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The Principle of Computational Equivalence

Basic Framework

Following the discussion of the notion of computation in the previous chapter, I am now ready in this chapter to describe a bold hypothesis that I have developed on the basis of the discoveries in this book, and that I call the Principle of Computational Equivalence.

Among principles in science the Principle of Computational Equivalence is almost unprecedentedly broad—for it applies to essentially any process of any kind, either natural or artificial. And its implications are both broad and deep, addressing a host of longstanding issues not only in science, but also in mathematics, philosophy and elsewhere.

The key unifying idea that has allowed me to formulate the Principle of Computational Equivalence is a simple but immensely powerful one: that all processes, whether they are produced by human effort or occur spontaneously in nature, can be viewed as computations.

In our practical experience with computers, we are mostly concerned with computations that have been set up specifically to perform particular tasks. But as I discussed at the beginning of this book there is nothing fundamental that requires a computation to have any such definite purpose. And as I discussed in the previous chapter the process of evolution of a system like a cellular automaton can for example perfectly well be viewed as a computation, even though in a sense all the computation does is generate the behavior of the system.

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