The Unreasonable Effectiveness of Mathematics in the Natural Sciences by Eugene Paul Wigner
My rating: 4 of 5 stars
Available online here
This brief essay asks why math proves so effective for describing / codifying physical laws, and whether our physical theories — built on (phenomenally successful) mathematics — offer the truth, the whole truth, and nothing but the truth.
There’s a popular story in which a drunk man is found on his hands and knees under a lamppost at night when a police officer comes along. The cops says, “What-cha doin’?” To which the drunk replies, “I dropped my keys, and I’m looking for them?” So, the cop says, “Well, they’re clearly not where you’re looking, why not look elsewhere?” And the drunk says, “Cuz this is where the light is.” I think this story can help us understand what Wigner is getting on about, if only we replace the drunk’s “light” with the scientist’s “elegant mathematics.” Wigner reflects upon why it should be that so many laws of nature seem to be independent from all but a few variables (which is the only way scientists could have discovered them –historically, mathematically, and realistically speaking.) On the other hand, could it be that Physics has led itself into epistemological cul-de-sacs by chasing elegant mathematics?
There’s no doubt that (for whatever the reason turns out to be) mathematics has been tremendously successful in facilitating the construction of theories that make predictions that can be tested with high levels of accuracy. However, that doesn’t mean that some of those theories won’t prove to be mirages.
A few of the examples used in this paper are somewhat esoteric and won’t be readily understood by the average (non-expert) reader. That said, Wigner puts his basic arguments and questions in reasonably clear (if academic) language. The essay is definitely worth reading for its thought-provoking insights.
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BOOK REVIEW: The Unreasonable Effectiveness of Mathematics in the Natural Sciences by Eugene Wigner