p(q|y) = p(q) p(y|q)/ ò p(h) p(y|h) dh
People who understand the formula can use it to work out various probability distributions — or inverse probabilities, as they are sometimes called. It is a way of arriving at statistical likelihoods based on partial information. The remarkable feature of Bayes’ theorem is that it had no practical applications in his own lifetime. Although simple cases yield simple sums, most uses demand serious computational power to do the volume of calculations. So in Bayes’ day it was simply an interesting but largely pointless exercise.
Bayes evidently thought so little of his theorem that he didn’t bother to publish it. It was a friend who sent it to the Royal Society in London in 1763, two years after Bayes’ death, where it was published in the society’s Philosophical Transactions with the modest title of An Essay Towards Solving a Problem in the Doctrine of Chances. In fact, it was a milestone in the history of mathematics. Today, with the aid of supercomputers, Bayes’ theorem is used routinely in the modelling of climate change and weather forecasting generally, in interpreting radiocarbon dates, in social policy, astrophysics, stock-market analysis and wherever else probability is a problem. And its discoverer is remembered today simply because nearly 250 years ago someone at the Royal Society decided that it was worth preserving his work, just in case.
The Royal Society has been doing interesting and heroic things like this since 1660, when it was founded, one damp weeknight in late November, by a dozen men who had gathered in rooms at Gresham College in London to hear Christopher Wren, 28 years old and not yet generally famous, give a lecture on astronomy. It seemed to them a good idea to form a society — that is all they called it at first — to assist and promote the accumulation of useful knowledge.
Nobody had ever done anything quite like this before, or would ever do it half as well again. The Royal Society (it became royal with the granting of a charter by Charles II in 1662) invented scientific publishing and peer review. It made English the primary language of scientific discourse, in place of Latin. It systematised experimentation. It promoted — indeed, insisted upon — clarity of expression in place of high-flown rhetoric. It brought together the best thinking from all over the world. It created modern science.
Nothing, it seems, was beneath its attention. Society members took an early interest in microscopy, woodland management, architectural load bearing, the behaviour of gases, the development of the pocket watch, the thermal expansion of glass. Before most people had ever tasted a potato, the Royal Society debated the practicality of making it a staple crop in Ireland (ironically, as a hedge against famine). Two years after its formation, Christopher Merret, one of the founding fellows, demonstrated a method for fermenting wine twice over, endowing it with a pleasing effervescence. He had, in short, invented champagne. The next year John Aubrey contributed a paper on the ancient stone monuments at Avebury, and so effectively created archaeology. And so it went on, decade after productive decade. When Benjamin Franklin flew his kite in a thunderstorm it was for the Royal Society that he very nearly killed himself. When a gas holder in Woolwich exploded with devastating consequences or gunpowder repeatedly failed to ignite or the Navy needed a cure for scurvy, the Royal Society was called in to advise.
At least three things have always set the society apart. First, from the outset, it was truly international. In 1665, Henry Oldenburg, himself German born, became editor of the society’s first journal (now one of seven), which was given the full and satisfying name Philosophical Transactions: Giving some Accompt of the Present Undertakings, Studies and Labours of the Ingenious in many Considerable Parts of the World. No words from the society’s early annals have more significance than that phrase “many Considerable Parts of the World”.
“The international aspect was clearly a central part of what made it a success so early,” says Stephen Cox, the society’s genial chief executive. “Right from the start we were getting papers from people like Marcello Malpighi and Christiaan Huygens, so very early on it had become a place where ideas from all over could be exchanged — a kind of early version of the internet really.” As Cox likes to note, the Royal Society had a foreign secretary 100 years before the British Government did.
In an age when sabres hardly ever ceased rattling, the society became the least nationalistic of national institutions. When Benjamin Franklin was a voice of revolution against Great Britain, he was still an esteemed and welcome member of the society; and when Captain James Cook circumnavigated the globe in British ships in the name of knowledge he did so with perfect assurances that he would not be molested by any American vessels he encountered. During the Napoleonic wars, Humphry Davy was able to travel on scientific business across Europe thanks to a letter of dispensation from Napoleon that he carried in his pocket. The Société Philomathique gave him a dinner in Paris and drank the health of the Royal Society, if not the King. In like spirit, the society refused to expel Fellows from enemy nations during either of the world wars and was one of the first bodies to re-establish links after them.
Quite as remarkable as its cosmopolitanism was a second distinctive characteristic of the Royal Society — namely, that it wasn’t necessary to be well born to be part of it. Having wealth and title didn’t hurt, of course, but being scientifically conscientious and experimentally clever were far more important. No one better illustrated this than a retiring linen draper from Delft named Antoni van Leeuwenhoek. Over a period of 50 years — a period that began when he was already past 40 — Leeuwenhoek submitted some 200 papers to the Royal Society, all accompanied by the most excellent and exacting drawings, of the things he found by looking through his hand-wrought microscopes. These were tiny wooden paddles with a little bubble of glass embedded in them. How he managed to work them is something of a wonder even now, but he achieved magnifications of up to 275 times and discovered the most incredible things: protozoa, bacteria and other wriggling life where no life was thought to be. The idea that there were whole worlds in a drop of fluid was a positive astonishment.
