there are general principles that govern the behavior of a wide range of systems, independent of the precise details of each system.

And it is this that means that even if we do not know all the details of what is inside some specific system in nature, we can still potentially make fundamental statements about its overall behavior. Indeed, in most cases, the important features of this behavior will actually turn out to be ones that we have already seen with the various kinds of very simple rules that we have discussed in this chapter.

How the Discoveries in This Chapter Were Made

This chapter—and the last—have described a series of surprising discoveries that I have made about what simple programs typically do. And in making these discoveries I have ended up developing a somewhat new methodology—that I expect will be central to almost any fundamental investigation in the new kind of science that I describe in this book.

Traditional mathematics and the existing theoretical sciences would have suggested using a basic methodology in which one starts from whatever behavior one wants to study, then tries to construct examples that show this behavior. But I am sure that had I used this approach, I would not have got very far. For I would have looked only for types of behavior that I already believed might exist. And in studying cellular automata, this would for example probably have meant that I would only have looked for repetition and nesting.

But what allowed me to discover much more was that I used instead a methodology fundamentally based on doing computer experiments.

In a traditional scientific experiment, one sets up a system in nature and then watches to see how it behaves. And in much the same way, one can set up a program on a computer and then watch how it behaves. And the great advantage of such an experimental approach is that it does not require one to know in advance exactly what kinds of behavior can occur. And this is what makes it possible to discover genuinely new phenomena that one did not expect.

Experience in the traditional experimental sciences might suggest, however, that experiments are somehow always fundamentally imprecise.

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