Mathematics as Information Compression Via the Matching and Unification of Patterns

This paper names a novel view on the groundworks of mathematics: by virtue of what arithmetic can be visualized expected largely about `facts condensation (IC) by way of the corresponding and consolidation of patterns’ (ICMUP). That is itself a novel approach to IC, couched in agreements of non-analytical beastlike human, as it stands inevitable in any analysis of the endowments of arithmetic. This new view on the endowments of mathematics re treatment of mental disorders involving electric shocks passing through the brain the plan that, as an aid to human thinking, arithmetic is inclined agree much evidence for the importance of IC cruel education, idea, and understanding. This perspective on the groundworks of arithmetic has of age lacking a complete programme of research developing the SP Theory of Intelligence and allure realisation in the SP Computer Model, a structure at which point a generalised history of ICMUP|the effective concept of SP-diversified-adjustment|plays a principal part. The paper shows accompanying an example by virtue of what arithmetic, outside some distinguished provision, concede possibility attain condensation of facts. Then it details examples appearance by what method variations of ICMUP concede possibility be visualized in widely-used buildings and movements in arithmetic. Examples are too likely to show how various facets of the arithmetic-accompanying trainings of logic and calculating can be assumed as ICMUP. Also considered is the intimate connection between IC and ideas of expectation, accompanying debates that there are benefits in nearing AI, intelligent skill, and ideas of probability by way of ICMUP. Also explained is by means of what the shared feeling middle from two points IC and concepts of anticipation has connection with the settled view that few parts of arithmetic are intrinsically probabilistic, and by what method that latest view can be settled accompanying the all-or-nothing, `exact’, forms of forethought or conclusion that are friendly in arithmetic and sanity. There are many potential benefits and applications of the arithmetic-as-IC outlook.

Author(s) Details:

J. Gerard Wolff,
CognitionResearch.org, Menai Bridge, UK.

Please see the link here: https://stm.bookpi.org/RHMCS-V3/article/view/8959

Keywords: Foundations of mathematics, information compression, SP Theory of Intelligence