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Today's selection-- from Against the Gods by Peter L. Bernstein. John Graunt and his breakthrough 1662 book, Natural and Political Observations made upon the Bills Of Mortality:
“Statistical sampling has had a long history, and twentieth-century techniques are far advanced over the primitive methods of earlier times. The most interesting early use of sampling was conducted by the King of England, or by his appointed proxies, in a ceremony known as the Trial of the Pyx and was well established by 1279 when Edward I proclaimed the procedure to be followed.
“The purpose of the trial was to assure that the coinage minted by the Royal Mint met the standards of gold or silver content as defined by the Mint's statement of standards. The strange word ‘pyx’ derives from the Greek word for box and refers to the container that held the coins that were to be sampled. Those coins were selected, presumably at random, from the output of the Mint; at the trial, they would be compared to a plate of the King's gold that had been stored in a thrice-locked treasury room called the Chapel of the Pyx in Westminster Abbey. The procedure permitted a specifically defined variance from the standard, as not every coin could be expected to match precisely the gold to which it was being compared.
“A more ambitious and influential effort to use the statistical process of sampling was reported in 1662, eight years after the correspondence between Pascal and Fermat (and the year in which Pascal finally discovered for himself whether God is or God is not). The work in question was a small book published in London and titled Natural and Political Observations made upon the Bills Of Mortality. The book contained a compilation of births and deaths in London from 1604 to 1661, along with an extended commentary interpreting the data. In the annals of statistical and sociological research, this little book was a stunning breakthrough, a daring leap into the use of sampling methods and the calculation of probabilities—the raw material of every method of risk management, from insurance and the measurement of environmental risks to the design of the most complex derivatives.
“The author, John Graunt, was neither a statistician nor a demographer—at that point there was no such thing as either. Nor was he a mathematician, an actuary, a scientist, a university don, or a politician. Graunt, then 42 years old, had spent his entire adult life as a merchant of ‘notions,’ such as buttons and needles.
“Graunt must have been a keen businessman. He made enough money to be able to pursue interests less mundane than purveying merchandise that holds clothing together. According to John Aubrey, a contemporary biographer, Graunt was ‘a very ingenious and studious person ... [who] rose early in the morning to his Study before shoptime . . . . [V]ery facetious and fluent in his conversation.’ He became close friends with some of the most distinguished intellectuals of his age, including William Petty, who helped Graunt with some of the complexities of his work with the population statistics.
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| Table of Casualties in Natural and Political Observations Made Upon the Bills of Mortality (5th edition, published 1676) |
“Petty was a remarkable man. Originally a physician, his career included service as Surveyor of Ireland and Professor of Anatomy and Music. He accumulated a substantial fortune as a profiteer during the wars in Ireland and was the author of a book called Political Arithmetick, which has earned him the title of founder of modern economics.
“Graunt's book went through at least five editions and attracted a following outside as well as inside England. Petty's review in the Parisian Journal des Stavans in 1666 inspired the French to undertake a similar survey in 1667. And Graunt's achievements attracted sufficient public notice for Charles II to propose him for membership in the newly formed Royal Society. The members of the Society were not exactly enthusiastic over the prospect of admitting a mere tradesman, but the King advised them that, ‘if they found any more such Tradesmen, they should be sure to admit them all, without any more ado.’ Graunt made the grade.
“The Royal Society owes its origins to a man named John Wilkins (1617-1672), who had formed a select club of brilliant acquaintances that met in his rooms in Wadham College. The club was a clone of Abbe Mersenne's group in Paris. Wilkins subsequently transformed these informal meetings into the first, and the most distinguished, of the scientific academies that were launched toward the end of the seventeenth century; the French Acadernie des Sciences was founded shortly after, with the Royal Society as its model.
