{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:11:35Z","timestamp":1760242295258,"version":"build-2065373602"},"reference-count":108,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2017,3,27]],"date-time":"2017-03-27T00:00:00Z","timestamp":1490572800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>An abstract, quantitative theory which connects elements of information \u2014key ingredients in the cognitive proces\u2014is developed. Seemingly unrelated results are thereby unified. As an indication of this, consider results in classical probabilistic information theory involving information projections and so-called Pythagorean inequalities. This has a certain resemblance to classical results in geometry bearing Pythagoras\u2019 name. By appealing to the abstract theory presented here, you have a common point of reference for these results. In fact, the new theory provides a general framework for the treatment of a multitude of global optimization problems across a range of disciplines such as geometry, statistics and statistical physics. Several applications are given, among them an \u201cexplanation\u201d of Tsallis entropy is suggested. For this, as well as for the general development of the abstract underlying theory, emphasis is placed on interpretations and associated philosophical considerations. Technically, game theory is the key tool.<\/jats:p>","DOI":"10.3390\/e19040143","type":"journal-article","created":{"date-parts":[[2017,3,27]],"date-time":"2017-03-27T10:49:10Z","timestamp":1490611750000},"page":"143","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Paradigms of Cognition"],"prefix":"10.3390","volume":"19","author":[{"given":"Flemming","family":"Tops\u00f8e","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,3,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. 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