Mathematics as information compression via the matching and unication of patterns

James Gerard Gerry Wolff (1)

1 AGROCAMPUS OUEST

This paper describes a novel perspective on the foundations of mathematics: how mathematics may be seen to be largely about`information compression (IC) via the matching and unication of patterns' (ICMUP). That is itself a novel approach to IC, couched in terms of non-mathematical primitives, as is necessary in any investigation of the foundations of mathematics. This new perspective on the foundations of mathematics reects the idea that, as an aid to human thinking, mathematics is likely to be consonant with much evidence for the importance of IC in human learning, perception, and cognition. This perspective on the foundations of mathematics has grown out of a long-term programme of research developing the SP Theory of Intelligence and its realisation in the SP Computer Model, a system in which a generalised version of ICMUPthe powerful concept of SP-multiple-alignmentplays a central role. The paper shows with an example how mathematics, without any special provision, may achieve compression of information. Then it describes examples showing how variants of ICMUP may be seen in widely-used structures and operations in mathematics. Examples are also given to show how several aspects of the mathematics-related disciplines of logic and computing may be understood as ICMUP. Also discussed is the intimate relation between IC and concepts of probability, with arguments that there are advantages in approaching AI, cognitive science, and concepts of probability via ICMUP. Also discussed is how the close relation between IC and concepts of probability relates to the established view that some parts of mathematics are intrinsically probabilistic, and how that * Dr Gerry Wol, BA (Cantab) PhD (Wales) CEng MBCS MIEEE, ORCID ID 0000-0002-4624-8904. CognitionResearch.org, Menai Bridge, UK; Visiting Researcher at Coventry University ; [e-mail]; [phone]; [phone]; Skype: gerry.wol; Web: www.cognitionresearch.org. 1 latter view may be reconciled with the all-or-nothing,`exact', forms of calculation or inference that are familiar in mathematics and logic. There are many potential benets and applications of the mathematics-as-IC perspective .

Mots clés: Foundations of mathematics; information compression; SP Theory of Intelligence

Domaines: Théorie de l'information et codage [math.IT]; Intelligence artificielle [cs.AI]

James Gerard Gerry Wolff. Mathematics as information compression via the matching and unication of patterns. Complexity, 2019. ⟨hal-02395680⟩