A theory and methodology to quantify knowledge
- Subject Areas
- Computational Biology, Ethical Issues, Science Policy, Statistics, Computational Science
- soft science, hard science, philosophy of science, research misconduct, questionable research practices, reproducibility, pseudo-science, positivism, falsification, relativism
- © 2018 Fanelli
- This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ Preprints) and either DOI or URL of the article must be cited.
- Cite this article
- 2018. A theory and methodology to quantify knowledge. PeerJ Preprints 6:e1968v5 https://doi.org/10.7287/peerj.preprints.1968v5
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.
R code used to generate all figures and analyses.