Philae comes in to land on 67P/Churyumov-Gerasimenko. It reached the comet using carefully calculated forces of attraction. Image: 2014 European Space Agency/Getty
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Wandering in the heavens: how mathematics explains Saturn’s rings

Ian Stewart shows how maths is changing cosmology, and explains why the best way to reach a comet near Mars is to go round the back of the sun.

The Enūma Anu Enlil, a series of 70 clay tablets, was found in the ruins of King Ashurbanipal’s library in Nineveh (on the eastern bank of the River Tigris, opposite modern-day Mosul in Iraq). The name means “in the days of Anu and Enlil”; Anu was the sky god, Enlil the wind god. The tablets, which date as far back as 1950BC, list 7,000 omens from Babylonian astrology: “If the moon can be seen on the first day, the land will be happy.” But tablet 63 is different: it gives the times when Venus first became visible, or disappeared, over a 21-year period. This Venus tablet of Ammisaduqa is the earliest known record of planetary observations.

The Babylonians were expert astronomers who produced star catalogues and tables of eclipses, planetary motion and changes in the length of day. They were also capable mathematicians, with a number system much like ours, but using base 60 rather than ten. They could solve quadratic equations and calculate the diagonal of a square with precision, and they applied their mathematical skills to the heavens. In those days, mathematics and astronomy were part and parcel of astrology and religion, and the whole package was intimately bound up with agriculture through the progression of the seasons.

The torch of astronomy passed by way of ancient Greece to India. In 6th-century India, mathematics was a sub-branch of astronomy, and astronomy still played second fiddle to reading omens in the stars. The Arab world made further advances in our understanding of the cosmos, and kept the ancient knowledge alive until Europe once more turned its attentions to the science of the heavens.

In 1601 Johannes Kepler became imperial mathematician to the Holy Roman emperor Rudolf II. Casting the emperor’s horoscope paid the bills, and it also left time for serious mathematics and astronomy. Kepler had inherited accurate observations of Mars from his former master Tycho Brahe, and from these he extracted three mathematical patterns, his laws of planetary motion. By then, thanks to Nicolaus Copernicus, it was known – though still controversial, to say the least – that the planets revolve round the sun, not the Earth. Their orbits were thought to be combinations of circles, but Kepler’s calculations showed that planets move in ellipses. His other two laws govern how quickly the planet moves and how long it takes to go round the sun.

In his epic Mathematical Principles of Natural Philosophy of 1687, Isaac Newton built on Kepler’s laws and deduced his law of universal gravitation: every body in the universe attracts every other body with a force that obeys a specific mathematical rule. These forces determine how moons, planets and stars move. Newton’s book paved the way to a rational scientific understanding of nature based on precise mathematical laws, and opened up the metaphor of the clockwork universe.

One of the great tests of Newtonian gravitation was Edmond Halley’s prediction about a comet. In ancient times comets, bright bodies with long curved tails that seemed to appear from nowhere, were seen as omens of disaster. From old records, Halley realised one particular comet was a repeat visitor, with an elliptical orbit that took it near the Earth every 76 years. He predicted its next return in 1758. By then Halley was dead, but his prediction proved correct.

Even today, Newton’s law remains vital to astronomy and space exploration; Einstein’s later refinements are seldom needed. A topical example concerns another comet, rejoicing in the name 67P/Churyumov-Gerasimenko, which takes about six and a half years to orbit the sun. In 2004 the European Space Agency (ESA) launched the Rosetta probe to visit the comet and find out what it looked like and what it was made of. Famously, it resembled a rubber duck: two round lumps joined by a narrow neck. On 12 November 2014 a small capsule, Philae, landed on the head of the duck, which was 480 million kilometres from Earth and travelling at over 50,000 kilometres per hour. Unfortunately Philae bounced and ended up on its side, but even so it had sent back vital and unprecedented data.

