The Unreasonable Effectiveness of Mathematics
Mathematics · · 6 min read · By No Design Editorial
Forget the golden ratio. The real puzzle is that mathematics invented for its own sake keeps describing a universe it was never aimed at.
The design argument in mathematics was never well served by claiming that one magic number is stamped across creation. The golden ratio in the Parthenon, the Mona Lisa, the human body and the nautilus shell does not survive contact with a measuring instrument, as George Markowsky catalogued in a 1992 paper.
What is real is smaller and better attested. The Fibonacci sequence genuinely does appear in how plants arrange their parts. Botanists call it phyllotaxis. Seeds pack at an angle related to the golden ratio because that ratio is the hardest number to approximate with a fraction, which spaces successive seeds more evenly than any simpler angle would.
But the larger fact is the one worth arguing from: the universe is pervasively, unaccountably mathematical, and nobody has a good naturalistic account of why.
That framing is not new. In 1960 the Nobel physicist Eugene Wigner published an essay called 'The Unreasonable Effectiveness of Mathematics in the Natural Sciences', in which he described the usefulness of mathematics for describing the physical world as a gift we neither understand nor deserve.
The pattern he was pointing at keeps repeating. Mathematicians develop a structure for its own sake, with no application in view, and decades or centuries later a physicist finds that the structure is exactly what some corner of reality runs on. Non-Euclidean geometry was an abstract curiosity before general relativity needed it. Group theory was pure algebra before particle physics required it.
There is no obvious reason a universe should be legible in that way, still less that it should answer to mathematics invented before anyone knew there was a question. That is a stranger fact than any single ratio, and it does not depend on measuring a painting.
From Chapter 11: Mathematics and Nature.
Tags: Mathematics, Wigner, Corrections, Quran