A theory and methodology to quantify knowledge

Abstract

This article proposes quantitative answers to meta-scientific questions including ‘how much knowledge is attained by a research field?’, ‘how rapidly is a field making progress?’, ‘what is the expected reproducibility of a result?’, ‘how much knowledge is lost from scientific bias and misconduct?’, ‘what do we mean by soft science?’, and ‘what demarcates a pseudoscience?’. Knowledge is suggested to be a system-specific property measured byK, a quantity determined by how much of the information contained in anexplanandumis compressed by anexplanans, which is composed of an information ‘input’ and a ‘theory/methodology’ conditioning factor. This approach is justified on three grounds: (i)Kis derived from postulating that information is finite and knowledge is information compression; (ii)Kis compatible and convertible to ordinary measures of effect size and algorithmic complexity; (iii)Kis physically interpretable as a measure of entropic efficiency. Moreover, theKfunction has useful properties that support its potential as a measure of knowledge. Examples given to illustrate the possible uses ofKinclude: the knowledge value of proving Fermat’s last theorem; the accuracy of measurements of the mass of the electron; the half life of predictions of solar eclipses; the usefulness of evolutionary models of reproductive skew; the significance of gender differences in personality; the sources of irreproducibility in psychology; the impact of scientific misconduct and questionable research practices; the knowledge value of astrology. Furthermore, measures derived fromKmay complement ordinary meta-analysis and may give rise to a universal classification of sciences and pseudosciences. Simple and memorable mathematical formulae that summarize the theory’s key results may find practical uses in meta-research, philosophy and research policy.

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