Here we see complex results, but with elements of structure as well. This is a little like Life, where groups of cells form distinct patterns which interact in interesting ways. Unfortunately, like Life, this rule set degenerates into semi-stable behaviour after large numbers of generations (after 3200 cycles, rule set 110 starts repeating the same pattern).

But the principal has been established. An extremely simple Cellular Automaton with an absurdly simple set of rules can produce behaviour with a level of complexity out of all proportion to its starting point. So what could a more complex CA, with more dimensions, more states and a more detailed set of rules, do?

This was the starting point for Wolfram's explorations, and here I must admit that I've read only a small part of the book. Given the size of the book and the density of its contents, it may take several months to read it, so here I'm going to have to skip to what I understand to be Wolfram's conclusions.

What Wolfram appears to be saying is that some phenomenon analogous to Cellular Automata may underly the basic laws of physics. He demonstrates that CA with rules not too much more complicated than those discussed here can display coherent behaviors like those of a turing machine, so why couldn't CA be the mechanism behind quarks and bosons? After all, is this so much more ridiculous than conceptualizing a subatomic particle as an excitation of a 10-dimensional string, which is what current string theories would suggest?

Cellular Automata would explain concepts like the speed of light - if cells can only be affected by those in their immediate vicinity, that gives the effect of an absolute speed of light. In fact, I remember some of the earliest discussions I read on CA referring to the fastest speed at which an effect could travel through the cells as the "speed of light".

And the nonlocal effects of quantum entanglement that so trouble theoretical physicists could be explained by a rule which only came into play in certain circumstances, but which took into account the state of cells other than those immediately adjacent.

There is one important consequence of this - unlike Newtonian physics, in which mathematical formulae can predict, say, the position of a planet, the only way to know state n of a Cellular Automaton is to get there via state n-1. Where groups of cells operate together as macro-phenomena, like the gliders in Life, it's reasonably easy to predict their behaviour at a certain level. But when complex interactions take place, like a glider hitting a random group of cells, the only way to know what will happen is to play the program.

This means that it will never be possible to create formulae that enable us to predict outcomes at the very smallest level. Even if we fully understand the rules of this hypothetical Cellular Automaton that underlies the physical world, we will never be able to run a simulation of it as fast as nature runs itself. And since a small change to just one cell can have a major effect throughout the system, as with Life, the only way to know what will happen is to play the program - which in this case we can't do.

If this is indeed what Wolfram is saying, and I'll know more when I've finished the book, then I think his ideas have merit. I disagree with a lot of what he says - I don't think the ideas are as new as he suggests, and I think he should give more credit to the pioneers in the field of Cellular Automata, like von Neumann and Conway. And I certainly don't like the way his ego intrudes so heavily into his writing style.

But underneath all that, he may be on to something.

I should just mention here that Wolfram goes on from these initial conclusions to state what he calls the Principle of Computational Equivalence. I won't attempt to explain this until I've read more about it, but I suspect that he may be going a little far here. Further than I'm prepared to agree with, anyway.