This Little Britain Read online

  England’s scientific community wasn’t simply the largest, it was also the best. Of the scientific ideas that poured out during the Scientific Revolution, a wholly disproportionate number came from England. These things are hard to measure with any objectivity, but some approximate indications are possible. For example, Professor Hatch, an American historian of science with, presumably, no nationalist axe to grind, has compiled a list of the greatest thinkers of the Scientific Revolution. Of his top sixteen names, five are English (Harvey, Bacon, Hobbes, Boyle and Newton). Of his ‘second sixteen’, four are English (Horrocks, Flamsteed, Halley, Hooke) and one a German (Henry Oldenburg) who came to live in London, where all his most significant work was carried out. In short, almost one third of all the most important endeavour in Western science was carried out in England, a country far smaller than Italy, Germany or France; a country that was not and had never been of much international consequence; a country that had long stood on the outer edge of Europe’s cultural mainstream. Newton’s own massive work was prompted, niggled and nudged out of his recalcitrant hands by the ferment of intellectual activity led by Hooke, Halley, Wren, Flamsteed and others.

  From the point of view of British exceptionalism, Newton’s legacy is simply too important to ignore. Yet, from this perspective, the more important point has less to do with one man’s genius than with the national culture that nurtured him. No sober historian could write even a two-page summary of British history that ignored, say, the empire or the Industrial Revolution. Yet sober historians—indeed, the best historians of our age—have been able to write entire histories of Britain that make no mention of the Scientific Revolution, none of Newton, none of the most important development in all human thought. Such an exclusion is, frankly, bananas.

  Why was Britain special? Why did the Scientific Revolution centre itself there and not in one of the more obvious candidates, France, Italy, Germany? The answer is complex and not fully understood. Yet the kernel of any answer must surely be a simple one. Britons were free to think what they liked. The contrasts are there wherever you look. In 1633, Galileo was tried as a heretic. In the 1680s, Newton was fêted as a genius. In 1553, the Spaniard Michael Servetus was burned at the stake for, among other things, his controversial views on the biology the human heart. William Harvey’s much more extensive views on the topic were gathered together in a book with a respectful (nay, fawning) inscription to the king. The first recognizable scientific society was the Italian ‘Academy of the Secrets of Nature’, which had a cool name but a short life: the Pope didn’t like it, and closed it down. The Royal Society, by contrast, so little threatened the state or the Church that Charles II liked to refer to the scientists as ‘mes fous’, my jesters. Ridicule may be bad, but it’s better than the barbecue.

  For Newton himself, two epitaphs best summarize the man and his work. Leibniz, so shamefully treated by his rival, told the queen of Prussia that all mathematics could be divided into two halves, Newton’s half and everything else; and that of the two, Newton’s was the better. The second epitaph came in a foreword written to a twentieth-century reissue of Newton’s Opticks:

  Nature was to him an open book, whose letters he could read without effort…In one person, he combined with experimenter, the theorist, the mechanic and, not least, the artist in exposition. He stands before us strong, certain and alone; his joy in creation and his minute precision are evident in every word and every figure.

  The author of that foreword: Albert Einstein.

  * The first problem was this: if you want to roll a ball from point A to a point B that is lower than and at some distance from A, then what shape of curved track will get that ball from A to B the fastest? You might think that such a problem could hardly be further removed from popular culture, but not so. In Spider Man 2, Peter Parker exclaims: ‘Did Bernoulli sleep before he found the curves of quickest descent?’ Not quite E = mc2 admittedly.

  * It was in his final letter on the subject that Newton used the famous sentence ‘if I have seen further it is by standing on the shoulders of Giants’. He never meant it, though. He was the giant, and by goodness he knew it.