Leeuwenhoek had practically no education. He filed his reports in Low Dutch because he had no English and no Latin. He didn’t even have High Dutch, it appears. But none of that mattered. What mattered was that he had a genius for microscopy and a profound respect for knowledge.
In 350 years, the Royal Society has had a mere 8,200 members, but what a roll call of names. In no very particular order they include Isaac Newton, Christopher Wren, Edmond Halley, Robert Boyle, Robert Hooke, Benjamin Franklin, John Locke, Humphry Davy, Charles Darwin, Ernest Rutherford, Isambard Kingdom Brunel, Joseph Banks, T. H. Huxley, James Watt, John Locke, Joseph Lister, Henry Cavendish, Michael Faraday, James Clerk Maxwell, Lawrence Bragg, Paul Dirac, Peter Medawar, Alexander Fleming, James Chadwick, Lord Rayleigh, William Ramsey, Lord Kelvin, Kathleen Lonsdale, Dorothy Hodgkin, Miriam Rothschild, Anne McLaren and literally hundreds more who changed the world by changing our understanding of it. To be part of such an establishment is an extraordinary achievement. This isn’t just the most venerable learned society in the world, it is the finest club.
Throughout its busy history the society has demonstrated an almost uncanny knack for selecting people before they gave any particular hint of the greatness that would make them immortal. Edmond Halley was made a Fellow before he received his degree from Oxford. Charles Darwin, elected in 1839, only three years after his youthful Beagle voyage, was not even known for his work on barnacles, much less on evolution. William Henry Fox Talbot became an FRS a good two years before the first vague notion of photography flitted through his head. And of course there was Thomas Bayes, scribbling a theorem that the world would have to wait nearly 250 years to use.
The society has also demonstrated an heroic, and indeed endearing, tendency to recognise the unsung. The example that leaps to mind for me here is that of Hermann Sprengel, the forgotten father of electric lighting. Everyone thanks Joseph Swan and Thomas Edison for giving us the homely glow of incandescent lighting, but in fact Sir William Grove (who, it more or less goes without saying, was himself a Fellow) had demonstrated a working incandescent bulb well over 30 years before them — seven years before Edison was even born. It’s just that Grove’s bulb didn’t last very long. What was needed was a vacuum that would allow a filament to burn for long periods. Sprengel, a German chemist working in London, invented a pump that could drain the air from a glass chamber down to one millionth of its normal volume, allowing filaments to burn for hours and making electric lighting a commercial possibility at last. Edison and Swan found the filaments and got the glory. Sprengel was forgotten almost at once by everyone except the Royal Society, which made him a Fellow in 1878, nearly fifteen years before he was recognised by any institution in his native Germany.
The best place I know to get some sense of what the Royal Society is and has achieved is a modest, crowded storeroom in the basement of its headquarters in Carlton House Terrace in London. Here, neatly shelved or tucked into drawers and cabinets, are three and a half centuries of accumulated treasures — Newton’s manuscript copy of the Principia, the Shelton regulator clock used by Captain Cook to time the transit of Venus on the Endeavour voyage, Joseph Priestley’s folding spectacles, Leeuwenhoek’s precious drawings, the papers of Robert Hooke and Robert Boyle — representing the moments of birth of some of the most enormous ideas human minds have ever had.
Keith Moore, the society’s librarian, reaches into an anonymous-looking metal cupboard and, with an air of gentleness and care, brings out a white box. Inside it, resting delicately, is an object that automatically provokes an awed hush: the death mask of Isaac Newton. Only by a remarkable chance did the mask come into the society’s possession. It had been lost for many years when, in 1839, a Mr Christie, a Fellow of the Society, developed a sudden desire to have a bust of Newton on his shelves and called in at a curio shop on Tichborne Street in London, near his place of work, to ask if it had anything. The shopkeeper replied that he had no statues, but did have a curious mask, which his father had bought many years before. After some rooting around, he found it and brought it to Christie to examine. It was Newton’s death mask. It had sat unregarded on a shelf for at least half a century, and in all likelihood would eventually have been lost altogether had Christie not made his lucky inquiry.
The mask is a transfixing object, not surprisingly, but what is more unexpectedly moving is a small, exquisite piece of apparatus that sits on the shelf alongside it: a reflecting telescope made by Newton himself in 1669. It is only six inches long but beautifully fashioned. Newton ground the glass himself, designed the swivelling socket, turned the wood with his own hand. In its time this was an absolute technological marvel, but it is also a thing of lustrous beauty. Nowhere could you find an item that more vividly demonstrates the beauty as well as the wonder of science.
When you look along the stacks or peek into the drawers it is impossible not to be struck with wonder at how much aggregated human effort — how much thought and toil and nights under canvas — is embedded in what we know about the world and Universe and how they are put together.
