A Singing, Dancing Universe Jon Butterworth Enjoys a Celebration of Mathematics-Led Theoretical Physics

Home , Graham Farmelo, John Randall (physicist), Lee Smolin, Paul Dirac

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under physicist and Nobel laureate William to the intensely scrutinized narrative on the discovery “may turn out to be the greatest Henry Bragg, studying small molecules such double helix itself, he clarifies key issues. He development in the field of molecular genet- as tartaric acid. Moving to the University points out that the infamous conflict between ics in recent years”. And, on occasion, the of Leeds, UK, in 1928, Astbury probed the Wilkins and chemist Rosalind Franklin arose scope is too broad. The tragic figure of Nikolai structure of biological fibres such as hair. His from actions of John Randall, head of the Vavilov, the great Soviet plant geneticist of the colleague Florence Bell took the first X-ray biophysics unit at King’s College London. He early twentieth century who perished in the diffraction photographs of DNA, leading to implied to Franklin that she would take over Gulag, features prominently, but I am not sure the “pile of pennies” model (W. T. Astbury Wilkins’ work on DNA, yet gave Wilkins the how relevant his research is here. Yet pulling and F. O. Bell Nature 141, 747–748; 1938). impression she would be his assistant. Wilkins such figures into the limelight is partly what Her photos, plagued by technical limitations, conceded the DNA work to Franklin, and distinguishes Williams’s book from others. were fuzzy. But in 1951, Astbury’s lab pro- PhD student Raymond Gosling became her What of those others? Franklin Portugal duced a gem, by the rarely mentioned Elwyn assistant. It was Gosling who, under Franklin’s and Jack Cohen covered much the same Beighton. Using wet DNA fibres, he took supervision, took the iconic X-ray diffraction ground in the 1977 A Century of DNA, but images revealing the black-cross diffraction ‘Photograph 51’. Williams debunks the myth that now seems dated. James Schwartz’s In pattern characteristic of helical molecules. that Wilkins “stole” it; he clarifies how, before Pursuit of the Gene (2008) hardly touches They were never published, and Astbury did moving on to Birkbeck, University of London, on biochemistry, whereas Siddhartha not follow up on them; if he had, the story of Franklin gave her materials and data on DNA Mukherjee’s 2016 The Gene devotes little DNA might have been very different. to Gosling, to pass on to Wilkins to use as he space to the backstory of the double helix. Many other “lost heroes” emerge in Wil- wished. It was after this that Wilkins showed Isaac Newton wrote to natural philosopher liams’s telling. Martin Henry Dawson and Photograph 51 to James Watson, who, with Robert Hooke that he had seen further than James Lionel Alloway made important con- Crick, used it to uncover the double helix. others only by standing on the shoulders of tributions to Oswald Avery’s demonstration There are a few errors — inevitable in giants. Unravelling the Double Helix looks that DNA probably made up genes. H. F. W. a book of such scope. Williams writes, for beyond giants to the many researchers, now Taylor, C. J. Threlfall and Michael Creeth cru- instance, that biochemist Linus Pauling took half-forgotten, whose contributions paved the cially participated in J. Masson Gulland’s work a “surprisingly long time” to recognize that way for an icon of science. ■ showing that DNA solutions changed viscos- his proposed three-strand structure of DNA ity owing to the rupture of hydrogen bonds was wrong. In fact, at a meeting before the Jan Witkowski is the former director of between nucleotides. All is scrupulously publication of the true, two-strand structure the Banbury Center at Cold Spring Harbor documented in more than 50 pages of notes. (J. D. Watson and F. H. C. Crick Nature 171, Laboratory, New York. Although there is little Williams can add 737–738; 1953), Pauling remarked that the e-mail: [email protected]

PARTICLE PHYSICS A singing, dancing Universe Jon Butterworth enjoys a celebration of mathematics-led theoretical physics.

athematics is an immensely The Universe discoveries, over-reliance on mathematical powerful tool for understanding Speaks in elegance as a guide and a general drift into the laws of the Universe. That was Numbers: How what physicist and writer Jim Baggott, in Mdemonstrated dramatically, for instance, Modern Maths Farewell to Reality (2013), called “fairy Reveals Nature’s by the 2012 discovery of the Higgs boson, Deepest Secrets tale physics”, divorced from its empirical predicted in the 1960s. Yet an ongoing, GRAHAM FARMELO base. Notable critiques have come from often fervid debate over the direction of Faber & Faber (2019) theoretical physicists including Peter Woit, theoretical physics pivots on the relationship Lee Smolin and, more recently, Sabine between physics and maths — specifically, Hossenfelder (see A. Ananthaswamy Nature whether maths has become too dominant. 558, 186–187; 2018). Science writer Graham The worry — expressed by a number of monoculture too focused on a small clutch Farmelo clearly intends The Universe Speaks theorists and writers over several decades of concepts and approaches. Those include in Numbers as a riposte. — is that theoretical physics has become a string theory, overstated predictions of new Farmelo takes us on a tour through the

Climate Change and the Health of Nations Economics for the Common Good Anthony J. McMichael Oxford Univ. Press (2019) Jean Tirole Princeton Univ. Press (2019) In this posthumously published volume, French economist Jean Tirole’s deft study epidemiologist Anthony McMichael journeys (translated by Steven Rendell) questions his through the deep history of Earth’s changing discipline’s role in society. Researchers, he climate and its human implications — such argues, should become socially responsible, as agricultural collapse resulting from shifts in probing issues beyond the euro’s stability, such temperature. A book with echoes for today. as climate change and resource distribution.

