More on this book
Kindle Notes & Highlights
Near the end of his life, he came up with a last, terrifying proposal for Ireland. He would cut the island’s population down to a tiny fraction, leaving just a handful behind to act as drovers on what would become a giant cattle ranch.
His success lay in convincing colleagues and successors of his core idea: that the systematic, reliable measurement of human populations, studied with increasingly powerful mathematical tools, could transform the way people and states did business.
In that work Graunt reduced life and death to data and, among much else, arrived at the first rigorous estimate of child mortality in England. Thirty-six percent of the nation’s children, he found, more than one out of three, would die before their sixth birthday.
King offered careful advice rather than proposing wholesale national transformations. For example, he used his analysis of the wealth of England and France to suggest, cautiously, that England under its new King William might not be able to afford the Nine Years’ War against Louis’s France. (He was right.)
As it matured, the branch of natural philosophy that sought to anticipate social outcomes faced a question that pure physics did not: not just to anticipate the future but to put a price on it.
To that catalog, add one more triumph: he was the first to create a rigorous, reliable way to put a price on a human life. “Comet” Halley can be seen, with only slight exaggeration, as the inventor of the mathematics of what we now call life insurance.
from Paris, Monsieur de la Quintinie’s “some further directions and observations about Melons,” which concludes with the still-sound advice to “trouble not your self to have big Melons, but good ones.”
When Justel died in 1693, Edmond Halley had a rummage through his papers. What he encountered in Neumann’s “curious Tables of the Bills of Mortality at the City of Breslaw” inspired him to apply his full powers of mathematical argument to fix the expectations for a human life, anywhere, at each moment between cradle and grave.
AS HALLEY DOVE into Neumann’s numbers he discovered within them this fact: the town was a sleepy place, quiet and rather insular. By the numbers, Breslau had very little interaction with the outside world: not many people left town, and few immigrated. Neumann’s accounts of deaths and births balance neatly, and the pattern of deaths by age remained basically constant across the five years of data.
The arithmetic was implacable: just 692 of the 1,238 children born each year—56 percent—survived to celebrate their seventh birthday. After the holocaust of infancy, Breslau’s children could persist in the reasonable hope that they would live to have babies of their own, as the death rate fell to roughly 6 percent through youth and young adulthood.
From this baseline, Halley came to the questions that allowed him to dissect the lives of strangers hundreds of miles distant. In a conventional exercise in Petty-style political arithmetic, he used Neumann’s figures to assess Breslau’s military potential.
instead of simply identifying patterns within Neumann’s numbers, Halley added the dimension of chance, of risk in the modern sense. What, he asked, should anyone bet on the odds of his or her survival for any given length of time?
Having established that it was possible to set the odds on when a life might end, Halley immediately asked how to apply mathematics to a measurement—Neumann’s observations—and answer the problem of setting not just the odds at any moment but how much a life was worth in time and in cash.
Halley’s dive into the seemingly mundane problem of insurance may seem surprising now, but he, like his Royal Society colleagues, pulled on his clothes each morning and walked out into the daylit world of people, places, and things—and turned his prepared mind to what he found there.
Attempts to insure England’s expanding seaborne wealth took shape over the seventeenth century, culminating in the founding of Edward Lloyd’s coffee shop in 1686. Lloyd catered to his seafaring clientele by offering shipping news updates regularly—which catalyzed the emergence of a marketplace in which shipowners and insurance underwriters could strike their bargains.
That’s what Halley set out to solve: what risk each of us—and hence our insurers—faces as each year passes, and, once that’s understood, how to take that knowledge to find out how much it should cost now to purchase a given payout when we do leave this earth.
when Halley calculated the price someone should pay now for a promise of money in the future, he was actually asking what mathematical relationship could connect an expectation that could come true years or decades down the road with a decision to be made in the here and now.
In other words: Halley’s calculations were among the first to examine risk in a financial transaction.
He had managed to connect the first result he had extracted from Neumann’s work, the odds or risk of dying over a given term, to a different equation, a compound interest calculation.
But—as Halley himself remarked—it was only with the mathematical discoveries of the preceding couple of generations that it had become possible to compute compounding quantities easily.
Translated into a different mathematical form, Halley’s manipulation of just five years of demographic records from a drowsy, distant town created the basic framework that could describe how much a payment now would be worth as an investment for the purchase of a policy for any number of years, based on an assumption of a given rate of return.
For all its insight, though, Halley’s actuarial work had very little impact on those in London’s new insurance industry.
It wasn’t until 1762 that the first London-based company to adjust premium payments by age opened its doors, thus just beginning to make use of Halley’s insights.
Instead, when it offered annuities—which can be understood (and modeled) as a kind of insurance—the Treasury made mistakes like charging the same price to a twenty-year-old buyer as to one who was fifty.
But even if the nascent business of gambling on lives was unready for the rigorous methods that Halley and others had developed, the thinking behind that work was diffusing through more and more minds over the last decades of the seventeenth century.
Once the Principia decisively demonstrated that nature obeys number, claims by people like Petty—and soon, Halley—that human nature must do so as well took on much greater force.