It’s worth visiting the ESA’s “Where is Rosetta?” web page to see an animation of the astonishing route the probe took. It wasn’t direct. The probe began by moving towards the sun, even though the comet was far outside the orbit of Mars, and moving away. Rosetta’s orbit swung past the sun, returned close to the Earth, and was flung outwards to an encounter with Mars. It then swung back to meet the Earth for a second time, then back beyond Mars’s orbit. By now the comet was on the far side of the sun and closer to it than Rosetta was. A third encounter with Earth flung the probe outwards again, chasing the comet as it now sped away from the sun. Finally, Rosetta made its rendezvous with destiny.

Why such a complicated route? The ESA didn’t just point its rocket at the comet and blast off. That would have required far too much fuel, and by the time it got there the comet would have been somewhere else. Instead, Rosetta performed a carefully choreographed cosmic dance, tugged by the combined gravitational forces of the sun, the Earth, Mars and other relevant bodies. Its route was designed for fuel efficiency; the price paid was that it took Rosetta ten years to get to its destination. Each close fly-by with Earth and Mars gave the probe a free boost as it borrowed energy from the planet. An occasional small burst from four thrusters kept the craft on track. And every kilometre of the trip was governed by Newton’s law of gravity.

Complex trajectories such as this one have now become standard in many unmanned space missions. They originated in mathematical studies of chaotic dynamics in the motion of three gravitating bodies, and go back to pioneering work by Edward Belbruno at the Jet Propulsion Laboratory in California in 1990. He realised that these techniques could put a Japanese probe, Hiten, into lunar orbit after a failure of its parent craft, even though there was hardly any fuel available.

Mathematics has always enjoyed a close relationship with astronomy; not just in the technology of space missions but in understanding planets, stars, galaxies – even the entire universe. How, for example, did the solar system form? We can’t go back to take a look, so we have to do some celestial archaeology, inferring what happened from the evidence that remains. Our main tool is mathematical modelling, which lets us test whether hypothetical scenarios make sense.

When Galileo first spied Saturn in 1610, he took it to be a trinity of planets. Image: Nasa/Eyevine

Observations and theoretical astrophysics tell us that the sun came into being about 4.8 billion years ago, and the planets of the solar system formed at much the same time. Everything condensed out of the solar nebula, a huge cloud of gas – mainly hydrogen and helium, the two commonest elements in the universe. The cloud was about 65 light years across, 15 times the distance to the nearest star today. One fragment, about four light years across, gave rise to the solar system; other fragments became other stars – many of which, we now know, have their own planets. As our fragment collapsed under its own gravitational field, most of the gas collected at the centre, where enormous pressures ignited nuclear reactions to create the sun. Much of the remaining gas clumped into smaller, but still gigantic, bodies: the planets. The rest either got swept away or remains as various items of clutter – asteroids; centaurs (small bodies with characteristics of both comets and asteroids); Kuiper Belt objects, in the debris field beyond Neptune; comets in the Oort Cloud, which is a quarter of the way to the next-nearest star.

This scenario, minus the nuclear physics, was first proposed in the 18th century, but fell out of favour in the 20th because it seemed not to account for the sun’s low angular momentum (a measure of how much rotation it has, taking into account its mass and speed) compared to that of the planets. But in the 1980s astronomers observed gas clouds round young stars, and mathematical modelling of the collapsing clouds showed plausible, and very dramatic, mechanisms that fitted the observations.

According to these ideas, the early solar system was very different from the sedate one we see today. The planets formed not as single clumps, but by a chaotic process of accretion. For the first 100,000 years, slowly growing “planetesimals” swept up gas and dust, and created circular rings in the nebula by clearing out gaps between them. Each gap was littered with millions of these tiny bodies. At that point the planetesimals ran out of new matter to sweep up, but there were so many of them that they kept bumping into each other. Some broke up, but others merged; the mergers won and planets built up, piece by tiny piece.

Late in 2014 dramatic evidence for this process was found: an image of a proto-planetary disc around the young star HL Tau, 450 light years away in the Taurus
constellation. This image showed concentric bright rings of gas, with dark rings in between. The dark rings are almost cer­tainly caused by nascent planets sweeping up dust and gas.

