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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?", "what demarcates a pseudoscience?".Knowledge is suggested to be a system-specific property measured by K, a quantity determined by how much of the information contained in an explanandum is compressed by an explanans, which is composed of an information "input" and a "theory/methodology" conditioning factor. This approach is justified on three grounds: 1) K is derived from postulating that information is finite and knowledge is information compression; 2) K is compatible and convertible to ordinary measures of effect size and algorithmic complexity; 3) K is physically interpretable as a measure of entropic efficiency. Moreover, the K function has useful properties that support its potential as a measure of knowledge. Examples given to illustrate the possible uses of K include: 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 from K may 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.PeerJ Preprints | https://doi.org/10.7287/peerj.preprints.1968v5 | CC BY 4.0 Open Access | rec:A science of science is flourishing in all disciplines and promises to boost discovery on all research 41 fronts [1]. Commonly branded "meta-science" or "meta-research", this rapidly expanding literature 42 of empirical studies, experiments, interventions, and theoretical models explicitly aims to take a 43 "bird's eye view" of science and a decidedly cross-disciplinary approach to studying the scientific 44 method, which is dissected and experimented upon as any other topic of academic inquiry. To fully 45 mature into an independent field, meta-research needs a fully cross-disciplinary, quantitative, and 46 operationalizable theory of scientific knowledge -a unifying paradigm that, in simple words, can help 47 tell apart "good" from "bad" science. 48This article proposes such a meta-scientific theory and methodology. By means of analyses and 49 practical examples, it suggests that a system-specific quantity named "K" can help answer 50 meta-scientific questions including "how much knowledge is attained by a research field?", "how 51 rapidly is a field making progress?", "what is the expected ...