Quote:
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[Todd’s Vannevar Bush (1890 - 1974) quote:] If scientific reasoning were limited to the logical processes of arithmetic, we should not get very far in our understanding of the physical world. One might as well attempt to grasp the game of poker entirely by the use of the mathematics of probability.
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OTOH, as noted in Wiki, from
The Unreasonable Effectiveness of Mathematics in the Natural Sciences, by the physicist Eugene Wigner in 1960, regarding the “The miracle of mathematics in the natural sciencesâ€:
Quote:
Wigner begins his paper with the belief, common to all those familiar with mathematics, that mathematical concepts have applicability far beyond the context in which they were originally developed. Based on his experience, he says "it is important to point out that the mathematical formulation of the physicist’s often crude experience leads in an uncanny number of cases to an amazingly accurate description of a large class of phenomena". He uses the law of gravitation, originally used to model freely falling bodies on the surface of the earth, as an example. This fundamental law was extended on the basis of what Wigner terms "very scanty observations" to describe the motion of the planets and "has proved accurate beyond all reasonable expectations." Another oft-cited example is Maxwell's equations, derived to model familiar electrical phenomena; additional solutions of the equations describe radio waves, which were later found to exist. Wigner sums up his argument by saying that "the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it". He concludes his paper with the same question he began with:
The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.
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