Until very recently, astronomers thought that once the solar system came into being it was very stable: the planets trundled ponderously along preordained orbits and nothing much changed. No longer: it is now thought that the larger worlds – the gas giants Jupiter and Saturn and the ice giants Uranus and Neptune – first appeared outside the “frost line” where water freezes, but subsequently reorganised each other in a lengthy gravitational tug of war.

In the early solar system, the giants were closer together and millions of planetesimals roamed the outer regions. Today the order of the giants, outwards from the sun, is Jupiter, Saturn, Uranus, Neptune. But in one likely scenario it was originally Jupiter, Neptune, Uranus, Saturn. When the solar system was about 600 million years old, this cosy arrangement came to an end. All of the planets’ orbital periods were slowly changing, and Jupiter and Saturn wandered into a 2:1 resonance – Saturn’s “year” became twice that of Jupiter. Repeated alignments of these two worlds then pushed Neptune and Uranus outwards, with Neptune overtaking Uranus. This disturbed the planetesimals, making them fall towards the sun. Chaos erupted in the solar system as planetesimals played celestial pinball among the planets. The giant planets moved out, and the planetesimals moved in. Eventually the planetesimals took on Jupiter, whose huge mass was decisive. Some were flung out of the solar system altogether, while the rest went into long, thin orbits stretching out to vast distances. After that, it mostly settled down.

These theories are not idle speculation. They are supported by huge computer calculations of the solar system’s dynamics over billions of years, carried out in particular by the research groups of Jack Wisdom of the Massachusetts Institute of Technology and Jacques Laskar of CNRS, the French national centre for scientific research. Some cunning mathematics is required even to set up these simulations: the deep structure of the laws of motion must not be disturbed by the unavoidable numerical approximations that occur. This structure includes the laws of conservation of energy and angular momentum, whose totals cannot change. Amazingly, the planetary migrations not only keep these quantities in balance, but happen because they balance.

Another playground for mathematicians and astronomers investigating Newtonian gravitation is the rings of Saturn. The most distant of the planets known to the ancients, Saturn is about 1.3 billion kilometres from Earth. In 1610, when Galileo looked at Saturn through his telescope, he sent his fellows a Latin anagram: smaismrmilmepoetaleumibunenugttauiras. This was a standard way to preannounce a discovery without giving it away. Kepler deciphered it as reading – in translation – “Be greeted, double knob, offspring of Mars,” and thought Galileo was claiming Mars had two moons (as Kepler had predicted, and rightly so). But Galileo later explained that his anagram actually meant: “I have observed the most distant of planets to have a triple form.” That is, Saturn consists of three bodies.

So much for anagrams.

Galileo’s image of the planet was blurred. Using a better telescope, the Dutch mathematician Christiaan Huygens realised that the middle body was the planet and the others were parts of a gigantic system of rings. Mathematics proves – contrary to an early suggestion by the French scholar Pierre-Simon Laplace – that the rings cannot be solid. In fact, they are made up of ice particles, ranging in size from fine dust to lumps ten metres across. There are several current theories for the rings’ formation: the break-up of a moon, or perhaps leftovers from Saturn’s own primordial nebula. Mathematics is being used to try to find out which explanation, if any, is correct.

Mathematical studies also explain many puzzling features of Saturn’s rings. For one thing, the rings are dense in some regions, but so thin in others that at first sight there seem to be gaps. Some of these gaps come from resonances between the rings and the periods of Saturn’s 62 moons, which can systematically disturb gas in orbits related to that of the moon itself. Other gaps are organised by “shepherd moons” that hustle out any sheepish moonlet that strays into the gap. When the spacecraft Voyager 1 flew past in 1980, some rings appeared to be braided. We now know that they are kinked and lumpy, another subtle consequence of Newtonian gravity in this complex system.

