# “These confounded dials…”

Reading The Seven Measures of the World by Piero Martin and Four Ways of Thinking by David Sumpter, for New Scientist, 23 October 2023

Blame the sundial. A dinner guest in a play 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’ve been slaves to number ever since. Not that we need complain, according to two recent books. Piero Martin’s spirited and fascinating The Seven Measures of the World traces our ever-more precise grasp of physical reality, while Four Ways of Thinking, by the Uppsala-based mathematician David Sumpter, shows number illuminating human complexities.

Martin’s stories about common units of measure (candelas and moles rub shoulders here with amperes and degrees 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 Beethoven set for his “Hammerklavier” sonata (138 beats per minute!) was caused by a broken metronome.

Martin’s greater purpose is to trace, in the way we measure our metres and minutes, kilogrammes and candelas, the outline of “a true Copernican revolution”.

In the past fundamental constants were determined with reference to material prototypes. In November 2018 it was decided to define international units of measure in reference to the constants themselves. The metre is now defined indirectly using the length of a second as measured by atomic clocks, while the definition of a kilogramme 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 not a few “whys”, but Martin is here to explain why such eye-watering accuracy is vital to the running of our world.

Sumpter’s Four Ways of Thinking is more speculative, organising reality around the four classes of phenomena defined by mathematician Stephen Wolfram’s little-read 1,192-page opus from 2002, A New Kind of Science. Sumpter is quick to reassure us that that his homage to the eccentric and polymathic Wolfram is not 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 point is, all phenomena are mathematically speaking, either stable, periodic, chaotic, or complex. Learn the differences between these phenomena, and you are half way to better understanding your own life.

Much of Four Ways is assembled semi-novelistically around a summer school in complex systems that Sumpter attended at the Santa Fe Institute in 1997. His half-remembered, half-invented mathematical conversations with fellow attendees won me over, though I have a strong aversion to exposition through dialogue.

I incline to think Sumpter’s biographical sketches are stronger. The strengths and weaknesses of statistical thinking are explored through the life of Ronald Fisher, the unlovely genius who in the 1940s a almost single-handedly created the foundations for statistical science.

That the world does not stand still to be measured, and is often best considered a dynamical system, is an insight given to Alfred Lotka, the chemist who in the first half of the 20th century came tantalisingly close to formulating systems biology.

Chaotic phenomena are caught in a sort of negative image through the work of NASA software engineer Margaret Hamilton, whose determination never to make a mistake — indeed, to make mistakes in her code impossible — landed the crew of Apollo 11 on the Moon.

Soviet mathematician Andrej Kolmogorov personifies complex thinking, 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 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.

# Ideas are like boomerangs

Reading In a Flight of Starlings: The Wonder of Complex Systems by Giorgio Parisi for The Telegraph, 1 July 2023

“Researchers,” writes Giorgio Parisi, recipient of the 2021 Nobel Prize in Physics, “often pass by great discoveries without being able to grasp them.” A friend’s grandfather identified and then ignored a mould that killed bacteria, and so missed out on the discovery of penicillin. This story was told to Parisi in an attempt to comfort him for the morning in 1970 he’d spent with another hot-shot physicist, Gerard ‘t Hooft, dancing around what in hindsight was a perfectly obvious application of some particle accelerator findings. Having teetered on the edges of quantum chromodynamics, they walked on by; decades would pass before either man got another stab at the Nobel. “Ideas are often like boomerangs,” Parisi explains, and you can hear the sigh in his voice; “they start out moving in one direction but end up going in another.”

In a Flight of Starlings is the latest addition to an evergreen genre: the scientific confessional. Read this, and you will get at least a frisson of what a top-flight career in physics might feel like.

There’s much here that is charming and comfortable: an eminent man sharing tales of a bygone era. Parisi began his first year of undergraduate physics in November 1966 at Sapienza University in Rome, when computer analysis involved lugging about (and sometimes dropping) metre-long drawers of punched cards.

The book’s title refers to Parisi’s efforts to compute the murmurations of starlings. Recently he’s been trying to work out how many solid spheres of different sizes will fit into a box. There’s a goofiness to these pet projects that belies their significance. The techniques developed to follow thousands of starlings through three dimensions of space and one of time bear a close resemblance to those used to solve statistical physics problems. And fitting marbles in a box? That’s a classic problem in information theory.

The implications of Parisi’s work emerge slowly. The reader, who might, in all honesty, be touched now and again by boredom, sits up straighter once the threads begin to braid.

Physics for the longest time could not handle complexity. Galileo’s model of the physical world did not include friction, not because friction was any sort of mystery, but because the mathematics of his day couldn’t handle it.

Armed with better mathematics and computational tools physics can now study phenomena that Galileo could never have imagined would be part of physics. For instance, friction. For instance, the melting of ice, and the boiling of water: phenomena that, from the point of view of physics, are very strange indeed. Coming up with models that explain the phase transitions of more complex and disordered materials, such as glass and pitch, is something Parisi has been working on, on and off, since the middle of the 1990s.

Efforts to model more and more of the world are nothing new, but once rare successes now tumble in upon the field at a dizzying rate; almost as though physics has undergone its own phase transition. This, Parisi says, is because once two systems in different fields of physics can be described by the same mathematical structure, “a rapid advancement of knowledge takes place in which the two fields cross-fertilize.”

This has clearly happened in Parisi’s own specialism. The mathematics of disorder apply whether you’re describing why some particles try to spin in opposite directions, or why certain people sell shares that others are buying, or what happens when some dinner guests want to sit as far away from other guests as possible.

Phase transitions eloquently connect the visible and quantum worlds. Not that such connections are particularly hard to make. Once you know the physics, quantum phenomena are easy to spot. Ever wondered at a rainbow?