  THE LAST SCIENTIST

  For the last half-century and more, the world of physics has been harbouring a dark secret. On the one hand, Einstein’s theory of general relativity seemed to explain the world of the very large: planets, stars, galaxies and the rest. On the other hand, quantum theory seemed to explain the world of the very small: electrons, quarks, muons and the rest. Yet although both theories have made repeated, detailed and accurate predictions about their respective spheres, they are nevertheless in flat contradiction to one another. Where Einstein’s universe is smoothly curved, the quantum universe is anything but. The result has been a physics rather like a car with only two gears: an ultra-low one for steep hill climbs in snow, and an ultra-high one for bowling along the motorway at a hundred miles an hour. The two gears work just fine when they’re left to do what they’re designed to do, but woe betide anyone who tries to shift from one to the other. Instead of a nice smooth shifting of gears, all you’ll get is an ugly crunching sound and the smell of (highly mathematical) smoke.

  The problem arises because the two theories are handling different things. There are just four fundamental forces of nature: gravity, electromagnetism, the weak force and the strong force. Einstein’s relativity handles gravity. Quantum mechanics deals with the other three. And what’s needed, of course, is a theory that combines all four forces in a single set of equations: a Theory of Everything, in fact.

  The first hint that such a theory might be available came from a young Italian researcher at the CERN particle accelerator in Switzerland. The researcher, Gabriele Veneziano, discovered to his surprise that a two-hundred-year-old mathematical formula seemed to capture perfectly much of the data being generated by all that atom-smashing. A flurry of research ensued, aimed at using the formula to model the strong force in quantum mechanics. It was discovered that if elementary particles were thought of as tiny vibrating strings, then their nuclear interactions would be correctly described by the formula. So far, so exciting. Then it all went wrong. More powerful atom-smashers produced data that flatly contradicted the early predictions of string theory. Other theories were developed which seemed to cope much better. By the late 1970s, string theory seemed like just one of those things: a promising idea that had turned out to be a bust.

  Not everyone, however, had given up. Physicists and mathematicians are driven by a sense of beauty—almost impossible to explain to a non-mathematician, but central nevertheless—and there at the heart of string theory lay a formula at once vastly simple and vastly rich in insight.* The American string theorist John Schwarz said, ‘the mathematical structure of string theory was so beautiful and had so many miraculous properties that it had to be pointing towards something deep’. So he, and a handful of other string theorists, persisted with their unfashionable work. Chief among the problems with which they wrestled was what appeared to be some apparently lethal inconsistencies. It was as though one part of the theory predicted that X = 1, while somewhere else in the theory it was predicting that X = 2. A self-contradictory theory was no theory at all; either the anomalies, or the theory itself, would have to go.

  Of the true believers, two of the truest were the American Schwarz and a Briton, Michael Green. Both men were mildly fanatical, starting from a position that a theory so beautiful simply had to be true—and that if that were the case, then those mathematical anomalies couldn’t really exist, however much it might look as if they did. For five years, they battled. Then, one summer’s night in Colorado in 1984, they were ready for the final showdown. The whole thing—the future of string theory—came down to one single monster equation. On one side of the blackboard the equation solved out to 496. If the number on the other side was the same, then string theory was saved. It the number was anything else—even 497 or 496.00001—then string theory would vanish in a puff of contradiction. In Green’s
words:

  I do remember a particular moment, when John Schwarz and I were talking at the blackboard and working out these numbers which had to fit, and they just had to match exactly. I remember joking with John Schwarz at that moment, because there was thunder and lightning—there was a big mountain storm in Aspen at that moment—and I remember saying something like, you know, ‘We must be getting pretty close, because the gods are trying to prevent us completing this calculation.’

  But complete it they did: 496 on the left-hand side of the blackboard, 496 on the right. What was more, in the course of all their work Schwarz and Green had given the theory enough demonstrable power to unite all four forces of nature—strong, weak, electromagnetic and gravitational—all in one theory. A revolution was born.

