Mathematics as Information Compression Via the Matching and Unification of Patterns | Chapter 11 | New Ideas Concerning Science and Technology Vol. 13

 This study presents a fresh take on mathematics' foundations, arguing that mathematics is essentially about "information compression (IC) via pattern matching and unification" (ICMUP). That, in and of itself, is a novel approach to IC, couched in terms of nonmathematical primitives, as is required in any exploration of mathematics' foundations. This new perspective on mathematics' foundations reflects the fact that mathematics is almost entirely the product of human brains, and that it was created as a tool to aid human thinking. Mathematics is likely to be in line with a growing body of evidence supporting the importance of IC in human learning, perception, and cognition. This is a pers study of the SP Theory of Intelligence and its implementation in the SP Computer Model, a system in which a generalised form of ICMUP—the powerful idea of SP-multiple-alignment—plays a key role. The book Unifying Computing and Cognition contains the most extensive overview of the SP System, which includes a detailed description of the SP Computer Model as well as several instances of what the model can do. This paper uses an example to demonstrate how mathematics can achieve information compression without any additional provisions. The book then goes on to show how ICMUP versions can be found in commonly used mathematical structures and operations. Examples         are also given to show how ICMUP can be used to understand certain elements of the mathematics-related fields of logic and computing. The close relationship between IC and probability concepts is also examined, with suggestions that studying AI, cognitive science, and probability concepts through ICMUP has advantages. The close relationship between IC and probability concepts is also discussed, as is how that relationship relates to the established view that some parts of mathematics are intrinsically probabilistic, and how that latter view can be reconciled with the all-or-nothing, "exact," forms of calculation or inference that are familiar in mathematics and logic. There are numerous possible advantages. and

Author (s) Details

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

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