“Much becomes obvious in hindsight,” Parisi writes. “Yet it is striking how in both physics and mathematics there is a lack of proportion between the effort needed to understand something for the first time and the simplicity and naturalness of the solution once all the required stages have been completed.”

The striking “murmurations” of airborne starlings are created when each bird in the flock pays attention to the movements of its nearest neighbour. Obvious, no?

But as Parisi in his charming way makes clear, whenever something in this world seems obvious to us, it is likely because we are perched, knowingly or not, on the shoulders of giants.

# Making waves

Reading Frank Close’s Elusive: How Peter Higgs solved the mystery of mass, for New Scientist, 29 June 2022

In Elusive, physicist Frank Close sets out to write about Peter Higgs, whose belief in the detectability of a very special particle that was to bear his name earned him a Nobel prize in 2013.

But Higgs’s life resists narrative. He has had a successful career. His colleagues enjoy his company. He didn’t over-publish, or get into pointless spats. Now in his mid-nineties, Higgs keeps his own counsel and doesn’t use email.

So that left Close with writing a biography, not of the man, but of “his” particle, the Higgs boson – and with answering some important questions. How do we explain fundamental forces so limited in their reach, they cannot reach outside the nucleus of an atom? Why is this explanation compelling enough that we entertained its outrageous implication: that there existed a fundamental field everywhere in the universe, a sort of aether, that we could not detect? Why did this idea occur to six thinkers, independently, in 1964? And how did it justify the cool €10 billion it took to hunt for the particle that this wholly conjectural field predicted?

To understand, let’s start with our universe. Forget solid matter for a moment. Think instead of fields. The universe is full of them, and when we put energy into these fields it’s as though we dropped a stone into a lake – we make waves. In this analogy, you are also in the lake: there is no shore, no “outside” from which you can see the whole wave. Instead, as the wave passes through a point in space, you will notice a change in some value at that point.

These changes show up as particles. Light, for example, is a wave in the electromagnetic field, yet when we observe the effect that wave has on a point in space, we detect a particle – a photon.

Some waves are easier to make than others, and travel farther. Photons travel outwards as fast as the universe allows. Gravitational waves are as fast, but decay sharply with distance.

The mathematics used to model such fields makes a kind of sense. But we also need a mathematics to explain why the other fields we know about are infinitesimally small, extending no farther than the dimensions of the atomic nucleus.

For the mathematics to work for such small fields, it requires another, more mysterious, infinite field: one that doesn’t decay with distance, and that always has a value greater than zero. This field interacts with everything bar light. If you are a photon, you get to zip along at the universal speed limit. But if you are anything else, this additional field slows you down.

We call the effect of this field mass. Photons are massless, so travel very quickly, while everything else has some amount of mass, and consequently travels more slowly. It is easy to set the electromagnetic field trembling – just light a match. To set off a wave in the mass-generating field, however, takes much more energy.

In 1998, CERN began work on its Large Hadron Collider (LHC), a 27-kilometre-long particle accelerator 100 metres under the French-Swiss border. On 4 July 2012, a particle collision in the LHC released such phenomenal energy that it set off a mass-generating wave. As this wave passed through the machine’s detectors a new particle was observed. In detecting this particle, physicists confirmed the existence of the mass-generating field – and our present model of how the universe works (the standard model of particle physics) was completed.

Both of Close’s subjects, Peter Higgs and his particle, prove elusive in the end. Newcomers should start their journey of discovery elsewhere – perhaps with Sean Carroll’s excellent webinars and books.

But Close, and this difficult, brilliant book, will be waiting, smiling, at the end of the road.

# To hell with the philosopause!

Reading Hawking Hawking: The Selling of a Scientific Celebrity by Charles Seife for the Spectator, 1 May 2021

I could never muster much enthusiasm for the theoretical physicist Stephen Hawking. His work, on the early universe and the nature of spacetime, was Nobel-worthy, but those of us outside his narrow community were horribly short-changed. His 1988 global best-seller A Brief History of Time was incomprehensible, not because it was difficult, but because it was bad.

Nobody, naturally, wanted to ascribe Hawking’s popular success to his rare form of Motor Neurone Disease, Hawking least of all. He afforded us no room for horror or, God forbid, pity. In 1990, asked a dumb question about how his condition might have shaped his work (because people who suffer ruinous, debilitating illnesses acquire compensating superpowers, right?) Hawking played along: “I haven’t had to lecture or teach undergraduates, and I haven’t had to sit on tedious and time-consuming committees. So I have been able to devote myself completely to research.”

The truth — that Hawking was one of the worst popular communicators of his day — is as evident as it is unsayable. A Brief History of Time was incomprehensible because after nearly five years’ superhuman effort, the author proved incapable of composing a whole book unaided. He couldn’t even do mathematics the way most people do it, by doodling, since he’d already lost the use of his hands. He could not jot notes. He could not manipulate equations. He had to turn every problem he encountered into a species of geometry, just to be able to think about it. He held his own in an impossibly rarified profession for years, but the business of popular communication was beyond him. As was communication, in the end, according to Hawking’s late collaborator Andy Strominger: “You would talk about words per minute, and then it went to minutes per word, and then, you know, it just got slower and slower until it just sort of stopped.”

Hawking became, in the end, a computerised patchwork of hackneyed, pre-stored utterances and responses. Pull the string at his back and marvel. Charles Seife, a biographer braver than most, begins by staring down the puppet. His conceit is to tell Stephen Hawking’s story backwards, peeling back the layers of celebrity and incapacity to reveal the wounded human within.

It’s a tricksy idea that works so well, you wonder why no-one thought of it before (though ordering his material and his arguments in this way must have nearly killed the poor author).

Hawking’s greatest claim to fame is that he discovered things about black holes — still unobserved at that time — that set the two great schools of theoretical physics, quantum mechanics and relativity, at a fresh and astonishingly creative loggerheads.

