General Science and Philosophy

   

Towards a New Mathematics for Science

Authors: J Gerard Wolff

In this paper, it is argued that, despite its many strengths and undoubted value in science, mathematics also has some weaknesses as a handmaiden for science. There appears to be potential in developing a new mathematics for science (NMFS) which is designed to overcome those weaknesses and to meet more fully the needs of science. As a background to the proposals: 1) The conclusions of a companion paper are noted - that mathematics is, fundamentally, a set of techniques for the compression of information and the application of those techniques; 2) 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; 3) Since science and mathematics are products of the human intellect, it should not be surprising to find that the workings of the human mind has an influence on both of them; and 4) The significance of information compression in science and mathematics is in line with an abundance of other evidence for the significance of information compression in human learning, perception, and thinking. Continuing the theme of information compression as a unifying principle, the "SP theory of intelligence" and its realisation in the "SP computer model" demonstrate how diverse aspects of intelligence may be modelled via information compression within the powerful framework of "multiple alignment". An NMFS is proposed, created as an amalgamation of mathematics as it is today with the SP system as it is today, including developments in both areas that are anticipated now. It is envisaged that, for reasons described in the paper, the proposed NMFS will overcome several of the apparent weaknesses in mathematics. In several sections, there is discussion of some possible implications for science of the proposed NMFS, including: potential for the long-sought-after unification of quantum mechanics and general relativity; expansion of the concept of "object" in physics; ambiguity in human perception as an analogy for the concept of superposition in quantum mechanics; the phenomenon of discontinuous dependencies in natural languages as an analogy for nonlocality and entanglement in quantum mechanics; a "waterspout" interpretation for some of the two-slits experiments; potential advantages of the proposed NMFS in the realm of statistics; and its potential to be a vehicle for the representation of *all* kinds of scientific knowledge, with consequent benefits in the processing of that knowledge.

Comments: 69 Pages.

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[v1] 2017-06-01 12:39:35

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