Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World

"The epic battle over a mathematical concept that shook the old order and shaped the world as we know it. On August 10, 1632, five leaders of the Society of Jesus convened in a somber Roman palazzo to pass judgment on a simple idea: that a continuous line is composed of distinct and limitlessly tiny parts. The doctrine would become the foundation of calculus, but on that fateful day the judges ruled that it was forbidden. With the stroke of a pen they set off a war for the soul of the modern world. Amir Alexander's Infinitesimal is the story of the struggle that pitted Europe's entrenched powers against voices for tolerance and change. It takes us from the bloody religious strife of the sixteenth century to the battlefields of the English civil war andthe fierce confrontations between leading thinkers like Galileo and Hobbes. We see how a small mathematical disagreement became a contest over the nature of the heavens and the earth: Was the world entirely known and ruled by a divinely sanctioned rationality and hierarchy? Or was it a vast and mysterious place, ripe for exploration? The legitimacy of popes and kings, as well as our modern beliefs in human liberty and progressive science, hung in the balance; the answer hinged on the infinitesimal. Pulsing with drama and excitement, Infinitesimal will forever change the way you look at a simple line--and celebrates the spirit of discovery, innovation, and intellectual achievement"--

Autorentext

Amir Alexander

Klappentext

*Pulsing with drama and excitement, *Infinitesimal celebrates the spirit of discovery, innovation, and intellectual achievement-and it will forever change the way you look at a simple line.

On August 10, 1632, five men in flowing black robes convened in a somber Roman palazzo to pass judgment on a deceptively simple proposition: that a continuous line is composed of distinct and infinitely tiny parts. With the stroke of a pen the Jesuit fathers banned the doctrine of infinitesimals, announcing that it could never be taught or even mentioned. The concept was deemed dangerous and subversive, a threat to the belief that the world was an orderly place, governed by a strict and unchanging set of rules. If infinitesimals were ever accepted, the Jesuits feared, the entire world would be plunged into chaos.

In Infinitesimal, the award-winning historian Amir Alexander exposes the deep-seated reasons behind the rulings of the Jesuits and shows how the doctrine persisted, becoming the foundation of calculus and much of modern mathematics and technology. Indeed, not everyone agreed with the Jesuits. Philosophers, scientists, and mathematicians across Europe embraced infinitesimals as the key to scientific progress, freedom of thought, and a more tolerant society. As Alexander reveals, it wasn't long before the two camps set off on a war that pitted Europe's forces of hierarchy and order against those of pluralism and change.

The story takes us from the bloody battlefields of Europe's religious wars and the English Civil War and into the lives of the greatest mathematicians and philosophers of the day, including Galileo and Isaac Newton, Cardinal Bellarmine and Thomas Hobbes, and Christopher Clavius and John Wallis. In Italy, the defeat of the infinitely small signaled an end to that land's reign as the cultural heart of Europe, and in England, the triumph of infinitesimals helped launch the island nation on a course that would make it the world's first modern state.

From the imperial cities of Germany to the green hills of Surrey, from the papal palace in Rome to the halls of the Royal Society of London, Alexander demonstrates how a disagreement over a mathematical concept became a contest over the heavens and the earth. The legitimacy of popes and kings, as well as our beliefs in human liberty and progressive science, were at stake-the soul of the modern world hinged on the infinitesimal.

Inhalt

Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Part I: The War Against Disorder:
The Jesuits Against the Infinitely Small

1. The Children of Ignatius.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2. Mathematical Order.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3. Mathematical Disorder.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4. "Destroy or Be Destroyed": The War on the Infinitely Small.. . . . 118
5. The Battle of the Mathematicians.. . . . . . . . . . . . . . . . . . . . . . . . . . 150

Part II: Leviathan and the Infinitesimal

6. The Coming of Leviathan. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
7. Thomas Hobbes, Geometer.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
8. Who Was John Wallis?.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
9. Mathematics for a New World.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260

Epilogue: Two Modernities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293