But a new golden era of astronomical observation dawned almost immediately after, and A Brief History was badly outdated before it even hit the shelves. It couldn’t even get the date of the universe right.

It used to be that genius that outlived its moment could reinvent itself. When new-fangled endocrine science threw Ivan Pavlov’s Nobel-winning physiology into doubt, he reinvented himself as a psychologist (and not a bad one at that).

Today’s era of narrow specialism makes such a move almost impossible but, by way of intellectual compensation, there is always philosophy — a perennially popular field more or less wholly abandoned by professional philosophers. Images of the middle-aged scientific genius indulging its philosopause in book after book about science and art, science God, science and society and so on and so forth, may raise a wry smile, but work of real worth has come out of it.

Alas, even if Hawking had shown the slightest aptitude for philosophy (and he didn’t), he couldn’t possibly have composed it.

In our imaginations, Hawking is the cartoon embodiment of the scientific sage, effectively disembodied and above ordinary mortal concerns. In truth, life denied him a path to sagacity even as it steeped him in the spit and stew of physical being. Hawking’s libido never waned. So to hell with the philosopause! Bring on the dancing girls! Bring on the cheques, from Specsavers, BT, Jaguar, Paddy Power. (Hawking never had enough money: the care he needed was so intensive and difficult, a transatlantic air flight could set him back around a quarter of a million pounds). Bring on the billionaires with their fat cheques books (naifs, the lot of them, but decent enough, and generous to a fault). Bring on the countless opportunities to bloviate about subjects he didn’t understand, a sort of Prince Charles only without Charles’s efforts at warmth.

I find it impossible, having read Seife, not to see Hawking through the lens of Jacobean tragedy, warped and raging, unable even to stick a finger up at a world that could not — but much worse, *chose* not — to understand him. Of course he was a monster, and years too late, and through a book that will anger many, I have come to love him for it.

# An engine for understanding

Reading Fundamentals by Frank Wilczek for the Times, 2 January 2021

It’s not given to many of us to work at the bleeding edge of theoretical physics, discovering for ourselves the way the world really works.

The nearest most of us will ever get is the pop-science shelf, and this has been dominated for quite a while now by the lyrical outpourings of Italian theoretical physicist Carlo Rovelli. Rovelli’s upcoming one, Helgoland, promises to have his reader tearing across a universe made, not of particles, but of the relations between them.

It’s all too late, however: Frank Wilczek’s Fundamentals has gazzumped Rovelli handsomely, with a vision that replaces our classical idea of physical creation — “atoms and the void” — with one consisting entirely of spacetime, self-propagating fields and properties.

Born in 1951 and awarded the Nobel Prize in Physics in 2004 for figuring out why atoms don’t just fly apart, Wilczek is out to explain why “the history of Sweden is more complicated than the history of the universe”. The ingredients of the universe are surprisingly simple, but their fates, playing out through time in accordance with just a handful of rules, generate a world of unimaginable complexity, contingency and abundance. Measures of spin, charge and mass allow us to describe the whole of physical reality, but they won’t help us at all in depicting, say, the history of the royal house of Bernadotte.

Wilczek’s “ten keys to reality”, mentioned in his subtitle, aren’t to do with the 19 or so physical constants that exercised Martin Rees, the UK’s Astronomer Royal, in his 1990s pop-science heyday. The focus these days has shifted more to the spirit of things. When Wilczek describes the behaviour of electrons around an atom, for example, gone are the usual Böhr-ish mechanics, in which electrons leap from one nuclear orbit to another. Instead we get a vibrating cymbal, the music of the spheres, a poetic understanding of fields, and not a fragment of matter in sight.

So will you plump for the Wilzcek, or will you wait for the Rovelli? A false choice, of course; this is not a race. Popular cosmology is more like the jazz scene: the facts (figures, constants, models) are the standards everyone riffs off. After one or two exposures you find yourself returning for the individual performances: their poetry, their unique expression.

Wilczek’s ten keys are more like ten book ideas, exploring the spatial and temporal abundance of the universe; how it all began; the stubborn linearity of time; how it all will end. What should we make of his decision to have us swallow the whole of creation in one go?

In one respect this book was inevitable. It’s what people of Wilczek’s peculiar genius and standing do. There’s even a sly name for the effort: the philosopause. The implication here being that Wilczek has outlived his most productive years and is now pursuing philosophical speculations.

Wilzcek is not short of insights. His idea of what the scientific method consists of is refreshingly robust: a style of thinking that “combines the humble discipline of respecting the facts and learning from Nature with the systematic chutzpah of using what you think you’ve learned aggressively”. If you apply what you think you’ve discovered everywhere you can, even in situations that have nothing to do with your starting point, then, if it works, “you’ve discovered something useful; it it doesn’t, then you’ve learned something important.”

However, works of the philosopause are best judged on character. Richard Dawkins seems to have discovered, along with Johnny Rotten, that anger is an energy. Martin Rees has been possessed by the shade of that dutiful bureaucrat C P Snow. And in this case? Wilczek, so modest, so straight-dealing, so earnest in his desire to conciliate between science and the rest of culture, turns out to be a true visionary, writing — as his book gathers pace — a human testament to the moment when the discipline of physics, as we used to understand it, came to a stop.

Wilczek’s is the first generation whose intelligence — even at the far end of the bell-curve inhabited by genius — is insufficient to conceptualise its own scientific findings. Machines are even now taking over the work of hypothesis-making and interpretation. “The abilities of our machines to carry lengthy yet accurate calculations, to store massive amounts of information, and to learn by doing at an extremely fast pace,” Wilczek explains, “are already opening up qualitatively new paths toward understanding. They will move the frontier of knowledge in directions, and arrive at places, that unaided human brains can’t go.”