Mathematics has illuminated many other cosmic puzzles: the formation of Earth’s moon, the future of the solar system, the formation and dynamics of galaxies – even the origin of the universe itself in the Big Bang. In ancient India, mathematics was a sub-branch of astronomy. Today, if anything, it is the other way round. Mathematicians are making discoveries and inventing methods; astronomers and cosmologists are making ever greater use of the latest mathematical tools and concepts to advance this utterly fascinating subject. Mathematical thinking teaches us more about humanity’s place in the universe. And it helps us to seek out new places.

Ian Stewart is an emeritus professor of mathematics at the University of Warwick

This article first appeared in the 19 December 2014 issue of the New Statesman, Christmas Issue 2014

Credit: BRIDGEMAN IMAGES
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A century ago, the Spanish flu killed 100 million people. Is a new pandemic on the way?

Our leaders need to act like the outbreak has already started – because for all we know it may have.

It is hard not to have a sneaking envy of the virus. As complex creatures, we are distracted by myriad demands on our attention; we will never know the dead-eyed focus of the viral world. It is akin to the psychopath: a cold, purposeful drive to achieve its own agenda, coupled with the skills and resourcefulness to succeed. In a world threatened by nuclear war and devastating climate change, it may actually be the virus that we should fear most.

This is the centenary year of the Spanish flu outbreak, when a virus killed between 50 and 100 million people in a matter of months. The devastation was worldwide; it is only known as Spanish flu because Spain, neutral in the ongoing hostilities of World War One, was the only country without press restrictions. Across Europe, people assumed their own outbreaks originated in the only place reporting on the disaster.

A number of authors have lined up with a kind of grim celebration of influenza’s annus mirabilis. As well as chronicling the fatal reach of this organism, they all offer a warning about a follow-up pandemic that is overdue – and for which, it seems, we are largely unprepared. “Somewhere out there a dangerous virus is boiling up in the bloodstream of a bird, bat, monkey, or pig, preparing to jump to a human being,” says Jonathan Quick in The End of Epidemics. “It has the potential to wipe out millions of us, including my family and yours, over a matter of weeks or months.”

If that seems a little shlocky, you should know that Quick is no quack. He is a former director at the WHO, the current chair of the Global Health Council and a faculty member at Harvard Medical School. The book’s blurb includes endorsements from the director of the London School of Hygiene and Tropical Medicine, the president of Médicins Sans Frontières, and the president of the Rockefeller Foundation.

The numbers Quick serves up are stupefying. Bill Gates, for instance, has said it is more likely than not that he will live to see a viral outbreak kill over 10 million people in a year. In Gates’s nightmare scenario, outlined by computer simulations created with disease-modelling experts, 33 million people die within 200 days of the first human infection. The potential for exponential spread means a death toll of 300 million is possible in the first year. “We would be in a world where scrappy, ravaged survivors struggle for life in a zombie-movie wasteland,” Quick tells us in his informed, cogent and – honestly – frightening book.

If you can’t imagine what that is like, you could try asking the Yupik people of Alaska, who were devastated by the 1918 Spanish flu. You might not get an answer, however, because they remain traumatised, and have made a pact not to speak about the pandemic that shattered their ancient culture.  (A pandemic is a disease that spreads across continents; an epidemic is usually contained within a country or continent.)They aren’t the only long-term sufferers. The Vanuatu archipelago suffered 90 per cent mortality and 20 of its local languages went extinct. Those in the womb in 1918 were also affected. A baby born in 1919 “was less likely to graduate and earn a reasonable wage, and more likely to go to prison, claim disability benefit, and suffer from heart disease,” reports Laura Spinney in Pale Rider.

Such arresting snippets of the flu’s legacy abound in Spinney’s thoughtful, coherent take on the 1918 outbreak. The book’s subtitle suggests that the Spanish flu changed the world, and Spinney certainly backs this up. Societies broke down and had to be rebuilt; recovering populations were reinvigorated by the simple calculus of Darwin’s “survival of the fittest”; public health provisions were first imagined and then brought into reality; artists and writers responded to a new global mood by establishing new movements.

