Logical Depth and Physical Complexity 论文

摘要

Abstract Some mathematical and natural objects (a random sequence, a sequence of zeros, a perfect crystal, a gas) are intuitively trivial, while others (e.g., the human body, the digits of 7r) contain internal evidence of a nontrivial causal history. Persons of Turing’s genius do not shy away from asking big questions, and hoping to see, in advance of the eventual slow progress of science, the essential outlines of the answers. “What is intelligence?” is one such question that clearly fascinated Turing. “How do complicated structures arise in nature?” is another. On this latter question, seeds planted by Turing have begun to mature to an extent that I think would please him.