Or put it this way: physicists can pursue a Theory of Everything all they like. They’ll never find it, because if they did find it, they wouldn’t understand it.

Where does that leave physics? Where does that leave Wilczek? His response is gloriously matter-of-fact:

“… really, this should not come as fresh news. Humans themselves know many things that are not available to human consciousness, such as how to process visual information at incredible speeds, or how to make their bodies stay upright, walk and run.”

Right now physicists have come to the conclusion that the vast majority of mass in the universe reacts so weakly to the bits of creation we can see, we may never know its nature. Though Wilczek makes a brave stab at the problem of so-called “dark matter”, he is equally prepared to accept that a true explanation may prove incomprehensible.

Human intelligence turns out to be just one kind of engine for understanding. Wilzcek would have us nurture it and savour it, and not just for what it can do, but because it is uniquely ours.

# What else you got?

Reading Benjamin Labatut’s When We Cease to Understand the World for the Spectator, 14 November 2020

One day someone is going to have to write the definitive study of Wikipedia’s influence on letters. What, after all, are we supposed to make of all these wikinovels? I mean novels that leap from subject to subject, anecdote to anecdote, so that the reader feels as though they are toppling like Alice down a particularly erudite Wikipedia rabbit-hole.

The trouble with writing such a book, in an age of ready internet access, and particularly Wikipedia, is that, however effortless your erudition, no one is any longer going to be particularly impressed by it.

We can all be our own Don DeLillo now; our own W G Sebald. The model for this kind of literary escapade might not even be literary at all; does anyone here remember James Burke’s Connections, a 1978 BBC TV series which took an interdisciplinary approach to the history of science and invention, and demonstrated how various discoveries, scientific achievements, and historical world events were built from one another successively in an interconnected way?

And did anyone notice how I ripped the last 35 words from the show’s Wikipedia entry?

All right, I’m sneering, and I should make clear from the off that When We Cease… is a chilling, gripping, intelligent, deeply humane book. It’s about the limits of human knowledge, and the not-so-very-pleasant premises on which physical reality seems to be built. The author, a Chilean born in Rotterdam in 1980, writes in Spanish. Adrian Nathan West — himself a cracking essayist — fashioned this spiky, pitch-perfect English translation. The book consists, in the main, of four broadly biographical essays. The chemist Franz Haber finds an industrial means of fixing nitrogen, enabling the revolution in food supply that sustains our world, while also pioneering modern chemical warfare. Karl Schwarzchild, imagines the terrible uber-darkness at the heart of a black hole, dies in a toxic first world war and ushers in a thermonuclear second. Alexander Grothendieck is the first of a line of post-war mathematician-paranoiacs convinced they’ve uncovered a universal principle too terrible to discuss in public (and after Oppenheimer, really, who can blame them?) In the longest essay-cum-story, Erwin Schrodinger and Werner Heisenberg slug it out for dominance in a field — quantum physics — increasingly consumed by uncertainty and (as Labatut would have it) dread.

The problem here — if problem it is — is that no connection, in this book of artfully arranged connections, is more than a keypress away from the internet-savvy reader. Wikipedia, twenty years old next year, really has changed our approach to knowledge. There’s nothing aristocratic about erudition now. It is neither a sign of privilege, nor (and this is more disconcerting) is it necessarily a sign of industry. Erudition has become a register, like irony. like sarcasm. like melancholy. It’s become, not the fruit of reading, but a way of perceiving the world.

Literary attempts to harness this great power are sometimes laughable. But this has always been the case for literary innovation. Look at the gothic novel. Fifty odd years before the peerless masterpiece that is Mary Shelley’s Frankenstein we got Horace Walpole’s The Castle of Otranto, which is jolly silly.

Now, a couple of hundred years after Frankenstein was published, “When We Cease to Understand the World” dutifully repeats the rumours (almost certainly put about by the local tourist industry) that the alchemist Johann Conrad Dippel, born outside Darmstadt in the original Burg Frankenstein in 1673, wielded an uncanny literary influence over our Mary. This is one of several dozen anecdotes which Labatut marshals to drive home that message that There Are Things In This World That We Are Not Supposed to Know. It’s artfully done, and chilling in its conviction. Modish, too, in the way it interlaces fact and fiction.

It’s also laughable, and for a couple of reasons. First, it seems a bit cheap of Labatut to treat all science and mathematics as one thing. If you want to build a book around the idea of humanity’s hubris, you can’t just point your finger at “boffins”.

The other problem is Labatut’s mixing of fact and fiction. He’s not out to cozen us. But here and there this reviewer was disconcerted enough to check his facts — and where else but on Wikipedia? I’m not saying Labatut used Wikipedia. (His bibliography lists a handful of third-tier sources including, I was amused to see, W G Sebald.) Nor am I saying that using Wikipedia is a bad thing.

I think, though, that we’re going to have to abandon our reflexive admiration for erudition. It’s always been desperately easy to fake. (John Fowles.) And today, thanks in large part to Wikipedia, it’s not beyond the wit of most of us to actually *acquire*.

All right, Benjamin, you’re erudite. We get it. What else you got?

# An intellectual variant of whack-a-mole

Reading Joseph Mazur’s The Clock Mirage for The Spectator, 27 June 2020

Some books elucidate their subject, mapping and sharpening its boundaries. The Clock Mirage, by the mathematician Joseph Mazur, is not one of them. Mazur is out to muddy time’s waters, dismantling the easy opposition between clock time and mental time, between physics and philosophy, between science and feeling.

That split made little sense even in 1922, when the philosopher Henri Bergson and the young physicist Albert Einstein (much against his better judgment) went head-to-head at the Société française de philosophie in Paris to discuss the meaning of relativity. (Or that was the idea. Actually they talked at complete cross-purposes.)

