if a system is computationally irreducible this means that there is in effect a tangible separation between the underlying rules for the system and its overall behavior associated with the irreducible amount of computational work needed to go from one to the other.

And it is in this separation, I believe, that the basic origin of the apparent freedom we see in all sorts of systems lies—whether those systems are abstract cellular automata or actual living brains.

But so in the end what makes us think that 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.

For certainly if we could, then this would show us that the behavior must be determined in a definite way, and so cannot be free. But at least with our normal methods of perception and analysis one

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