It still begs the question of why many (if not all) phenomena are lawful and why there is a mathematical treatment of randomness. However, this argument demonstrates only that if a physical process can be represented as a pair of variables, then there will be a mathematical relationship between them. Therefore nothing escapes the scope of mathematics. Another proposed explanation is this: Given an independent and a dependent pair of physical variables, their relationship can be either (1) random, in which case we can use the mathematics of statistics to describe it, or (2) lawful or possibly a mixture of the two. But this does not explain why physical phenomena can be represented mathematically in the first place. It may require a considerable amount of effort to determine which math to use where and, as with Newton and some of his contributions to the development of the calculus, the mathematics may be invented to meet the needs of science at the moment.
But considering, in retrospect, that understanding of the physical world in terms of mathematics is a human trait, and that humans are biological creatures, I should not have been surprised that, once again, biology, and indeed one of the most powerful theories of biology, evolution, should provide a measure of understanding.ĭiscovering the fit of mathematics to the physical world is not typically an easy task. The present question, the fit of "our" mathematics to the external world has generally been approached as a question of philosophy and the nature of the physical world. Plausible hypotheses arose not from cognitive psychology, as I had expected, but from the biology of evolution. While working on my book, The Humane Interface, I found it necessary to try to understand why we had certain mental abilities and not others. Albert Einstein put the problem this way in his Sidelights on Relativity, "How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?"
Why should one physical parameter be a mathematical function of some others? This is the philosophical problem that Nobel physicist Eugene Wigner called "the unreasonable effectiveness of mathematics in the natural science" in his 1960 paper of that name in Communications of Pure and Applied Mathematics. For example, group theory proved to be eminently useful in crystallography and in understanding the organization of elementary particles. Even quite abstract mathematical constructs - which were created without any reference to physics or the physical world - turn out later (sometimes much later) to be excellent representations of newly-discovered experimental data. In physics we often describe phenomena in terms of mathematical relationships between quantities that represent observable attributes of the natural world: Double the tension on a spring and the amount it extends doubles the intensity of light from a point source changes precisely in inverse proportion to the square of the distance from the source. Jef Raskin - Effectiveness of MathematicsĮffectiveness of Mathematics A reply to Eugene Wigners paper, "The unreasonable effectiveness of mathematics in the Natural Sciences" and Hammings essay "The unreasonable effectiveness of mathematics."
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