Not every outcome could be spun as a positive. Scientists, for instance, were humiliated by their inability to halt the flu’s progress, creating an opportunity for quack medicines to arise and establish themselves. Some of our greatest writers lived through the trauma, but could never bring themselves to discuss it in their stories. Virginia Woolf noted that it was “strange indeed that illness has not taken its place with love and battle and jealousy among the prime themes of literature”.

Spinney’s background as a science writer shines through: her handling of the workings of the flu is detailed and deft. She brings both the influenza A virus (the only type responsible for pandemics) and the human immune system to life, laying out the biochemical processes that kill and cure with clarity and care. She exposes the chilling roots of often-used but seldom-explained viral names such as “H1N1” (Spanish flu) or “H5N1” (bird flu). H is for haemagglutinin, the lollipop-shaped appendage that allows a virus to break into a cell and take over the means of production. N is for neuraminidase, the “glass-cutter” structure that allows replicated viruses to break out again and unleash hell upon the host. So far, we know of 18 H’s and 11 N’s and they all have ever-evolving sub-types that make a long-lasting general vaccine against the flu an elusive dream: “Every flu pandemic of the 20th century was triggered by the emergence of a new H in influenza A,” says Spinney.

For all her technical expertise, Spinney has a light touch and a keen eye for the comic. She relates how a ferret sneezing in the face of a British researcher in 1933 exposed influenza’s ability to travel between biological species, for instance. She also excels with the bigger picture, detailing the century of scientific detective work that has allowed us to piece together the genetic elements of the 1918 virus and gain insights into its creation. It seems to have jumped to humans on a farm in Kansas, via domestic and wild birds indigenous to North America. There may also have been some ingredients from pigs, too, but that’s not settled.

Spinney’s afterword questions whether our collective memory for such events ever reflects the truth of the moment. “When the story of the Spanish flu was told, it was told by those who got off most lightly: the white and well off,” she tells us. “With very few exceptions, the ones who bore the brunt of it, those living in ghettoes or at the rim, have yet to tell their tale. Some, such as the minorities whose languages died with them, never will.”

That said, Catharine Arnold has done a remarkable job of relating the tales of a diverse set of sufferers, crafting an arresting and intimate narrative of the 1918 pandemic. She pulls the accounts of hundreds of victims into a gripping tale that swoops down into the grisly detail, then soars up to give a broad view over the landscape of this calamitous moment in human history.

Arnold’s remembrances come from the unknown and from celebrities. A Margery Porter from south London emphasised that “we just couldn’t stand up. Your legs actually gave way, I can’t exaggerate that too much.” John Steinbeck described the experience of infection as almost spiritual. “I went down and down,” he said, “until the wingtips of angels brushed my eyes.”

The reality was, inevitably, less poetic. A local surgeon removed one of Steinbeck’s ribs so that he could gain access to the author’s infected lung. Most victims’ bodies turned blue-black as they died. Healthcare workers reported appalling scenes, with delirious patients suffering horrific nosebleeds. “Sometimes the blood would just shoot across the room,” a navy nurse recalled. If their lungs punctured, the patients’ bodies would fill with air. “You would feel somebody and he would be bubbles… When their lungs collapsed, air was trapped beneath their skin. As we rolled the dead in winding sheets, their bodies crackled – an awful crackling noise with sounded like Rice Krispies when you pour milk over them.”

The killer in 1918 was often not the flu virus itself but the “cytokine storm” of an immune system overreacting to the infection. Strong, fit young people, with their efficient immune systems, were thus particularly at risk, their bodies effectively shutting themselves down. Then there were the ravages of opportunistic bacteria that would lodge in the devastated tissue, causing pneumonia and other fatal complications. Arnold paints a grim but vivid picture of exhausted gravediggers and opportunistic funeral directors cannily upping their prices. The morgues were overflowing, and morticians worked day and night. In the end, mass graves were the only answer for the poverty-stricken workers attempting to bury their loved ones before they, too, succumbed.