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history of the field. His main protagonists are James Clerk Maxwell, Albert Einstein and Paul Dirac (subject of Farmelo’s out- standing 2009 biography, The Strangest Man). The unification of electricity, magnetism and light in Maxwell’s equations is a highlight of any good physics degree. I suspect most physicists can remember the moment when, after a few algebraic tricks with currents and voltages, the speed of light appeared, as if by magic. The Universe isn’t just speaking in numbers: it’s singing and dancing. That constant value of the speed of light led to Einstein’s special theory of relativity in 1905. From this, in an amazing concep- tual (and mathematically abetted) leap, Einstein conjured up general relativity in 1915 (see page 306), then the curvature of space-time, and eventually the gravitational waves discovered by the Laser Interferome- ter Gravitational-Wave Observatory (LIGO) 100 years later. And in 1928, Dirac, demand- ing mathematical consistency between quantum mechanics and special relativity, gave us both an understanding of the spin of developing the standard model of particle mathematical physicists engaged in the field, the electron — without which the periodic physics. During what Farmelo calls “the long notably Freeman Dyson, made important table of the elements makes no sense — divorce” between mathematics and theoreti- contributions, most physicists didn’t need and predicted the existence of antimatter, cal physics from the 1930s to the 1970s, our to go beyond well-established mathematical discovered experimentally a few years later. current understanding techniques to progress. These are brilliant successes of the math- of fundamental phys- Dyson himself (quoted ematical approach, and Farmelo leads ics was assembled. by Farmelo) says that us through them adeptly, with a mixture Dirac and Einstein MATHEMATICS AND “we needed no help of contemporary accounts and scientific were hardly involved from mathematicians. insight. He also casts a sceptical eye on the in those developments. PHYSICS WORK We thought we were stories the players tell about themselves — That the most very smart and could and here the tensions start to be felt. Take fruitful period in the EFFECTIVELY do better on our own.” Einstein’s warning to those who want to development of parti- TOGETHER, TO THE And, as Farmelo puts it, learn about theoretical physicists’ methods: cle physics coincided the feeling was mutual: “Don’t listen to their words, fix your atten- with its estrangement physicists “rarely gen- tion on their deeds.” As Farmelo recounts, from pure mathemat- BENEFIT OF erated ideas that were this is given interesting context by studies of ics could be seen as of the slightest inter- Einstein’s notebooks, showing how he later undermining Farmelo’s BOTH. est to mathematical overstated the role of mathematics, and case. However, the researchers”. Many underplayed that of physical insight, in his pace of progress prob- on both sides of the own breakthrough. ably had more to do with the rapid experi- divorce were content with the situation. mental advances of the time than with any There has been a re-engagement since A PRODUCTIVE UNION intrinsic issue in the relationship between the 1980s. In the mainstream of particle Farmelo’s argument is that mathematics the two subjects. physics, theorists and experimentalists and physics work effectively together, to This was a fertile patch for experimen- were calculating and confirming multi- the benefit of both. Dirac and Einstein were tation, and theorists were continually ple results that established the standard evangelists for mathematically led physics, buffeted by new and startling results, from model as, at the very least, a remark- but their pleas were more or less ignored by the appearance of the muon to the obser- ably precise ‘effective theory’. But oth- their younger colleagues, such as Richard vation of structure inside the proton; these ers, led by luminaries such as Michael Feynman and Steven Weinberg, who were demanded explanation. Although the few Atiyah, Edward Witten and pioneers of

How Dogs Work Listening In: Cybersecurity in an Insecure Age Raymond Coppinger & Mark Feinstein Susan Landau Yale Univ. Press (2019) Univ. Chicago Press (2019) Digitization, notes mathematician Susan Cognitive scientists Raymond Coppinger and Landau, offers amazing potential and Mark Feinstein explore the biological basis of convenience — at the cost of privacy and a need canine behaviour and its interplay with the to ramp up security. She issues both a warning environment, examining everything from dogs’ to protect data, and a call to modify how much wildly varying morphologies to why they bark. control we relinquish in our cyber-reliance.

