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 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: (i) K is derived from postulating that information is finite and knowledge is information compression; (ii) K is compatible and convertible to ordinary measures of effect size and algorithmic complexity; (iii) 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.
Keywords: bias; knowledge; meta-research; meta-science; pseudoscience; reproducibility.