Einstein won. At the time, there was more novel insight to be got from physics than from psychological introspection. But time passes, knowledge accrues and fashions change. The inference (not Einstein’s, though people associate it with him) that time is a fourth dimension, commensurable with the three dimensions of space, is looking decidedly frayed. Meanwhile Bergson’s psychology of time has been pruned by neurologists and put out new shoots.

Our lives and perceptions are governed, to some extent, by circadian rhythms, but there is no internal clock by which we measure time in the abstract. Instead we construct events, and organise their relations, in space. Drivers, thinking they can make up time with speed, acquire tickets faster than they save seconds. Such errors are mathematically obvious, but spring from the irresistible association we make (poor vulnerable animals that we are) between speed and survival.

The more we understand about non-human minds, the more eccentric and sui generis our own time sense seems to be. Mazur ignores the welter of recent work on other animals’ sense of time — indeed, he winds the clock back several decades in his careless talk of animal ‘instincts’ (no one in animal behaviour uses the ‘I’ word any more). For this, though, I think he can be forgiven. He has put enough on his plate.

Mazur begins by rehearsing how the Earth turns, how clocks were developed, and how the idea of universal clock time came hot on the heels of the railway (mistimed passenger trains kept running into each other). His mind is engaged well enough throughout this long introduction, but around page 47 his heart beats noticeably faster. Mazur’s first love is theory, and he handles it well, using Zeno’s paradoxes to unpack the close relationship between psychology and mathematics.

In Zeno’s famous foot race, by the time fleet-footed Achilles catches up to the place where the plodding tortoise was, the tortoise has moved a little bit ahead. That keeps happening ad infinitum, or at least until Newton (or Leibniz, depending on who you think got to it first) pulls calculus out of his hat. Calculus is an algebraic way of handling (well, fudging) the continuity of the number line. It handles vectors and curves and smooth changes — the sorts of phenomena you can measure only if you’re prepared to stop counting.

But what if reality is granular after all, and time is quantised, arriving in discrete packets like the frames of a celluloid film stuttering through the gate of a projector? In this model of time, calculus is redundant and continuity is merely an illusion. Does it solve Zeno’s paradox? Perhaps it makes it 100 times more intractable. Just as motion needs time, time needs motion, and ‘we might wonder what happens to the existence of the world between those falling bits of time sand’.

This is all beautifully done, and Mazur, having hit his stride, maintains form throughout the rest of the book, though I suspect he has bitten off more than any reader could reasonably want to swallow. Rather than containing and spotlighting his subject, Mazur’s questions about time turn out (time and again, I’m tempted to say) to be about something completely different, as though we were playing an intellectual variant of whack-a-mole.

But this, I suppose, is the point. Mazur quotes Henri Poincaré:

Not only have we not direct intuition of the equality of two periods, but we have not even direct intuition of the simultaneity of two events occurring in two different places.

Our perception of time is so fractured, so much an ad hoc amalgam of the chatter of numerous, separately evolved systems (for the perception of motion; for the perception of daylight; for the perception of risk, and on and on — it’s a very long list), it may in the end be easier to abandon talk of time altogether, and for the same reason that psychologists, talking shop among themselves, eschew vague terms suchas ‘love’.

So much of what we mean by time, as we perceive it day to day, is really rhythm. So much of what physicists mean by time is really space. Time exists, as love exists, as a myth: real because contingent, real because constructed, a catch-all term for phenomena bigger, more numerous and far stranger than we can yet comprehend.

# “The English expedition of 1919 is to blame for this whole misery”

Four books to celebrate the centenary of  Eddington’s 1919 eclipse observations. For The Spectator, 11 May 2019.

Einstein’s War: How relativity triumphed amid the vicious nationalism of World War I
Matthew Stanley
Dutton

Gravity’s Century: From Einstein’s eclipse to images of black holes
Ron Cowen
Harvard University Press

Daniel Kennefick
Princeton University Press

Einstein’s Wife: The real story of Mileva Einstein-Maric
Allen Esterson and David C Cassidy; contribution by Ruth Lewin Sime.
MIT Press

On 6 November 1919, at a joint meeting of the Royal Astronomical Society and the Royal Society, held at London’s Burlington House, the stars went all askew in the heavens.
That, anyway, was the rhetorical flourish with which the New York Times hailed the announcement of the results of a pair of astronomical expeditions conducted in 1919, after the Armistice but before the official end of the Great War. One expedition, led by Arthur Stanley Eddington, assistant to the Astronomer Royal, had repaired to the plantation island of Principe off the coast of West Africa; the other, led by Andrew Crommelin, who worked at the Royal Greenwich Observatory, headed to a racecourse in Brazil. Together, in the few minutes afforded by the 29 May solar eclipse, the teams used telescopes to photograph shifts in the apparent location of stars as the edge of the sun approached them.

The possibility that a heavy body like the sun might cause some distortion in the appearance of the star field was not particularly outlandish. Newton, who had assigned “corpuscles” of light some tiny mass, supposed that such a massive body might draw light in like a lens, though he imagined the effect was too slight to be observable.

The degree of distortion the Eddington expeditions hoped to observe was something else again. 1.75 arc-seconds is roughly the angle subtended by a coin, a couple of miles away: a fine observation, but not impossible at the time. Only the theory of the German-born physicist Albert Einstein — respected well enough at home but little known to the Anglophone world — would explain such a (relatively) large distortion, and Eddington’s confirmation of his hypothesis brought the “famous German physician” (as the New York Times would have it) instant celebrity.

“The English expedition of 1919 is ultimately to blame for this whole misery, by which the general masses seized possession of me,” Einstein once remarked; but he was not so very sorry for the attention. Forget the usual image of Einstein the loveable old eccentric. Picture instead a forty-year-old who, when he steps into a room, literally causes women to faint. People wanted his opinions even about stupid things. And for years, if anyone said anything wise, within a few months their words were being attributed to Einstein.

