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: 鈥淭he town鈥檚 so full of these confounded dials /聽The greatest part of the inhabitants, /聽Shrunk up with hunger, crawl along the streets鈥�.
We have been slaves to number ever since. Not that we need complain, according to two recent books. Experimental physicist Piero Martin鈥檚 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鈥檚 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鈥檚, 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鈥檚 greater purpose is to trace the outline of 鈥渁 true Copernican revolution鈥� 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鈥檚 constant, h.
The dizzying 鈥渉ows鈥� of this revolution beg many 鈥渨hys鈥�, mostly of the 鈥淲hy go to all that bother?鈥� sort, but Martin is here to explain why such eye-watering accuracy is vital to the running of our world.
厂耻尘辫迟别谤鈥檚 Four Ways of Thinking is more speculative, organising reality around the four classes of phenomena defined by mathematician Stephen Wolfram鈥檚 A New Kind of Science. Sumpter is quick to reassure that his homage to the polymathic Wolfram isn鈥檛 so much 鈥渁 new kind of science鈥� as 鈥渁 new way to convince your friends to go jogging with you鈥� or perhaps 鈥渁 new way of controlling chocolate cake addiction鈥�.
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 厂耻尘辫迟别谤鈥檚 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鈥檛 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 鈥� indeed, to make mistakes in her code impossible 鈥� 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 鈥渆ach of us follows our individual rules of interaction and out of that emerges the complexity of our society鈥�?
Maybe not. But the journey was gripping.