  In no time at all, string theory was all the rage. At its core, it might be beautiful, but its beauty was wondrous strange. According to the theory, the fundamental units of nature are tiny vibrating strings of energy so small that, if you were to expand an atom to the size of the solar system, one string would be about the size of a tree. And that’s not even the strange bit. According to the theory, there are three regular dimensions of space, a fourth one of time, then six further spatial dimensions: teeny-weeny ones, curled up on themselves so tightly that we never get a chance to see them. These tiny extra dimensions were enough to do the trick. Einstein’s universe could now shake hands with its quantum twin. The car of modern physics suddenly found a full range of gears. String theory certainly isn’t proven or anything like it, yet it’s the first wholly plausible model of what a Theory of Everything might look like. Just three hundred years after Newton’s Principia launched the quest for the deep mathematical truths behind the structure of the universe, physicists may have come to a credible final solution—first glimpsed on a stormy Colorado night as the gods thundered their disapproval.

  The story is a nice one, adding a touch of drama to what is not exactly the most dramatic of human activities, yet it carries some broader lessons too. Three hundred years earlier, back at the birth of physics, Newton’s Principia arose not simply from one man’s genius, but also from the creative energy of the world’s leading scientific nation. Three hundred years on, and that energy has spread across continents. Those responsible for the creation of string theory include, to name just a few, Gabriele Veneziano (an Italian), Yoichiro Nambu (a Japanese-born American), Holger Nielsen (a Dane), Leonard Susskind, John Schwarz and Ed Witten (all Americans), Joel Scherk (a Frenchman) and Michael Green (a Briton). Yet even in our more international age, scientific brilliance is not evenly distributed. The easiest way to measure that brilliance comes to us courtesy of Alfred Nobel.*

  The first Nobel Prizes were awarded in 1901 and they have been awarded almost every year since (the war years being partial exceptions). Because multiple awards are often made, there have now been slightly more than five hundred awards made for scientific achievement. Unsurprisingly, it is the United States which heads the medal table, with more than two-fifths of scientific Nobels having been awarded to American scientists. Britain comes second in the table with seventy-four prizes, followed by Germany, France and Sweden. To lie second in this table is a pretty decent achievement by any standard. The United States has a population of 300 million, about five times that of Britain. Since the Americans have won just three times the number of Nobel Prizes then, on a size-for-size basis, Britain has done at least as well, or rather better.

  Yet the scale of the British scientific achievement is obscured by comparing us to the American powerhouse. It’s when you look at how we do in comparison with other countries that the British achievement really leaps out. Britain has won as many Nobel Prizes in science as France, Russia, Italy, Spain, Japan, Canada, Australia, China, India, Africa and Latin America combined. Only Germany, with its sixty-five prizes, comes even close to matching the British haul. British success has been shared reasonably evenly both across the disciplines (physics, chemistry and medicine) and over the decades. If you take Anglo-American science as a whole, then it has accounted for an eye-popping 70 per cent of all prizes awarded over the last four decades.*

  This is an extraordinary record. It’s easy enough to understand why Britain wins more than its share of prizes compared with the poorer countries of China, India, Africa and Latin America. In a way, it’s unfair even to make the comparison. But what about France, Spain, Italy, Japan, Canada, Australia, Russia? The Royal Society of Newton’s era puzzles us with the degree of its success, relative to its home country’s size and influence. The same puzzle occurs in relation to the twentieth century. If anything, indeed, this later puzzle is still more baffling. In Newton’s time, scientists were still learning how to do science. It was hardly surprising that the new, innovative ways of thought weren’t equally dispersed across Europe. Somewhere, in short, was likely to be in the lead, and the country that was least likely to griddle scientists (for disagreeing with the Pope) or stop their mouths (for disagreeing with the king)—or indeed the country that had moved farthest from witch-burning and belief in magic—was the one most likely to take that leading position.