In those messages, Pepys sought Newton’s help to win a game of dice. Newton took the question very seriously, responding in a series of three letters over the next month that calculated specific answers for each of the three different scenarios Pepys proposed. To no one’s surprise, he got his sums right and showed that Pepys was a lousy gambler:
In 1670, in the midst of a series of subtle and difficult observations of optical phenomena, he faced the problem of experimental error: how to reduce the probability that his measurements missed the true value by more than a certain, acceptable amount of imprecision. His solution then was to perform experiments multiple times and to average the results to produce the strongest possible claim that what he had observed was real.
Except when, like Pepys, one could draw upon a true expert to help work out gambler’s odds, most of Newton and Halley’s contemporaries drew on the idea of systematic analysis of uncertainty but not on the evolving mathematics of such analysis.
By 1695, England had been at war with France for six years. Paying for an army in the field in Flanders was proving ever more difficult, to the point where the English faced a plausible risk of financial defeat, a surrender forced not by any triumph by Louis XIV’s soldiers but by simple lack of cash.
Individual insurance companies created their own firefighting teams, which led to times when a brigade would lay down their tools and let a house burn if it was discovered the property hadn’t bought protection.
One of the earliest specialized lines of insurance bought and sold at Lloyd’s was coverage of the slave trade, a reminder of the extent to which the early British Empire formed a transatlantic market in humans.
As a professor, Newton had been required to deliver just a single series of mathematical lectures once each year. At the Mint he became, in effect, the operations manager for what was almost certainly the largest metalworks in England.
The warden governed the mint’s physical plant, which is to say that officially, Professor Newton had to make sure the holes in the roof were patched, the horses were fed, and the machinery in the workshops was maintained in good running order. That formal list of duties wasn’t supposed to trouble the (presumptively) unworldly new warden. For the better part of a century, almost every incumbent had treated the post as a sinecure, leaving the actual work to deputies.
Newton ignored the precedent. He took his oath of office on May 2, and from that day forward his name appears constantly in Mint records. By midsummer, more or less by force of personality, he seized control of the Mint’s coining operation from the current master, the gambler, spendthrift, and speculator Thomas Neale.
William had led England into war with France in 1689. Now in its seventh year, that war showed no signs of coming to an end anytime soon. It was hugely expensive—so much so that the king reported that Parliament’s prior grants of “so many, and such large, Aids” had run out, and that “the Funds which have been given, have proved very deficient.”
it wasn’t just the price tag that bedeviled the English military effort. There was, William reminded Parliament, a more fundamental problem. The nation’s money was no good.
William hadn’t exaggerated. Shortly after Newton came to the Mint, he found that more than one in ten silver coins were counterfeit, while many of those that were genuine had been clipped down to far less than their legal silver content.
the money used for all daily exchange, the day-to-day business of the nation, contained less than half of the silver required to make up its face value. The danger was obvious and was being played out in markets and shops all over England: Who would willingly accept a shilling coin that contained less than a sixpence worth of precious metal?
Two fundamental causes had combined to rob England of its metal money. One emerged in 1662, when the Royal Mint installed the first machine-driven coin production line.
The newly mechanized mint produced beautiful money. As intended, the machine-inscribed edging made it extremely difficult to debase the currency by clipping or trimming coins—the process by which, by the 1690s, currency criminals had stolen roughly half of the metal originally minted into England’s coinage.
while skilled metalworkers could make passable fakes, it was, at least, much harder than before to do so, given the depth of the designs struck into each face of a coin. There was only one problem: older, handmade coins dating back to the reign of Queen Elizabeth and before remained legal tender.
And yet, by law, a misshapen, thin, underweight silver shilling with a barely legible portrait of James or Elizabeth was worth exactly the same as a shiny, bright, full-weight one struck on the new assembly line.
From the start, then, it made obvious sense for all those who laid hands on one of the newer coins to hoard it as a reserve of silver bullion and to spend only their stock of increasingly debased pre-1662 money.
As the decades passed, England grew ever more enmeshed in what was increasingly a global network of trade, and by the 1680s the exchange rate between silver and gold differed from place to place in Europe. Critically, if you melted down the silver in a full-weight, post-1662 English coin, it would buy more gold as bullion in Paris and Amsterdam than the face value of that coin would say it was, measured by the gold in English guineas.
A complaint by the goldsmiths’ guild in 1690 claimed that in just six months traders had sent 282,120 ounces of silver across the Channel, enough for about 10 percent of the total Mint production of the previous five years. Some of that weight might have come from candlesticks and silverware, but a parliamentary investigation confirmed that most of it had started out as the king’s coins, melted down and smuggled out.
THIS WAS GRESHAM’S Law—bad money drives out good—with a vengeance: clipped, underweight currency and fakes were literally driving the realm’s full-weight modern coinage out of the country.
At the height of the currency crisis, a golden guinea traded for about thirty silver shillings—one and a half pounds, and close to a month’s wages for those at the bottom of the working world. Meanwhile a pound of steak at Spitalfields market cost about three pennies, and a gallon of ale could be bought for a shilling or less. For a very rough analogue, imagine trying to get through a day with nothing smaller than thousand-dollar bills or five-hundred-pound notes (and no credit cards).
Without an adequate supply of small denominations, the silver coinage that was the engine of daily life, trade suffered and then almost stopped:
The Mint made nearly half a million pounds’ worth of silver currency between 1686 and 1690. But so much silver poured out of England in the next five years and so little bullion was available that between 1691 and 1695 the Mint made just a total of £17,000 in new silver coins.