“This is only a small part of it,” Keith tells me. “There are 8,000 more boxes in storage in Wiltshire.” He smiles. “You generate a lot of material in 350 years.”
Which brings me to my third remarkable fact about the society: it’s still there. More than that, it is still there and it is still important. How many enterprises can you name that are still doing today what they were formed to do 350 years ago?
It has had its moments of faltering, goodness knows. At times its quenchless curiosity has threatened to give way to mere morbidity. In the early days it was particularly fascinated with monstrous births and that kind of thing, and sometimes it engaged in experiments that were patently imprudent.
One such was in November 1667, when a penurious student named Arthur Coga was induced to let two Fellows transfuse sheep’s blood into him in return for the payment of a guinea. No one had any idea what would happen — whether it would kill him or fill him with boundless energy — and this degree of uncertainty left some of the more reflective members feeling distinctly uneasy. In the event, the transfusion didn’t do much of anything. Before an audience that included the Bishop of Salisbury, 14 ounces of blood were pumped out of the sheep and into Coga. It seemed to do him no harm. Afterwards, one of those present reported, “the patient was well and merry, and drank a glass or two of canary, and took a pipe of tobacco”. He went home, slept well and reported no ill effects. Just under two weeks later, the operation was repeated for a new audience. Soon afterwards, however, reports began to trickle in from all over Europe that the experiment had been tried several times elsewhere, often with fatal results. The society, happily, never tried anything like that again.
Today the Royal Society’s interests remain an inspiration to recite. It provides 350 research fellowships and its grants support the work of 3,000 scientists all over the world. It bestows great numbers of medals and prizes, maintains an active programme of lectures and debates, and holds a beloved Summer Science Exhibition, which no one who appreciates science and can get to London should miss. It acts as the scientific conscience of the nation. It publishes seven journals and an endless stream of papers. It remains emphatically international in its outlook, maintaining close links with 91 science academies around the world. If we have an Earth worth living on 100 years from now, the Royal Society will be one of the organisations our grandchildren will wish to thank.
Poke your head through any door in the Royal Society building and what you are likely to find is people in meetings. My own involvement, like that of most outsiders, has been as a member of a committee — in my case a committee to select the winners of the annual books prize and another involved with the 350th anniversary celebrations — and on almost every visit to the building I have opened three or four wrong doors to find other people meeting. For a long time I wondered what they could possibly all be meeting about. Then I was given a copy of an extraordinary volume — a sturdy hardback called the Royal Society Year Book.
Flick through it at random and you find that it is involved in an impossibly varied range of activities. There is a Dorothy Hodgkin Fellowships Committee, a Hooke Committee, a Trans-Antarctic Association UK Advisory Committee, a Darwin Correspondence Project, a Sir Harold Hartley Lecture Committee, a South-East Asia Rainforest Research Committee, a Newton International Fellowships, and dozens and dozens more. There is even an Anatomy, Physiology, Endocrinology and Pharmacology (Except Clinical Aspects) of Animal Systems, Neurosciences, Psychology and Reproductive Biology, and Relevant Agricultural Studies Committee (known informally, and perhaps a bit mercifully, as “Panel 8”).
Altogether at the Royal Society there are 96 committees, all devoted to promoting important research, honouring an achievement, improving education, badgering governments into behaving intelligently, or otherwise effecting an enhancement to what we know or an improvement to how we proceed.
The most important committees of all are the ten devoted to electing new Fellows. Today there are 1,400 Fellows, including 69 Nobel laureates, and it is they who run the Society. “It is,” Stephen Cox tells me, “like a company with 1,400 non-executive directors. They set policy and identify key areas of concern. It’s their society.”
Because of all that it has achieved in its time, there is a tendency to equate the Royal Society with things like atoms and gravity and other bits of hard science, but what impresses me is the boundlessness of its range. Consider the contribution of John Lubbock, friend and neighbour of Charles Darwin. Lubbock was a banker by profession, but was in addition a distinguished botanist, astronomer, expert on the social behaviour of insects, politician and antiquarian. Among much else, he coined the terms palaeolithic, mesolithic and neolithic in 1865. But his real contribution to life was to push through Parliament the first Ancient Monuments Protection Act, which became law in 1882. People forget how much of Britain’s historic fabric was nearly destroyed in the past. Before Lubbock’s intervention, nearly half of Avebury was cleared away for housing, and at one point it was even threatened that Stonehenge, then still in private hands, might be dismantled and shipped to America. Without Lubbock, many stone circles, tumuli and other historical features of the landscape would have vanished long ago. Lubbock also, not incidentally, invented the bank holiday. The Royal Society and its Fellows, you see, have long been at the heart of all kinds of things.
© Bill Bryson 2010. Extract from Seeing Further: The Story of Science and the Royal Society edited by Bill Bryson, published by HarperCollins in 2010 at £25. Similar material occurs on pages 38-39 of Bryson’s book At Home, Black Swan 2011 (£8.99).