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respects they seem far more random than patterns produced by systems like rule 110 that we already know are universal.

But how can we be sure that we are not being misled by limitations in our powers of perception and analysis—and that an extraterrestrial intelligence, for example, might not immediately recognize regularity that would show that universality is impossible?

For as we saw in Chapter 10 the methods of perception and analysis that we normally use cannot detect any form of regularity much beyond repetition or at most nesting. So this means that even if some higher form of regularity is in fact present, we as humans might never be able to tell.

In the history of science and mathematics both repetition and nesting feature prominently. And if there was some common higher form of regularity its discovery would no doubt lead to all sorts of important new advances in science and mathematics.

And when I first started looking at systems like cellular automata I in effect implicitly assumed that some such form of regularity must exist. For I was quite certain that even though I saw behavior that seemed to me complex the simplicity of the underlying rules must somehow ultimately lead to great regularity in it.

But as the years have gone by—and as I have investigated more and more systems and tried more and more methods of analysis—I have gradually come to the conclusion that there is no hidden regularity in any large class of systems, and that instead what the Principle of Computational Equivalence suggests is correct: that beyond systems with obvious regularities like repetition and nesting most systems are universal, and are equivalent in their computational sophistication.

Explaining the Phenomenon of Complexity

Early in this book I described the remarkable discovery that even systems with extremely simple underlying rules can produce behavior that seems to us immensely complex. And in the course of this book, I have shown a great many examples of this phenomenon, and have

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