Mathematics and the Physical Universe (B)

Once again:  In his “Anti Gravity” column for the August 2019 issue of Scientific American (this one entitled “Do the Math: It sure comes in handy for doing physics”), Steve Mirsky focuses on the debate between scientists who think that mathematics is the language of the cosmos (and even, for some still today, the language of God) and scientists who consider the importance of mathematics for physics vastly overrated.

When Freeman Dyson (the eminent Anglo-American mathematical physicist “who at 95,” according to Mirsky, “is safely referred to as a living legend”) addressed the conference that was held on the debate at Princeton’s Institute for Advanced Study (IAS) at the end of May, he mentioned the “period of estrangement” between mathematics and physics to which the late Sir George Attiyeh (mentioned in my previous post on this topic) had helped to put an end.  Dyson said that he had noticed the rift when he first joined Albert Einstein and other luminaries on the faculty at IAS:

“When I became a professor, [which] just coincided with the time when [Robert] Oppenheimer [former head of the Manhattan Project] became director . . . , there was a divorce — largely occasioned by the fact Oppenheimer had no use for pure mathematics, and the pure mathematicians had no use for bombs.”

Dyson was evidently asked, following his remarks, what major issues remain to be addressed by physicists and mathematicians, Dyson answered it as follows:

“The question of what’s important is entirely a matter of taste.  I like to think of going to the zoo . . . you can either admire the architecture of the zoo or you can admire the animals.  And so, at the present time, mathematicians are very busy admiring the architecture.  The physicists are admiring the animals.  Which is actually more important isn’t to me the interesting question.  The interesting question is, Why do they fit so well?”

And, indeed, that is a very, very interesting question.

It’s the same general issue as that raised by the Nobel-laureate physicist Eugene Wigner in his famous 1960 paper “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.”

The English physicist, astronomer, and mathematician Sir James Jeans (d. 1949) had perhaps been thinking along similar lines when he remarked, in his 1944 book The Mysterious Universe, that “The stream of knowledge is heading towards a non-mechanical reality; the Universe begins to look more like a great thought than like a great machine. Mind no longer appears to be an accidental intruder into the realm of matter. . . .  we ought rather hail it as the creator and governor of the realm of matter.”