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Mathematical Principles

Mathematical principles

principle of computational equivalence | principle of mathematical induction

Statements

The principle of computational equivalence states that systems found in the natural world can perform computations up to a maximal ("universal") level of computational power, and that most systems do in fact attain this maximal level of computational power. Consequently, most systems are computationally equivalent.

The principle of mathematical induction states that the truth of an infinite sequence of propositions P_i for i = 1, ..., ∞ is established if (1) P_1 is true and (2) P_k implies P_(k + 1) for all k.

Alternate description

Almost all processes that are not obviously simple can be viewed as computations of equivalent sophistication.

History

Common classes

mathematical principles

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