“Why is it that no one understands me and everyone likes me?” Einstein wondered. His appeal lay in his supposed incomprehensibility. Charlie Chaplin understood: “They cheer me because they all understand me,” he remarked, accompanying the theoretical physicist to a film premiere, “and they cheer you because no one understands you.”

Several books serve to mark the centenary of the 1919 eclipse observations. Though their aims diverge, they all to some degree capture the likeness of Einstein the man, messy personal life and all, while rendering his physics a little bit more comprehensible to the rest of us. Each successfully negotiates the single besetting difficulty facing books of this sort, namely the way science lends itself to bad history.

Science uses its past as an object lesson, clearing all the human messiness away to leave the ideas standing. History, on the other hand factors in as much human messiness as possible to show how the business of science is as contingent and dramatic as any other human activity.

While dealing with human matters, some ambiguity over causes and effects is welcome. There are two sides to every story, and so on and so forth: any less nuanced approach seems suspiciously moralistic. One need only look at the way various commentators have interpreted Einstein’s relationship with his first wife.

Einstein was, by the end of their failing marriage, notoriously horrible to Mileva Einstein-Maric; this in spite of their great personal and intellectual closeness as first-year physics students at the Federal Swiss Polytechnic. Einstein once reassured Elsa Lowenthal, his cousin and second-wife-to-be, that “I treat my wife as an employee I can not fire.” (Why Elsa, reading that, didn’t run a mile, is not recorded.)

Albert was a bad husband. His wife was a mathematician. Therefore Albert stole his theory of special relativity from Mileva. This shibboleth, bandied about since the 1970s, is a sort of of evil twin of whig history, distorted by teleology, anachronism and present-mindedness. It does no one any favours. The three separately authored parts of Einstein’s Wife: The real story of Mileva Einstein-Maric unpick the myth of Mileva’s influence over Albert, while increasing, rather than diminishing, our interest in and admiration of the woman herself. It’s a hard job to do well, without preciousness or special pleading, especially in today’s resentment-ridden and over-sensitive political climate, and the book is an impressive, compassionate accomplishment.
Matthew Stanley’s Einstein’s War, on the other hand, tips ever so slightly in the other direction, towards the simplistic and the didactic. His intentions, however, are benign — he is here to praise Einstein and Eddington and their fellows, not bury them — and his slightly on-the-nose style is ultimately mandated by the sheer scale of what he is trying to do, for he succeeds in wrapping the global, national and scientific politics of an era up in a compelling story of one man’s wild theory, lucidly sketched, and its experimental confirmation in the unlikeliest and most exotic circumstances.

The world science studies is truly a blooming, buzzing confusion. It is not in the least bit causal, in the ordinary human sense. Far from there being a paucity of good stories in science, there are a limitless number of perfectly valid, perfectly accurate, perfectly true stories, all describing the same phenomenon from different points of view.

Understanding the stories abroad in the physical sciences at the fin de siecle, seeing which ones Einstein adopted, why he adopted them, and why, in some cases, he swapped them for others, certainly doesn’t make his theorising easy. But it does give us a gut sense of why he was so baffled by the public’s response to his work. The moment we are able to put him in the context of co-workers, peers and friends, we see that Einstein was perfecting classical physics, not overthrowing it, and that his supposedly peculiar theory of relativity — as the man said himself –“harmonizes with every possible outlook of philosophy and does not interfere with being an idealist or materialist, pragmatist or whatever else one likes.”

In science, we need simplification. We welcome a didactic account. Choices must be made, and held to. Gravity’s Century by the science writer Ron Cowen is the most condensed of the books mentioned here; it frequently runs right up to the limit of how far complex ideas can be compressed without slipping into unavoidable falsehood. I reckon I spotted a couple of questionable interpretations. But these were so minor as to be hardly more than matters of taste, when set against Cowen’s overall achievement. This is as good a short introduction to Einstein’s thought as one could wish for. It even contrives to discuss confirmatory experiments and observations whose final results were only announced as I was writing this piece.

No Shadow of a Doubt is more ponderous, but for good reason: the author Daniel Kennefick, an astrophysicist and historian of science, is out to defend the astronomer Eddington against criticisms more serious, more detailed, and framed more conscientiously, than any thrown at that cad Einstein.

Eddington was an English pacifist and internationalist who made no bones about wanting his eclipse observations to champion the theories of a German-born physicist, even as jingoism reached its crescendo on both sides of the Great War. Given the sheer bloody difficulty of the observations themselves, and considering the political inflection given them by the man orchestrating the work, are Eddington’s results to be trusted?

Kennefick is adamant that they are, modern naysayers to the contrary, and in conclusion to his always insightful biography, he says something interesting about the way historians, and especially historians of science, tend to underestimate the past. “Scientists regard continuous improvement in measurement as a hallmark of science that is unremarkable except where it is absent,” he observes. “If it is absent, it tells us nothing except that someone involved has behaved in a way that is unscientific or incompetent, or both.” But, Kennefick observes, such improvement is only possible with practice — and eclipses come round too infrequently for practice to make much difference. Contemporary attempts to recreate Eddington’s observations face the exact same challenges Eddington did, and “it seems, as one might expect, that the teams who took and handled the data knew best after all.”

It was Einstein’s peculiar fate that his reputation for intellectual and personal weirdness has concealed the architectural elegance of his work. Higher-order explanations of general relativity have become clichés of science fiction. The way massive bodies bend spacetime like a rubber sheet is an image that saturates elementary science classes, to the point of tedium.

Einstein hated those rubber-sheet metaphors for a different reason. “Since the mathematicians pounced on the relativity theory,” he complained, “I no longer understand it myself.” We play about with thoughts of bouncy sheets. Einstein had to understand their behaviours mathematically in four dimensions (three of space and one of time), crunching equations so radically non-linear, their results would change the value of the numbers originally put into them in feedback loops that drove the man out of his mind. “Never in my life have I tormented myself anything like this,” he moaned.