  In the twentieth century, no such easy explanation offers itself. The scientific outlook was common to all of Europe, North America and beyond. Popes no longer impeded science; kings no longer mattered; witches were no longer the stuff of bonfires. To be sure, Britain was a bit richer than some of its neighbours, some of the time, but British scientific excellence persisted well after its neighbours’ economies had caught and surpassed its own. Likewise, it’s true that British political liberties have provided a generally benign climate for scientific research; die Hitlerzeit in Germany did much to wreck that country’s extraordinary scientific prowess. Yet this explanation too falls far short of what it is called upon to explain. German liberty and economic might returned speedily after the war, with Konrad Adenauer and the Wirtschaftswunder, yet German scientific achievement has (by its own high standards) been anaemic ever since 1933. Democratic France and Italy have been less impressive still. The elite British universities have probably been more effective at nurturing talent than their more state-directed Continental cousins, yet it’s hard to avoid the feeling that, as with the British literary achievement, there’s something about Britishness and science that makes them go happily together. The empirical spirit, so precocious in Newton’s England, so notable in the British philosophical tradition, seems alive and well today, and that Nobel medal table seems to prove it.

  There’s probably truth in this conclusion, yet satisfaction in the past should not breed complacency as to the future. Increasingly, British Nobel Prize winners are likely to be based not here, but in the USA. Increasing wealth is likely to be on the brink of unlocking the huge creative energies of China and India: the latter country today produces more mathematicians than the whole of the EU. Meanwhile, the number of those studying physics in British schools has dropped by some 40 per cent over the last decade and a half. This section is entitled ‘The Last Scientist’ because Michael Green may just possibly have played a pivotal role in concluding the intellectual quest launched by Newton some three hundred years ago; but it’s called this for another reason too. Britain may have had a great track record in science, but in a competitive world you need to compete: that means physics teachers in schools, plenty of cash for universities. No political party has yet sought to address these challenges with the urgency they deserve. Will the next generation of policy-makers do any better? Maybe. Maybe not. The future of British science depends on the answer.

  * The formula, should you care to admire it, looks like this:

  B(x,y)=∫10tx−1(1−t)y−1dt

  * Nobel was a manufacturer of explosives, dynamite his most famous product. In April 1888, he woke up to find his own obituary splashed across his morning newspaper, under the headline ‘Le Marchand de mort est mort’—the merchant of death is dead. The obituaries were a cock-up, of course: it was not Alfred but his brother, Ludwig, who had died. All the s
ame, the incident is thought to have made Alfred reflect on the way the public perceived him; his lavishly endowed prizes being the happy result.

  * To take a somewhat broader measure, British scientists produce about 12% of all papers cited in peer-reviewed journals—an impressive feat.

  A PAINFUL ADMISSION

  Alfred Nobel never endowed a prize in mathematics. Some people maintain that he refused to do so because his mistress once had an affair with the Swedish mathematician Gösta Mittag-Leffler, but then again, some people maintain that the CIA killed President Kennedy and has an underground bunker in Nevada full of aliens in cages. There’s not much evidence for any of these hypotheses and, most likely, Nobel ignored the subject because his bent was more practical, and because there were already some well-run maths prizes around at the time.

  This book, however, sets out to track down British exceptionalism in every area, every age. It seemed to me that, if British science has been exceptional, it was perfectly likely that British maths has been too. Slave to my readers that I am, I made it my job to find out. But find out how? Although I know which end of a calculator is up, my knowledge of holomorphic dynamics, functional analysis and homological approaches to field theory is, I freely admit it, a little rusty. Luckily for me, a Canadian mathematician, John Charles Fields, did in 1936 what Alfred Nobel had failed to do, and established a prize that has come to be the gold standard award in the subject. The prize is awarded every four years, with multiple awards commonplace. Though only mathematicians under forty are eligible, most of the best work in mathematics is done by relative youngsters in any case, so that the awards are reasonably representative. The prize has been running for long enough that, as with the Nobels, it’s possible to put together some kind of international medal table.