Chapter 12: The Principle of Computational Equivalence

Section 2: Outline of the Principle

Note for mathematicians [about PCE]

The way I discuss the Principle of Computational Equivalence is in a sense opposite to what would be typical in modern mathematics. For rather than starting with very specific definitions and then expanding from these, I start from general intuition and then use this to come up with more specific results. In the years to come there will no doubt be many attempts to formulate parts of the Principle of Computational Equivalence in ways that are closer to the traditions of modern mathematics. But at least at first, I suspect that huge simplifications will be made, with the result that all sorts of misleading conclusions will probably be reached, perhaps in some cases even seemingly contradicting the principle.

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