For the rest of us, however, A little, prophylactic exposure to Einstein’s actual work pays huge dividends. It sweeps some of the weirdness away and reveals Einstein’s actual achievement: theories that set all the forces above the atomic scale dancing with an elegance Isaac Newton, founding father of classical physics, would have half-recognised, and wholly admired.

# Implausible science and ambiguous art

Visiting Broken Symmetries at FACT, Liverpool for the Financial Times, 30 November 2018

In The Science of Discworld 4: Judgement Day, mathematician Ian Stewart and reproductive biologist Jack Cohen have fun at the expense of the particle-physics community.

Imagine a group of blind sages in a hotel, poking at a foyer piano. After some hours, they arrive at an elegant theory about what a piano is — one that involves sound, frequency, harmony, and the material properties of piano strings.

Then one of their number suggests that they carry the piano upstairs and drop it from the roof. This they do — and spend the rest of the day dreaming up and knocking over countless ugly hypotheses involving hypothetical “twangons” and “thudons” and, oh, I don’t know, “crash bosons”.

The point — that the physicists working at CERN’s Large Hadron Collider in Geneva might be constructing the very quantum reality they were hired to study — is lost on none of the 10,000-odd scientists and engineers involved with the project. And this awareness — that the very idea of science is up for grabs here — may explain why CERN’s scientists have taken so warmly to the artists dropped in their midst.

They come on brief visits from the 22 countries that contribute to CERN’s budget. The more established of them — people like Trevor Paglen and Tomás Saraceno — stay for weeks at a time, pursuing some special project. There are joint residencies next year that will see artists shuttling between CERN and astronomical observatories in Chile. Most productive of all are the lucky few chosen for CERN’s Collide International residency programme.

Winning the Collide International gets you two fully funded months in CERN’s labs and labyrinths, rubbing shoulders with arguably the best (and certainly the strangest) minds in physics.

For the exhibition Broken Symmetries at FACT in Liverpool, Arts at CERN director Monica Bello and Peruvian scientist and curator Jose Carlos Mariategui have commissioned new work by CERN’s recent residents, runners-up and honorable mentions. It’s a celebration of CERN’s three-year curatorial collaboration with FACT, the Foundation for Art and Creative Design. Next April the show moves to CCCB , the Centre for Contemporary Culture in Barcelona, where it will effectively advertise CERN’s next three-year partnership, with Barcelona’s city council.

From there, Broken Symmetries travels to Le Lieu Unique in Nantes, France and iMAL, the centre for digital cultures and technology in Sint-Jans-Molenbeek, Belgium, where it finally shuts up shop in the summer of 2020. All this travelling has a point. Since the end of the nineteenth century, physics has been — out of intellectual and financial necessity — an international institution.

So there is a nice double-meaning to the title of the video made for this show by Ruth Jarman and Joe Gerhardt, who work under the name Semiconductor. The View from Nowhere refers to the scientific ideal of objective observation. But by echoing PM Theresa May’s notorious “citizens of nowhere” jibe, it just as effectively trumpets the rootless cosmopolitanism of the scientific community.

The video itself is almost pure anthropology, as the pair explore why it is that people working on the same project explain what they’re doing in so many different ways. Language is full of traps. The hidden world of particles can only be conceptualised by analogies and metaphors, which themselves are limited or misleading. The visual stylings of artists are just as unreliable, of course, but at least they supplement the vocabulary available to researchers. This is one of the possibilities that excites the architect of the residency programme, Monica Bello: “Since I began, it has been very important to me to bring artworks and experiences to the scientific community. This,” she points out, “is an audience in itself.”

Some art here addresses its patrons directly, in the eighteenth-century manner. Through narrative, memoir and archive, Taiwan-born Londoner Yu-Chen Wang explores the human scale of the CERN project. Her video installation We aren’t able to prove that just yet, but we know it’s out there seeks to acknowledge CERN’s unsung multitudes: its technicians, analysts and engineers.

South Korean artist Yunchul Kim reveals the aesthetic elements of his patrons’ work. His sketchbooks, recently on show at the Korean Cultural Centre in London, stripped the components of the Large Hadron Collider (almost all hand-turned — there’s nothing mass-produced about the LHC) down to their design elements. Here, with a three-part sculpture called Cascade, Kim fashions a mechanism that, in homage to the LHC, makes sub-atomic activities visible. Each time a cosmic particle hits his handmade detector, a signal is sent to a gigantic chandelier-like structure. This, in response, pumps a clear, viscous liquid through countless narrow capillary tubes which trail across the floor of the gallery and up into swooping tubes of clear Perspex. Because the refractive index of the capillaries matches the refractive index of the Perspex, the capillaries vanish inside the tubes, leaving beads of liquid apparently suspended in mid-air, rather as one might imagine particles suspended in the magnetic ring of CERN’s collider.

Visitors to CERN run the risk of being inundated by information, and some artists here have saved themselves from drowning by clutching at esoteric straws. Works like Lea Porsager’s Cosmic Strike (a concoction of 3D-animated strings and a neutrino horn from the LHC stores) and Haroon Mirza and Jack Jelfs’s one1one — a bopping 100bpm disco floor drawing on incantation, ritual, and the relationship between written and spoken word — are not the betrayals of hard science they might at first seem. Physics at this extreme tips into metaphysics very easily, witness the ongoing arguments over whether elegant but untestable string theories count as science at all.

