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 compressing information 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 of why we find the world - aspects of it at least - to be compressible. Information compression 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. The idea that mathematics may be seen to be largely about the compression of information is in keeping with the view, supported by evidence that is outlined in the paper, that much of human learning, perception, and cognition may be understood as information compression. That connection is itself in keeping with the observation that mathematics is the product of human ingenuity and an aid to human thinking.
Comments: 25 Pages.
[v1] 2017-06-01 12:32:16
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