Daily Meh is an edited stream of consciousness, by Simen.

The Unreasonable Effectiveness of Mathematics in the Natural Sciences

A classic, by Nobel Laureate in physics, Eugene Wigner. It’s — at least to this reader — in passages dense, and the examples he uses include quantum mechanics, which is hardly accessible to the general reader (such as me).

His point, though, is fairly accessible: it’s surprising, at least so surprising that we ought to be able to give an explanation for it, that mathematical theories so accurately explain natural phenomena. For instance, Wigner invokes the example of Newton:

Philosophically, the law of gravitation as formulated by Newton was repugnant to his time and to himself. Empirically, it was based on very scanty observations. The mathematical language in which it was formulated contained the concept of a second derivative and those of us who have tried to draw an osculating circle to a curve know that the second derivative is not a very immediate concept. The law of gravity which Newton reluctantly established and which he could verify with an accuracy of about 4% has proved to be accurate to less than a ten thousandth of a per cent and became so closely associated with the idea of absolute accuracy that only recently did physicists become again bold enough to inquire into the limitations of its accuracy. Certainly, the example of Newton’s law, quoted over and over again, must be mentioned first as a monumental example of a law, formulated in terms which appear simple to the mathematician, which has proved accurate beyond all reasonable expectations.

Why indeed this coincidence, where Newton on somewhat scanty evidence formulated a law that just so happens to be extremely accurate, far more accurate than one might expect?

See also Wikipedia.