algorithmic information

System complexity measures {algorithmic information content} {algorithmic complexity, system} {Kolmogorov complexity, system} can be numbers of bits for smallest program that can run on universal Turing machines and produce same output.

algorithm

Programs produce output from input and algorithm. Theory predicts facts from data and formulas. Algorithms and formulas are similar.

number

Random numbers have programs about as long as themselves. Information has no redundancy and cannot compress {irreducible information}.

proof

Infinitely many mathematical results require algorithms or proofs as large as output and so have no useful proofs. For example, axioms have no proof. Therefore, the principle of sufficient reason is not always true.

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3-Computer Science-Systems-Complexity Theory

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Date Modified: 2022.0224