Diann Bauer’s Scalar Oscillation, a collaboration with the sound artist Seth Ayyaz, tackles the science head-on. How are we to encapsulate, in painting or poetry or any human medium, the scalar richness of the world, which is so much bigger than we are and so much more intricate than we can possibly perceive? A single sound shrinks to a click, then expands to reveal the oceanic reverberations hidden at its heart. Clean-edged, constructivist visuals try, and fail, to reduce the world to a single sign. Suzanne Treister takes an even more literal approach with The Holographic Universe Theory of Art History, which treats images like particles in an accelerator, projecting over 25,000 pictures from art history (from cave paintings to contemporary art) at 25 frames per second in a looped sequence.

James Bridle’s State of Sin simply offers the scientists of CERN something they can use: random numbers. A family of goofy tripods gathers numbers from the gallery environment: the temperature of the air, the airflow generated by a desk fan, from sounds in the gallery and from fluctuations in the light spilling from a neon tube. Bridle’s point being, CERN’s complex computations require a constant supply of random numbers, and such true randomness cannot be computed, but must be fetched from the messiness of the world.

How many visitors will “get” Bridle’s work? How many, resting their chins on the frame of Juan Cortes’s ingenious clockwork galaxy Supralunar, will realise that the sounds shivering through their jawbones are drawn in real time from the movements of optic fibres inside the clockwork, and that they echo with surprising accuracy the patterns in astronomical data from which scientists have inferred the existence of dark matter? The answer to such boorish questions has traditionally been, “You get out of art what you bring to it, so it doesn’t matter.”

But with this sort of art, I think it does matter. Art that derives from other cultural production must always contend with a creeping sense of its own bankruptcy. Pop art succeeded in making art out of pre-existing media because it flaunted that bankruptcy, chose mass media, and was prepared to laugh at itself.

The art of Broken Symmetries, on the other hand, feeds off highly abstruse media — off bubble-chamber drawings and statistical analyses, all of them generated in pursuit of one fixed and timeless standard cosmological model. This art can’t but struggle to find a purchase in a world full of (indeed, glutted with) other, more familiar, more lively aesthetic vocabularies.

My uneasy feeling is that the artists have done rather too good a job of pointing up the existential implausibility of the whole enterprise. I was reminded of John Gardner’s short, savage novel Grendel, which tells the Beowulf legend from the monster’s point of view.

“They only think they think,” grumbles Grendel, who has the measure of both our intellect and our vanity. “No total vision, total system, merely schemes with a vague family resemblance, no more identity than bridges and, say, spider-webs. But they rush across chasms on spider-webs, and sometimes they make it, and that, they think, settles that!”

# The physics of dance

Visiting a rehearsal of 8 Minutes, Alexander Whitley’s Sadler’s Wells main-stage debut, for New Scientist, 17 June 2017

IN A basement studio in south London, seven dancers are interpreting some recent solar research from the Rutherford Appleton Laboratory in Oxfordshire. They are tackling the electromagnetic properties of the sun’s surface, and have got themselves, literally, into a knot. “Something about your grip here is stopping her moving,” frets choreographer Alexander Whitley. “Can we get his hips to go the other way?”

Bit by bit, a roiling form emerges. Imagine a chain, folded in on itself, stretching and reforming. Its movements are coherent and precise, but wildly asymmetrical. This is no tidy, courtly dance. At one point the chain abruptly unwinds. The relief is palpable as the dancers exploit their few seconds of freedom. Very quickly, the chain kinks and folds in on itself again: a folding problem intensely claustrophobic to watch, never mind perform.

Whitley formed his dance company in 2014, and 8 Minutes will be its debut on London’s Sadler’s Wells main stage at the end of June. It is named after the time it takes for light from the sun to reach Earth. “If you imagine travelling this distance at the speed of light, and you subtract all the relativistic effects, it’s quite bizarre,” muses Hugh Mortimer, Whitley’s collaborator and a researcher at Rutherford.

Mortimer designed climate change-detecting spectrometers for the Sentinel-3 satellite, and a sea-surface temperature monitor currently operating from the Queen Mary 2 liner. He hopes to build space-based instruments that analyse the atmospheres of exoplanets. But quite another fascination drew him into collaboration with Whitley’s dance company: the way the most abstruse science can be explained through ordinary experience.

He continues his thought experiment: “For 6 minutes, you’d be sitting in darkness. By the 7th minute you would notice a point of light looming larger: that’s the Earth. You’d arrive at the moon, pass by Earth, and a few seconds later you’d pass the orbit of the moon again. And the point is, passing the moon and the Earth and the moon again a few seconds later would feel intuitively right. It would feel ordinary.”

However difficult an idea, someone, somewhere must be able to grasp it, or it’s not an “idea” in any real sense. How, then, are we to grasp concepts as alien to our day-to-day experience as electromagnetism and the speed of light? It’s a question that has cropped up before in these pages, although seldom through the medium of dance. In 1988, for example, computer scientist Tony Hey wrote about his lunch with US physicist Richard Feynman, who explained particle spin “using the belt from his trousers” (New Scientist, 30 June 1988, p 75).

As for Whitley, he says: “We grasp quite advanced concepts first and foremost through movement. That forms a semantic template for the complex thinking we develop when we acquire language. Right, left, up, down, front, back – also the idea of containment, the concept of an inside and an outside – these ideas come through our bodies.”

This is especially true in children, he argues, because they don’t yet have fully developed rational capabilities. “I think there’s strong potential for using movement to give them a different understanding of and engagement with scientific ideas,” Whitley says.

Mortimer discovered the truth of this idea for himself quite recently: “Alexander runs a creative learning project for 9 and 10-year-olds based on our collaboration. Sitting in on some sessions, I found myself thinking about solar-dynamic processes in a new and clearer way.”

Will the audience at the work’s premiere leave understanding more about the sun? From what I saw, I’m optimistic. They won’t have words, or figures, for what they’ll have seen, but they will have been afforded a glimpse into the sheer dynamism and complexity of our nearest star.