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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 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.
Following a first round of peer-review, the text was edited to improve clarity, correct various typos, and avoid distracting complications. The discussion was organized in sections and expanded to include a section on the theory's predictions and falsifiability. The SI relative to statistical arguments was removed whereas that concerning the decline of K with divergences was expanded.