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Mathematics and logic as information compression by multiple alignment, unification and search
"... This article introduces the conjecture that mathematics, logic and related disciplines may usefully be understood as information compression by ‘multiple alignment’, ‘unification ’ and ‘search’. As a preparation for the two main sections of the article, concepts of HartleyShannon information theory ..."
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This article introduces the conjecture that mathematics, logic and related disciplines may usefully be understood as information compression by ‘multiple alignment’, ‘unification ’ and ‘search’. As a preparation for the two main sections of the article, concepts of HartleyShannon information theory and Algorithmic Information Theory are briefly reviewed together with a summary of the essentials of the simpler ‘standard ’ methods for information compression. Related areas of research are briefly described: philosophical connections, information compression (IC) in brains and nervous systems, and IC in relation to inductive inference, Minimum Length Encoding and probabilistic reasoning. Then the concepts of information compression by ‘multiple alignment’, ‘unification ’ and ‘search ’ (ICMAUS) are outlined together with a brief description of the SP61 computer model that is a partial realisation of the ICMAUS framework. The first of the two main sections describes how many of the commonlyused forms and structures in mathematics, logic and related disciplines (such as theoretical linguistics and computer programming) may be seen as devices for IC. In some cases, these forms and structures may be interpreted in terms of the ICMAUS framework. The second main section describes a selection of examples where processes of calculation and inference in mathematics, logic and related disciplines may be understood as IC. In many cases, these examples may be understood more specifically in terms of the ICMAUS concepts and illustrated with output from the SP61 model. 1 Associated issues are briefly discussed. Abbreviations used in the article: IC—information compression; ICMAUS—information compression by multiple alignment, unification and search; MA—multiple alignment; ML—mathematics and logic;
C. Roy Keys Inc.
"... this paper shows (Section 2) that Fibonacci series underlies fractal fluctuations on all spacetime scales ..."
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this paper shows (Section 2) that Fibonacci series underlies fractal fluctuations on all spacetime scales
ARISTOTELIAN REALISM
"... Aristotelian, or nonPlatonist, realism holds that mathematics is a science of the real world, just as much as biology or sociology are. Where biology studies living things and sociology studies human social relations, mathematics studies the quantitative or structural aspects of things, such as rat ..."
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Aristotelian, or nonPlatonist, realism holds that mathematics is a science of the real world, just as much as biology or sociology are. Where biology studies living things and sociology studies human social relations, mathematics studies the quantitative or structural aspects of things, such as ratios, or patterns, or complexity,