Seeing Further. Группа авторов
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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 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, twenty-eight 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,
Letter from Thomas Bayes to John Canton concerning logarithms, 24 November 1763.
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. John Locke contributed a paper on the poisonous fish of the Bahamas. 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 a hundred years before the British government did.
In an age when sabres hardly ever ceased rattling, the Society became the least nationalistic of national institutions. The name itself is telling. Royal Society of London describes a location, not an allegiance. Had it been the Royal Society of Great Britain it would have been a very different organisation whether it wished it or not. So throughout its history it has been the most admirably neutral and cosmopolitan of entities. 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.
Engraving of Antoni van Leeuwenhoek by Verkolje.
A letter from Antoni van Leeuwenhoek to the Royal Society regarding observations of duckweed, its roots and reproduction, 25 December 1702.
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 fifty years – a period that began when he was already past forty – Leeuwenhoek submitted some two hundred 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.
A replica of Leeuwenhoek’s microscope.
Leeuwenhoek’s observations of his own facial hair, 22 February 1676.
Leeuwenhoek’s observations of rotifers and their parasitic worms, 4 November 1704.
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, Joseph Lister,