Piero Martin
Yale University Press
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David Sumpter
Allen Lane
Blame the sundial. A dinner guest in a poem by the Roman writer Plautus, his stomach rumbling, complains that: “The town’s so full of these confounded dials / The greatest part of the inhabitants, / Shrunk up with hunger, crawl along the streets”.
We have been slaves to number ever since. Not that we need complain, according to two recent books. Experimental physicist Piero Martin’s spirited and fascinating traces our ever more precise grasp of physical reality, while by mathematician David Sumpter shows number illuminating human complexities. Sumpter wrote the bestselling , published during the covid-19 pandemic.
Martin’s stories about common units of measure (candelas and moles rub shoulders with amperes and kelvin) tip their hats to the past. The Plautus quotation is Martin’s, as is the assertion (very welcome to this amateur pianist) that the unplayable tempo Ludwig van Beethoven set for his Hammerklavier sonata (an incredibly fast metronome setting of minim = 138) was caused by a broken metronome.
Martin’s greater purpose is to trace the outline of “a true Copernican revolution” in the way we measure our metres, minutes and kilograms.
In the past, fundamental constants were determined with reference to material prototypes. But in 2018, a revision of the International System of Units (SI) was agreed by the General Conference on Weights and Measures: international units of measure would be defined in reference to the constants themselves.
The metre is now defined indirectly using the length of a second as measured by atomic clocks, while a kilogram is defined as a function of two physical constants, the speed of light, c, and Planck’s constant, h.
The dizzying “hows” of this revolution beg many “whys”, mostly of the “Why go to all that bother?” sort, but Martin is here to explain why such eye-watering accuracy is vital to the running of our world.
ł§łÜłľ±čłŮ±đ°ů’s Four Ways of Thinking is more speculative, organising reality around the four classes of phenomena defined by mathematician Stephen Wolfram’s A New Kind of Science. Sumpter is quick to reassure that his homage to the polymathic Wolfram isn’t so much “a new kind of science” as “a new way to convince your friends to go jogging with you” or perhaps “a new way of controlling chocolate cake addiction”.
The big point Sumpter takes from the book is that all phenomena are, mathematically speaking, either stable, periodic, chaotic or complex. Learn the differences between these phenomena, and you are halfway to better understanding your own life.
Much of his book is built semi-novelistically around a summer school in complex systems that Sumpter attended at the Santa Fe Institute in New Mexico in 1997.
His half-remembered, half-invented mathematical conversations with fellow attendees won me over, though I have a strong aversion to the stilted quality of exposition through dialogue.
I prefer ł§łÜłľ±čłŮ±đ°ů’s biographical sketches, especially when he explores the strengths and weaknesses of statistical thinking through the life of Ronald Fisher, a genius who in the 1940s almost single-handedly created the foundations for statistical science.
That the world doesn’t stand still to be measured, and is often best considered a dynamical system, is an insight Sumpter attributes to Alfred Lotka, the chemist who in the first half of the 20th century came tantalisingly close to formulating systems biology.
Sumpter illustrates chaotic phenomena through the work of NASA software engineer Margaret Hamilton, whose determination never to make a mistake — indeed, to make mistakes in her code impossible — helped to land the crew of Apollo 11 on the moon.
Mathematician Andrey Kolmogorov personifies complex thinking for Sumpter as he abandons the axiom-based approach to mathematics and starts to think in terms of information and computer code.
Can mathematics really elucidate life? Do we really need mathematical thinking to realise, as Sumpter writes, that “each of us follows our individual rules of interaction and out of that emerges the complexity of our society”?
Maybe not. But the journey was gripping.