No one was spared from grief or suffering at the hands of the “Spanish Lady”, as the flu came to be known. Louis Brownlow, the city commissioner for Washington DC, reported nursing his stricken wife while answering telephone calls from desperate citizens. One woman called to say that of the three girls she shared a room with, two had died, and the third was on her way out. Brownlow sent a police officer to the house. A few hours later, the sergeant reported back from the scene: “Four girls dead.”

Some of the other stories Arnold has unearthed are equally heartbreaking. A Brooklyn boy called Michael Wind wrote of the moment his mother died after less than a day of being ill. He and his five siblings were at her bedside, as was their father, “head in hands, sobbing bitterly”. The following morning, knowing that he was soon to die too, their father took the three youngest children to the orphanage.

Arnold writes beautifully, and starkly, of the tragedy that unfolded in the autumn months of 1918: “the Spanish Lady played out her death march, killing without compunction. She did not discriminate between statesmen, painters, soldiers, poets, writers or brides.” She chronicles the Lady’s path from the United States and Canada through Europe, Africa and Asia, culminating in New Zealand’s “Black November”. The book is utterly absorbing. But how do we respond to its horrors and tragedies? What are we to do with our collective memories of such visceral, world-shattering events? Learn from them – and fast, argues Jonathan Quick.

Unlike Arnold and Spinney, Quick is not content to be a chronicler or a bystander. He is, he says, both terrified at the looming disaster and furious at the lack of high-level reaction to its threat. He is determined to create a movement that will instigate change, mimicking the way activists forced change from governments paralysed by, and pharmaceutical companies profiteering from, the Aids pandemic. Quick has channelled his fury: The End of Epidemics is, at heart, a call to arms against influenza, Ebola, Zika and the many other threats before us.

 

So what are we to do? First, our leaders need to act like the outbreak has already started – because for all we know it may have. We must strengthen our public health systems, and create robust agencies and NGOs ready to monitor and deal with the threat. We must educate citizens and implement surveillance, prevention and response mechanisms, while fighting misinformation and scaremongering. Governments must step up (and fund) research.

We can’t develop a vaccine until the threat is manifest, but we can prepare technology for fast large-scale production. We can also invest in methods of early diagnoses and virus identification. Invest $1 per person per year for 20 years and the threat will be largely neutralised, Quick suggests. Finally – and most importantly – there is an urgent need to create grass-roots support for these measures: citizen groups and other organisations that will hold their leaders to account and prevent death on a scale that no one alive has ever experienced. Is this achievable? Traumatised readers of Quick’s book will be left hoping that it is.

For all the advances of the last century, there are many unknowns. Scientists don’t know, for instance, which microbe will bring the next pandemic, where it will come from, or whether it will be transmitted through the air, by touch, through body fluids or through a combination of routes.

While there is considerable attention focused on communities in West Africa, East Asia or South America as the most likely source of the next outbreak, it’s worth remembering that most scientists now believe the 1918 influenza outbreak began on a farm in Kansas. Quick suggests the
next pandemic might have a similar geographical origin, thanks to the industrialised livestock facilities beloved by American food giants.

Viruses naturally mutate and evolve rapidly, taking up stray bits of genetic material wherever they can be found. But it’s the various flu strains that live inside animals that bring sleepless nights to those in the know. They can exist inside a pig, bat or chicken without provoking symptoms, but prove devastating if (when) they make the jump to humans. As more and more humans live in close proximity to domesticated animals, encroach on the territories inhabited by wild animals, and grow their food on unprecedented scales, our chance of an uncontrollable epidemic increase.

The meat factories known as “Concentrated Animal Feeding Operations” (CAFOs) are particularly problematic. They provide cheap meat, poultry, dairy and
eggs from animals kept in what Quick terms “concentration camp conditions”, simultaneously creating the perfect breeding ground for new and dangerous pathogens. Pigs, he points out, eat almost everything, so their guts are the perfect mixing bowls for a new and deadly influenza strain. “CAFOs were the birthplace of swine flu, and they could very likely be the birthplace of the next killer pandemic,” Quick warns.

