The Universe Speaks in Numbers

Like many with an early enthusiasm for mathematics, I read and was inspired by G. H. Hardy's A Mathematician's Apology. This 1922 recollection Hardy included in that essay come to mind when reading this book:

My audience there was composed almost entirely of physicists, and I may have spoken a little provocatively on that account; but I would still stand by the substance of what I said. I began by saying that there is probably less difference between the positions of a mathematician and of a physicist than is generally supposed… I went on to say that neither physicists nor philosophers have ever given any convincing account of what ‘physical reality’ is, or of how the physicist passes, from the confused mass of fact or sensation with which he starts, to the construction of the objects which he calls ‘real’. Thus, we cannot be said to know what the subject-matter of physics is; but this need not prevent us from understanding roughly what a physicist is trying to do. It is plain that he is trying to correlate the incoherent body of crude fact confronting him with some definite and orderly scheme of abstract relations, the kind of scheme he can borrow only from mathematics.

In The Universe Speaks in Numbers, Farmelo relates the efforts of theoretical physicists to accurately describe reality while navigating a rather dysfunctional relationship with peer mathematicians. Indeed, while on one hand, we have "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" published in 1960 by physicist Eugene Wigner, we have here the mathematical structure of various physical theories only gaining from pure mathematics advances or empirical predictions by happenstance or singular effort. This even at times between experts sharing a common building. Indeed, the chapter “The Long Divorce” covering the middle of the Twentieth Century suggests a darker, more dismissive tone to Wigner’s observation as summed up in this quote attributed here to Freeman Dyson:

In the 1950s… we needed no help from mathematicians. We thought we were very smart and could do better on our own.

The distance between the two camps, at times admitting acrimony, makes the efforts of some to bridge that gap, such as theoretical physicist Roman Jackiw and mathematician Michael Atiyah, seem heroic.

Actual mathematics is not explained here, and no mathematical knowledge is prerequisite. We learn of the impact Maxwell’s equations modeling electromagnetism on Eisenstein’s development of a ‘light quanta’ theory without having to see or understand those equations. The few equations exhibited are done so only to illustrate the elegant simplicity marking that success. Other technical topics such as quaternions, the standard model, gauge theory, and more are introduced superficially so that the tempo of the unfolding history is not interrupted. This makes this work a much more approachable introduction to modern cosmology and its development than other attempts at popularization, such as Lisa Randall's Warped Passages. That allows for just a few hundred pages to cover the arc from Newton and Euler to a reestablishment of communication (if not effective cooperation) under string theory in the early 1990s as relayed in one of many modern first-hand accounts serving as a basis for this work:

‘It was an embarrassment and a bit of a shock to [us] mathematicians that the string theorists’ voodoo mathematics worked so well,’ Dave Morrison later told me, adding that ‘there was no denying that their physics-based intuition was working, even though it made no sense to us’. Michael Atiyah later said of the physicist’ coup, ‘It was as if they had gone up in a balloon, landed in the geometer’s territory and captured its capital city.’

This evolution of our understanding of reality is told through the significant individual contributions of key pioneers such as Dirac (his 1939 lecture “The Relation between Mathematics and Physics” could be a preface here), Feynman, Freeman Dyson, “Frank” Yang Chen-Ning, and others along with biographical details and personality notes. This focus on the individuals involved as personalities means there is much here about quirks as quarks. This approach is also evident in the author’s The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom.

Over the decades, drawn from differing cultures and backgrounds, these colorful thinkers described here brought about a happy reconciliation:

In the 1950s the two groups were living in different worlds, he [Freeman Dyson], but he is now happy to see them regularly talking together, exchanging ideas, and occasionally working on the same problems. ‘Pure mathematics and theoretical physicists are now very much in the same world’, he says, but it’s not clear how it relates to the real one.’

The author lays out a half dozen predictions on how the ‘real one’ will emerge from the fruits of this cooperation, such as “Space and time are not fundamental concepts-they emerge from quanta of some kind.” Whether his predictions pan out or not, I hope he uses the same storytelling skills, research, and simplifying explanations to tell us in future works the how and why of it all.

Tom Schulte reads and ponders along Bayou Castine near the shores of Lake Pontchartrain in Louisiana.