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Defoe had been warning his fellow Britons about the perils of the Alley for almost three decades. Now, near midsummer, he was ready with his most desperate alarm yet, a pamphlet titled The Anatomy of Exchange Alley, written in the voice of “a jobber,” or unlicensed dealer in stocks.
The South Sea Company had opened for business in 1711. The firm had never really managed to do the work implied by its name, shipping goods and slaves to the Spanish ports of South America. Instead, it played in what was then just being born, a marketplace for credit, all the notes and bonds and much stranger inventions that the British government was using to build its ever-growing mountain of debt.
They proposed a heroic attempt at what we would now call financial engineering—taking the whole of the national debt, accumulated over a seemingly endless series of wars, and turning it into shares of a private company—theirs—which could be traded back and forth at will in the nascent stock exchange.
“Stock-jobb the nation.” That was the crux of Defoe’s polemic: schemes like this transformed the national debt—a public necessity—into a form that could be manipulated for private profit.
What would happen in Exchange Alley over the next year wasn’t simply the work of “a Trade founded in Fraud, born of Deceit, and nourished by Trick, Cheat, Wheedle, Forgeries, Falshoods.” The South Sea Bubble—the headlong rise and the sudden collapse of London’s nascent stock market—wasn’t the original sin of early modern capitalism—or rather, it was never only that.
The Bubble is a part of the history of finance but is not confined to it. Rather, it opens a window on the circumstances from which later financial thinking emerged: the grand shift over the preceding century in the way human beings understood their experience of the material world, an intellectual transformation better known as the scientific revolution.
those who solved problems of planetary motion or the flight of cannonballs did not confine themselves to natural philosophy. From the beginning, they used the same methods and habits of mind to tackle human questions, to guide the choices made by individuals and societies.
On August 7, the College of the Holy and Undivided Trinity acknowledged the obvious and decided to pay its members an allowance whether or not they remained in residence after that date.
The more things change
Newton’s definitive biographer, Richard Westfall, points out that the program for the work to come was laid down in 1664, when Newton, just twenty-one, was still enrolled at Trinity College. That’s when he first dove into the mathematical inquiries that would dominate his first several months back home, and when he produced an extraordinary series of forty-five queries in which he grappled with fundamental issues of time, matter, motion, and much more.
The study of curves was a central fascination of seventeenth-century mathematics, and Newton had plunged into the field when he read a translation of René Descartes’s Geometry a year before the plague hit.
Even though Cartesian coordinates offered a new and powerful way of representing equations as shapes on his coordinate system, many of Newton’s contemporaries saw such equations as a property of a given figure, a line or a circle or some more complicated form. But it took Newton just a few months after encountering Descartes to realize, as his biographer, Richard Westfall reports, “The equation is more basic than the curve; the equation defines, or as Newton put it, expresses the nature of the curve.”
Newton’s insight—starting first with the equation, rather than the shape—was foundational because it would, first hesitantly and then through centuries of development, yield a new way of seeing the world through mathematics.
The interpretation that Newton would develop focused on arguably the most important implication: equations describe the evolution of a system—how its solutions build a picture on a page.
Seventeenth-century attempts to analyze more complicated expressions often employed a particular mathematical tool, the infinite series—endless sequences of terms (for example, 1, ½, ¼, ⅛…and so on).
As he played with his series, he noticed that in some of them each step in the calculation added a smaller and smaller amount to the total. Extending the operation by hand—row after row of numbers, a strangely beautiful triangle, growing across the page—produced a better and better fit to the ultimate answer. The endpoint, well beyond the stamina of even so heroic a numbers-cruncher as Newton, was obvious: the last terms in such series must dwindle toward nothing.
In one case, Newton wanted to be able to identify how much a curve was curving at any point: how steep it might be, and how that steepness—Newton called it “the crookedness in lines”—changed at each point along the figure. Here, he used infinitesimals to produce a straight line whose slope could be calculated and that touched the curve at just that one point and no other—what’s called a tangent.
every curve was a map of motion, a mathematician’s travelogue. A point travels through space, and its trail, its trace, creates the stuff of geometry.
His breakthrough came when he realized that his two seemingly separate questions—how a curve bends and how much of the Cartesian plane it encloses—are actually twin faces of the same problem.
Newton never underestimated his own powers. He had to have grasped the importance of his accomplishment in those few months of enforced seclusion on his farm. Yet for most of the next two decades, he kept this new mathematical insight almost entirely to himself.
This much is true: the tree itself was real. After his death, the original at Woolsthorpe was still known in the neighborhood as Sir Isaac’s tree.
He calculated the strength of the so-called centrifugal force that should be hurling us into space. He put together that number with a rough approximation for the earth’s size—a number refined over the previous two centuries of European exploration by sea. Taken together, that was enough information to estimate the outward acceleration experienced at the surface of a revolving earth—how strongly any of us are being pushed out into space.
That result, at once imprecise and spectacular, would also have placed Newton in the vanguard of European natural philosophy if only anyone had heard about it. He was not yet fixed in his habit of silence, a determination reached a few years later, after a few bruising exchanges with other learned men. But isolated on his farm, he remained focused on the work at hand, applying his almost daily expanding mathematical skill to physical questions.
The insight was there, but his first attempt to write down the mathematics of gravity wasn’t quite right; he would arrive at his famous “universal law of gravitation” only in the mid-1680s. But the apple (if Newton’s late-in-life tale is to be believed) did give him the critical piece of the puzzle: laws of nature are universal.
For example, in the early 1660s he wanted to know how the shape of the human eye might affect the perception of color. To find out, he turned to the nearest experimental subject, himself, and stuck a bodkin—a blunt needle—into the bottom of his eye socket and levered up.
