Even early in antiquity attempts were presumably made to see whether simple abstract rules could reproduce the behavior of natural systems. But so far as one can tell the only types of rules that were tried were ones associated with standard geometry and arithmetic. And using these kinds of rules, only rather simple behavior could be obtained—adequate to explain some of the regularities observed in astronomy, but unable to capture much of what is seen elsewhere in nature.

And perhaps because of this, it typically came to be assumed that a great many aspects of the natural world are simply beyond human understanding. But finally the successes based on calculus in the late 1600s began to overthrow this belief. For with calculus there was finally real success in taking abstract rules created by human thought and using them to reproduce all sorts of phenomena in the natural world.

But the particular rules that were found to work were fairly sophisticated ones based on particular kinds of mathematical equations. And from seeing the sophistication of these rules there began to develop an implicit belief that in almost no important cases would simpler rules be useful in reproducing the behavior of natural systems.

During the 1700s and 1800s there was ever-increasing success in using rules based on mathematical equations to analyze physical phenomena. And after the spectacular results achieved in physics in the early 1900s with mathematical equations there emerged an almost universal belief that absolutely every aspect of the natural world would in the end be explained by using such equations.

Needless to say, there were many phenomena that did not readily yield to this approach, but it was generally assumed that if only the necessary calculations could be done, then an explanation in terms of mathematical equations would eventually be found.

Beginning in the 1940s, the development of electronic computers greatly broadened the range of calculations that could be done. But disappointingly enough, most of the actual calculations that were tried yielded no fundamentally new insights. And as a result many people came to believe—and in some cases still believe today—that computers could never make a real contribution to issues of basic science.

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