A theory and methodology to quantify knowledge
Daniele Fanelli · 2018
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. The three arguments of the K function are quantifiable using methods of classic and algorithmic information theory. This approach is justified on three grounds: 1) K results 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 from a variety of fields are given to illustrate the possible uses of K. These examples include quantifying: the knowledge value of proving Fermat's last theorem; the accuracy of measurements of the electron's mass; the half life of eclipse predictions; 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 QRP; the knowledge value of astrology. Furthermore, a cumulative K may complement ordinary meta-analysis and may give rise to a universal classification of sciences and pseudosciences. Simple and memorable mathematical formulae summarize the theory's key results and implications. In addition to practical uses in meta-research, these formulae may have conceptual applications in philosophy and in research policy, and may guide scientists to make progress on all frontiers of knowledge.