[No text on this page] Examples of network evolution according to the same basic underlying rules as on page 511 , but now with all possible clusters of nodes that do not overlap being replaced at each step.

it is then discovered that many of the extensions that were added were in fact quite unnecessary, so that in the end, after perhaps a decade has passed, it becomes recognized that models equivalent to the simple ones I originally proposed do indeed work quite well. … Yet with an equation one may need to do elaborate mathematical analysis in order to find out what behavior it can lead to. It does not help that models based on equations are often stated in a purely implicit form, so that rather than giving an actual procedure for determining how a system will behave—as a program does—they just give constraints on what the behavior must be, and provide no particular guidance about finding out what, if any, behavior will in fact satisfy these constraints.

The most important point seems to be that it is mostly derived from experience with building things and doing engineering—where it so happens that one avoids encountering systems like the ones in the previous section . … Yet to do this reliably, we have to restrict ourselves to systems whose behavior we can readily understand and predict—for unless we can foresee how a system will behave, we cannot be sure that the system will do what we want. … But because the only situations in which we are routinely aware both of underlying rules and overall behavior are ones in which we are building things or doing engineering, we never normally get any intuition about systems like the ones at the end of the previous section .

computer technology to make single pictures of cellular automata, it requires considerably more to do large-scale systematic experiments. … But beyond the practicalities of carrying out such experiments, it was also necessary to have the idea that the experiments might be worth doing in the first place. … But from experience in practical computing one knows that it is usually very difficult to foresee what even a simple program will do.

To update the color of the cell represented by a particular block, what the universal cellular automaton must then do is to determine which of the 8 cases applies to that cell. And it does this by successively eliminating cases that do not apply, until eventually only one case remains. … The first stripe carries the color of the left-hand neighbor, and causes all cases in the rule where that neighbor does not have the appropriate color to be eliminated.

So this means that whatever kinds of computations can be done by the universal system, none of the other systems will ever be able to do computations that have any higher level of sophistication. … But despite this, at an abstract level one can always imagine having systems that do computations beyond what any of the cellular automata, Turing machines or other types of systems in the previous chapter can do. … Needless to say, I do not believe that this is the case, and in fact if one could find a truly fundamental theory of physics along the lines I

When one does practical computing one tends to assess the difficulty of a computation by seeing how much time it takes and perhaps how big a program it involves and how much memory it needs. But normally one has no way to tell whether the scheme one has for doing a particular computation is the most efficient possible. … But what my discoveries have shown is that in fact even very small programs can be quite capable of doing all sorts of sophisticated computations.

But do they really require intelligence to generate? … But just using definite pathways—or definite underlying rules—does not in any way preclude intelligence. … And the same is true if we pick up data of any kind that is encoded in a format we do not know.

The phenomenon of computational irreducibility implies that to find out what some specific system with complex behavior will do can require explicit simulation that involves an irreducible amount of computational work. … Traditional intuition suggests that to be able to do sophisticated computations one would inevitably need a system with complicated underlying rules. … And one thing this would mean is that doing

But inevitably there are many details that it does not capture. And indeed some of the photographs on the facing page do not in the end look much like patterns produced at any step in the evolution shown below.