By mid-March 1666 the city of Cambridge marked six weeks without a single plague death. The university reopened, and Newton returned to his rooms on or around March 20. Then, on Wednesday, June 6, Jane Ellingworth, a seamstress living on Penny Farthing Lane, felt poorly. Her father brought her a cup of ale and urged her to bed. She died the next day. The infection spread, with deaths reaching double digits in the city within two weeks.
SOUNDS FAMILIAR
So were 87 out of the city’s 109 churches, including old St. Paul’s Cathedral. When that giant building caught fire, the tons of lead in its roof melted, creating a river of liquid metal flowing into the Thames.
As early as 1664, for example, before he plunged into the question of gravitation, he laid out a geometrical approach for calculating compound interest—his first contribution to the mathematics of money.
William Petty lived the cliché: he was a genuine Renaissance man. By the time he reached his thirties he had been a music professor, an anatomist—a physician eager to dissect more or less any mammal that came his way—and a more than competent chemist. He was a constant inventor, turning his hand to everything from farm implements to ship design. Mathematics was an early love, and he had a gift for practical calculations. That would prove the skill that would make him rich, through his work as Ireland’s first comprehensive geographer.
Where Newton focused on the analysis of matter in motion, Petty aimed “to have understood passions as well as fermentations”—human feeling as much as any natural process. But, he emphasized, his program was to be as rigorous as any purely physical inquiry.
Here, fortunate ill-fortune intervened. No natural sailor, he broke his leg aboard and was turned ashore at the Norman port city of Caen. The Jesuits of the University of Caen took him in and exposed him to some of the new, humanistic learning then spreading across Europe.
Charles tried and failed more than once to import Irish soldiers to aid him against Oliver Cromwell’s New Model Army, Parliament’s military force. With the king’s final defeat and execution on January 30, 1649, the victors saw in the Confederation a rebellious province that had, more or less, lined up with the losers.
Cromwell invaded seven months after the king’s death, landing at Dublin on August 15, 1649. It was a bloody, brutal campaign. After his first major victory, the capture of Drogheda, two thousand Irish Royalist soldiers were executed, an atrocity followed by a general massacre of both combatants and civilians at Wexford.
The soldiers who did the actual fighting went without pay, and the same went for the army’s suppliers—to whom were added the so-called adventurers, those bold souls who were willing to lend money to the new English government. In return they received the promise of…Ireland, almost all of it, to be taken from Catholic landowners along with anyone else who had chosen the wrong side during the Civil War.
This “Civil Survey” was widely believed to be inaccurate at best, and, by the end of 1654, thousands of trained men with guns remained without their promised reward.
Petty offered to measure everything: the whole of Ireland, its ownership, its geography, all of its “rivers, mountains, ridges, rocks, sloughs and bogs,” along with the houses, barns, fences, and all the rest that made up the island’s real property.
The work itself was trickier than anticipated, as the patchwork of tiny landholdings found in many districts demanded more fine-grained and hence more time-consuming cartography than Petty had expected.
It would take until 1659 to fill in the last corners in the far west, but the Dublin authorities began handing land to soldiers by the middle of 1655, less than half a year after what came to be called the Down Survey had begun. Its maps do not, of course, measure the human misery that flowed from their information.
In 1641, Catholics had owned 60 percent of Ireland. By the end of the century, Irish Catholic ownership of Irish land had fallen to just over 20 percent, and in another fifty years less than 5 percent remained in Catholic hands.
That outcome was, of course, the point of Petty’s masterwork. He delivered what he’d promised: a blueprint for what was in essence a form of ethnic cleansing.
The human cost of the Down Survey capped a decade-long demographic catastrophe that killed as many as one of every three Irish men, women, and children.
He would later calculate that half a million Irish men, women, and children had lost their lives as a direct or indirect result of the years of war, “for whose Blood some body should answer both to God and the King.” But he accepted no reproach for his part in separating the survivors from their property.
The lesson Petty drew from his Irish experience was that applying formal rigor to observation and measurement—the same concept his London circle of virtuosos had begun to explore—actually worked in the real world.
The final result rendered all the prolific variety of a landscape into a form—maps—that could be read by anyone. Most important, the Down Survey caught the same kind of insight Newton would later capture to transform natural science. It combined observation with numbers.
To casual observers, London’s community of virtuosos in the first years of the restored Stuart monarchy were heroic talkers but seemingly little more than that.
In these first years at the Royal Society, Petty began to look to the future in order to find a way of analyzing social life much more broadly that would enable him to predict—and shape—political outcomes over time.
At its simplest, Petty’s political arithmetic was an exercise in applied demographics.
His most extensive attempts to apply political arithmetic in the real world landed—unsurprisingly—on the luckless Irish. Over the last two decades of his life he would produce a variety of plans intended to secure English control of Ireland (and his own interests as an Irish landowner), torquing his analysis in response to the tangled politics after the restoration of the Stuart dynasty.
In this early version of his arithmetic applied to people, that meant proposing a change to who lived in Ireland as a way to make the territory more productive and its people less restive. He wrote, “If an exchange was made of but about 200,000 Irish and the like number of English brought over in their rooms, then the natural strength of the British would be equal to that of the Irish,” which would mean, Petty added, that “the Irish would never stir upon a National or Religious Account,” while the like number of Irish who were shifted across the Irish Sea would be far outnumbered by the
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So ethnic cleansing
Petty’s approach wouldn’t offer what we would recognize as a measure of gross domestic product in anything like a modern calculation, but it is recognizably an ancestor to such national accounting.
Fifteen years later, Isaac Newton would publish his great account of celestial motion. It’s easy to exaggerate the connection with Petty’s attempt to quantify economics and politics, certainly—but the resonance between them is no mere coincidence either.