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string theory including Michael Green HISTORY and John Schwarz, were probing its mathematical boundaries. Whether the mathematical approach eventually became too dominant, taking England’s Galileo over in terms of academic recognition and funding, is the crux of much of Georgina Ferry relishes a biography of the formidable today’s debate. Farmelo gives a lively Moon-mapping Tudor scientist Thomas Harriot. description of the back-and-forth of contributions typical of any thriving inter- disciplinary area, with physical problems he phrase ‘publish or perish’ came into Thomas Harriot: A of the Algonquian peo- stimulating mathematical breakthroughs use in the twentieth century to encap- Life in Science ple, and of the region’s and mathematics throwing up new sulate academic pressures. It is also a ROBYN ARIANRHOD natural resources and Oxford University Press insights and techniques in physics. He Tlesson from the life of Thomas Harriot, who climate. Arianrhod (2019) steers clear of discussing the infeasibly lived when there were no academic journals, shows that his interest large ‘string landscape’ of possible physi- and who never taught at a university. in local people was far from typical: he learnt cal theories to which the mathematical A contemporary of William Shakespeare, their language, admired how they inter- approach seems to have led — contrary Harriot was an English mathematician, planted beans, squashes and maize (corn), to hopes of a unique ‘theory of eve- astronomer and natural philosopher whose and respected their religion. Meanwhile, the rything’. Instead, he concentrates on original work bears comparison with that military expedition leaders fatally soured developments more directly useful and of Johannes Kepler and Galileo Galilei. Yet, relations by overreacting to perceived wrong testable in physics, where some of this outside the enthusiastic circle of historians doing and making unreasonable demands. mathematical sophistication begins to of early modern science who call themselves Previous biographers — the US authors feed back into an understanding of the Harrioteers, his name is almost unknown: he Henry Stevens in 1900 and John Shirley in standard model. never published his mathematical work. In 1983 — were prompted by the Brief and True The standard model is a complex, Thomas Harriot: A Life in Science, mathemati- Report. Neither fully addressed Harriot’s subtle and immensely successful theo- cian Robyn Arianrhod sets out to explain how scientific contributions, as Arianrhod tries retical structure that leaves significant historians have nevertheless been able to place to do. Harriot’s will mentioned a trunk full questions unanswered. Farmelo makes him, almost four centuries after his death in of mathematical papers. A few were circu- a convincing case that, in attempting to 1621, among the founders of modern science. lated and partly published by friends such as answer those questions, mathematics Harriot is elusive. The earliest known docu- the mathematician Walter Warner after his has a crucial role. Yet whether theoreti- ment concerning him lists him as a “plebeian” death, but what became of the collection was cal physics has become too enamoured scholar registering to study at the University unknown until 1784, when it turned up in of beautiful mathematics will, I suspect, of Oxford in 1577. He never married and left some disorder at Petworth House, home to remain a topic of hot debate. no children. By 1583, he was employed by heirs of the ninth Earl of Northumberland, The long experimental search for the Walter Raleigh, naval commander, explorer Harriot’s patron after Raleigh. Only since the Higgs was motivated by the fact that, and favourite of Queen Elizabeth I, to teach mid-twentieth century have scholars made before we accepted the existence of a astronomy and navigation — a field he sense of the thousands of manuscript sheets. quantum energy field that fills the whole greatly improved — to sea captains. He was What they reveal is astonishing. To men- Universe — part of the theory that pre- celebrated in his lifetime by the writer Gabriel tion only a portion of Harriot’s work, he dis- dicted the particle — we demanded more Harvey as among the “profound mathema- covered Snell’s law of refraction two decades evidence than ‘it makes the maths come ticians”, alongside Thomas Digges and John before mathematician Willebrord Snell; for- out right’. The need for evidence is even Dee. Afterwards, he was largely forgotten. mulated laws of motion and falling bodies stronger if the argument is ‘it makes the He has a higher profile in the United States, independently of Galileo and decades before maths look beautiful’. The Universe might thanks to the one work he did publish. A Brief Isaac Newton; produced the first drawing speak in numbers, but it uses empirical and True Report of the New Found Land of Vir- of the Moon through a telescope and made data to do so. ■ ginia is a first-person account of a 1585–86 important observations of sunspots, again voyage sent by Raleigh to survey what is now independently of Galileo; played with binary Jon Butterworth is professor of physics part of North Carolina. The party landed arithmetic nearly a century before Gottfried in the Department of Physics and on Roanoke Island and surveyed it and the Wilhelm Leibniz; and was the first to develop Astronomy, University College London, nearby mainland; almost all its members fully symbolic algebra. There are well- and the author of Smashing Physics returned to England in June 1586. Harriot was grounded suspicions that René Descartes and A Map of the Invisible. He blogs at “employed in discovering”. His report, pub- saw some of Harriot’s papers before publish- lifeandphysics.com lished in 1588, includes the first detailed Eng- ing The Geometry in 1637. e-mail: [email protected] lish description of the language and customs Where Harriot falls down, say some

Magnificent Principia Mrs Moreau’s Warbler Colin Pask Prometheus (2019) Stephen Moss Faber (2019) Isaac Newton remains a giant of physics, as his Names make sense of the world; they also reveal 1687 Principia confirms. Maths historian Colin something about us. Stephen Moss unveils the Pask presents an easily digestible guide to the often surprising roots of avian etymology and work, enlivened with passages from Newton’s offers insight into fierce, long-standing debates life. An invitation to wonder at what some see as such as that over Prunella modularis, variously the greatest single scientific book ever published. known as the dunnock and hedge sparrow.