Graham Farmelo gave a lecture here at Oxford yesterday about his book The Universe Speaks in Numbers. His theme, to quote from the web site, is that physicists these days seek the laws of nature “with the help of cutting-edge mathematics.”
This situation is controversial. Everyone knows that Newton and Gauss did real physics, but what about the two modern heroes Farmelo focused on, Atiyah and Witten? Is string theory real physics?
An unexpected twist in the discussion turned up at coffee just now with André Weideman, Yuji Nakatsukasa, and Trond Steihaug. Steihaug is studying Newton’s notebooks, and he was telling us how they show Newton carrying out systematic numerical calculations to many digits of accuracy. Gauss, too, was known for his extensive calculations.
Suddenly we noticed the oddity in Farmelo’s title, displayed on the poster behind us. The universe speaks in “numbers”? Of course, the word is intended as shorthand for mathematics. But that shorthand is long obsolete, for in fact, most mathematicians of recent generations have very little interest in the real numbers Newton and Gauss were calculating! I just checked and found that the only numbers that appear in the 106-page joint paper by Atiyah and Witten are the integers 0, 1,…, 10, 11, 24, 27, 36, 48, 72, and 144, together with i, π, and e.
All this suggests a possibility Farmelo cannot have intended. Maybe the universe indeed speaks in numbers; and maybe physics lost its way when it came under the spell of a kind of mathematics that is number-free?
[17 May 2019]