Excerpt

Written near the end of the productive stage of his career, Kolmogorov’s “Three Approaches” is a work of maddening genius. Alternately inspiring, enigmatic, and incomplete, the text spawned entire subfields in computer science, mathematics, and philosophy—and, at the same time, a thousand misconceptions. Though it is unquestionably part of the complexity-science canon, few papers are as misread and misunderstood by outsiders. Perhaps one should expect nothing less from a paper that proposes a quantitative measure of information, structure, complexity, and order that can never, in the end, be calculated. To read “Three Approaches“ is to see a mind at the height of its powers, straining for a new ontology of form beyond anything previously conceived.

To understand Kolmogorov’s ambition—to do justice to it—one must first understand that he is writing in the shadow of a paper written seventeen years prior: Claude Shannon’s “Mathematical Theory of Communication” (1948). Shannon’s paper was the origin point of modern information theory, and the heart of the probabilistic approach that Kolmogorov intends to transcend.

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