The conservation of information: Measuring the cost of successful search

Abstract

Many spaces that need to be searched in the sciences are too unwieldy for random search to stand any hope of success. Success instead requires a nonrandom search. But how does one find a nonrandom search that stands a good chance of success? Even to pose the question this way suggests that such nonrandom searches do not magically materialize but need themselves to be discovered by a process of search. The question then naturally arises whether such a “search for a search” is any easier than the original search. This paper establishes a conservation of information theorem according to which the information required to find a successful search is always at least as large as the information required to successfully complete the original search. This result shows that information, like money, obeys strict accounting principles, leaves a trail, and can only originate from a prior information source.

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