There are other possibilities, though – bioterror, for instance. Bill Gates is among
those who have warned that terrorist groups are looking into the possibility of releasing the smallpox virus in a crowded market, or on a plane. Then there is the possibility of a scientist’s mistake. In 1978 a woman died after smallpox was released from a laboratory at the University of Birmingham, UK. In 2004 two Chinese researchers accidentally infected themselves with the SARS virus and spread it to seven other people, one of whom died. In 2014, a cardboard box full of forgotten vials of smallpox was found in a National Institutes of Health facility in Bethesda, Maryland. A year later, the US military accidentally shipped live anthrax spores to labs in the US and a military base in South Korea. It’s not impossible that human error could strike again – with catastrophic results.

Such possibilities lie behind our discomfort with what scientists have to do to further our understanding. Researchers in Rotterdam, for instance, wanted to know whether the deadly H5N1 bird flu could develop a capacity for airborne transmission like the common cold virus. Having failed to modify its genetics to achieve this, they began to pass an infection between ferrets, the animals whose response to the virus most mimics that of humans. Ten ferrets later, healthy animals were catching the virus from the cage next door. Knowing how easily H5N1 can become airborne is exactly the kind of discovery that will bolster our vigilance. It is, after all, many times more fatal than the H1N1 strain that caused the Spanish flu. At the same time, there was a huge – but understandable –
furore over whether the research should
be published, and thus be available to potential bioterrorists.

We might have to live with such dilemmas, because it is important to be ready to challenge the killer virus when it arrives. As we have seen with Aids and the common cold, developing vaccines takes time, and there is no guarantee of success, even with a concerted research effort.

****

Will we be ready? Quick suggests that our best chance lies in the world’s business leaders realising what’s at stake: economies would be devastated by the next pandemic. In 1918, Arnold points out, the British government was telling citizens it was their patriotic duty to “carry on” and make sure the wheels of industry kept turning. The result was a perfect environment for mass infection. Political leaders made similar mistakes across the Atlantic: on 12 October President Wilson led a gathering of 25,000 New Yorkers down the “Avenue of the Allies”. “That same week,” Arnold reports, “2,100 New Yorkers died of influenza.”

It’s worth noting that Spanish flu did not abate because we outsmarted it. The pandemic ended because the virus ran out of people it could infect. Of those who didn’t die, some survived through a chance natural immunity, and some were lucky enough to have maintained a physical separation from those carrying the invisible threat. The virus simply failed to kill the rest, enabling their bodies to develop the antibodies required to repel a further attack. A generation or two later, when the antibody-equipped immune systems were in the grave, and humans were immunologically vulnerable (and complacent) once again, H1N1 virus re-emerged, causing the 2009 swine flu outbreak.

As these books make clear, this is a history that could repeat all too easily in our time. Of the three, Pale Rider is perhaps the most satisfying. It has greater complexity and nuance than Arnold’s collection of harrowing tales, fascinating though they are. Spinney’s analysis is more circumspect and thus less paralysing than Quick’s masterful exposition of our precarious situation. But the truth is we need all these perspectives, and probably more, if we are to avoid sleepwalking into the next pandemic. Unlike our nemesis, humans lack focus – and it could be our undoing. 

Michael Brooks’s most recent book is “The Quantum Astrologer’s Handbook” (Scribe)

Pale Rider: The Spanish Flu of 1918 and How it Changed the World
Laura Spinney
Vintage, 352pp, £25

Pandemic 1918: The Story of the Deadliest Influenza in History
Catharine Arnold
Michael O’Mara, 368pp, £20

The End of Epidemics
Jonathan D Quick with Bronwyn Fryer
Scribe, 288pp, £14.99

Michael Brooks holds a PhD in quantum physics. He writes a weekly science column for the New Statesman, and his most recent book is At the Edge of Uncertainty: 11 Discoveries Taking Science by Surprise.

This article first appeared in the 19 December 2014 issue of the New Statesman, Christmas Issue 2014