Against the Gods: The Remarkable Story of Risk (16 page)

Most critical decisions would be impossible without sampling. By the
time you have drunk a whole bottle of wine, it is a little late to announce
that it is or is not drinkable. The doctor cannot draw all your blood
before deciding what medicine to prescribe or before checking out your
DNA. The president cannot take referendums of 100% of all the voters
every month before deciding what the electorate wants-nor can he eat
all the broccoli in the world before expressing his distaste for it.

Sampling is essential to risk-taking. We constantly use samples of
the present and the past to guess about the future. "On the average" is
a familiar phrase. But how reliable is the average to which we refer?
How representative is the sample on which we base our judgment?
What is "normal," anyway? Statisticians joke about the man with his
feet in the oven and his head in the refrigerator: on the average he feels
pretty good. The fable about the blind men and the elephant is
famous precisely because each man had taken such a tiny sample of
the entire animal.

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 thricelocked 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.2 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."3 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.

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.4

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 Scavans 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.5 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 Academie 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."6 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."7 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 simultane ously in many minds."8 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.

The raw material that Graunt gathered was contained in "Bills of Mortality" that the City of London had started collecting in 1603. That was only incidentally the year in which Queen Elizabeth died; it was also the year in which London suffered one of the worst infestations of the plague. Accurate knowledge of what was going on in the field of public health was becoming increasingly important.10

The bills of mortality revealed the causes of death as well as the number of deaths and also listed the number of children christened each week. The accompanying illustration shows the documents for two weeks in the year 1665.*
There were 7,165 deaths from plague in just the one week of September 12-19, and only four of 130 parishes were free of the disease.' 1