“Wilkins later became Bishop of Chichester, but he is more interesting as an early author of science fiction embellished with references to probability. One of his works carried the entrancing title of The Discovery of a World in the Moone or a discourse tending to prove that 'tis probable there may be another habitable world in that planet, published in 1640. Anticipating Jules Verne, Wilkins also worked on designs for a submarine to be sent under the Arctic Ocean.
We do not know what inspired Graunt to undertake his compilation of births and deaths in London, but he admits to having found ‘much pleasure in deducing so many abstruse, and unexpected inferences out of these poor despised Bills of Mortality .... And there is pleasure in doing something new, though never so little.’ But he had a serious objective, too: ‘[T]o know how many people there be of each Sex, State, Age, Religious, Trade, Rank, or Degree, &c. by the knowing whereof Trade and Government may be made more certain, and Regular; for, if men know the People as aforesaid, they might know the consumption they would make, so as Trade might not be hoped for where it is impossible.’ He may very well have invented the concept of market research, and he surely gave the government its first estimate of the number of people available for military service.
“Information about births and deaths had long been available in parish churches, and the City of London itself had started keeping weekly tallies from 1603 onward. Additional data were available in Holland, where the towns were financing themselves with life annuities-policies purchased for a lump sum that would pay an income for life to the owner of the policy, and occasionally to survivors. Churches in France also kept records of christenings and deaths.
Hacking reports that Graunt and Petty had no knowledge of Pascal or Huygens, but, ‘Whether motivated by God, or by gaming, or by commerce, or by the law, the same kind of ideas emerged simultaneously in many minds.’ Clearly Graunt had chosen a propitious moment for publishing and analyzing important information about the population of England.
“Graunt was hardly aware that he was the innovator of sampling theory. In fact, he worked with the complete set of the bills of mortality rather than with a sample. But he reasoned systematically about raw data in ways that no one had ever tried before. The manner in which he analyzed the data laid the foundation for the science of statistics. The word ‘statistics’ is derived from the analysis of quantitative facts about the state. Graunt and Petty may be considered the co-fathers of this important field of study.
“Graunt did his work at a time when the primarily agricultural society of England was being transformed into an increasingly sophisticated society with possessions and business ventures across the seas. Hacking points out that so long as taxation was based on land and tillage nobody much cared about how many people there were. For example, William the Conqueror's survey known as the Domesday Book of 1085 included cadasters—registers of ownership and value of real property—but paid no heed to the number of human beings involved.
“As more and more people came to live in towns and cities, however, headcounts began to matter. Petty mentions the importance of population statistics in estimating the number of men of military age and the potential for tax revenues. But for Graunt, who appears to have been a tradesman first, at a time of rising prosperity, political considerations were of less interest.
“There was another factor at work. Two years before the publication of Graunt's Observations, Charles II had been recalled from exile in Holland. With the Restoration in full sway, the English were finally rid of the intellectual repression that the Puritans had imposed on the nation. The death of absolutism and Republicanism led to a new sense of freedom and progress throughout the country. Great wealth was beginning to arrive from the colonies across the Atlantic and from Africa and Asia as well. Isaac Newton, now 28 years old, was leading people to think in new ways about the planet on which they lived. Charles II himself was a free soul, a Merry Monarch who offered no apologies for enjoying the good things of life.
“It was time to stand up and look around. John Graunt did, and began counting.
“Although Graunt's book offers interesting bits for students of sociology, medicine, political science, and history, its greatest novelty is in its use of sampling. Graunt realized that the statistics available to him represented only a fraction of all the births and deaths that had ever occurred in London, but that failed to deter him from drawing broad conclusions from what he had. His line of analysis is known today as ‘statistical inference’—inferring a global estimate from a sample of data; subsequent statisticans would figure out how to calculate the probable error between the estimate and the true values. With his ground-breaking effort, Graunt transformed the simple process of gathering information into a powerful, complex instrument for interpreting the world—and the skies—around us."
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author: Peter L. Bernstein |
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title: Against the Gods: The Remarkable Story of Risk
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publisher: Wiley |
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page(s): 74-81 |
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