Authors: J Gerard Wolff
This paper notes first that the effectiveness of mathematics in science appears to some writers to be "mysterious" or "unreasonable". Then reasons are given for thinking that science is, at root, the search for compression in the world. At more length, several reasons are given for believing that mathematics is, fundamentally, a set of techniques for information compression via the matching and unification of patterns (ICMUP), and their application. From there, it is argued that the effectiveness of mathematics in science is because it provides a means of achieving the compression of information which lies at the heart of science. The anthropic principle provides an explanation for why we find the world -- aspects of it at least -- to be compressible. ICMUP may be seen to be important in both science and mathematics, not only as a means of representing knowledge succinctly, but as a basis for scientific and mathematical inferences -- because of the intimate relation that is known to exist between information compression and concepts of prediction and probability. Since ICMUP is a key part of the "SP theory of intelligence", evidence presented in this paper strengthens the already-strong evidence for the SP theory as a unifying principle across artificial intelligence, mainstream computing, mathematics, human learning, perception, and cognition, and neuroscience. The evidence and ideas in this paper may provide the basis for a "new mathematics for science" with potential benefits and applications in science and science-related areas.
Comments: 44 Pages.
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