Infinitesimal : how a dangerous mathematical theory shaped by Amir Alexander PDF

By Amir Alexander

ISBN-10: 0374176817

ISBN-13: 9780374176815

ISBN-10: 0374534993

ISBN-13: 9780374534998

"The epic conflict over a mathematical idea that shook the outdated order and formed the area as we all know it. On August 10, 1632, 5 leaders of the Society of Jesus convened in a somber Roman palazzo to cross judgment on an easy notion: non-stop line consists of specific and limitlessly tiny components. The doctrine could develop into the basis of calculus, yet on that fateful day the judges governed that it was

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Takes us from the bloody spiritual strife of the 16th century to the battlefields of the English civil conflict and the fierce confrontations among top thinkers like Galileo and Hobbes. This Read more...

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Additional info for Infinitesimal : how a dangerous mathematical theory shaped the modern world

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Mathematical Order 3. Mathematical Disorder 4. “Destroy or Be Destroyed”: The War on the Infinitely Small 5. The Battle of the Mathematicians PART II: LEVIATHAN AND THE INFINITESIMAL 6. The Coming of Leviathan 7. Thomas Hobbes, Geometer 8. Who Was John Wallis? 9. Mathematics for a New World Epilogue: Two Modernities Dramatis Personae Time Line Notes Acknowledgments Index Also by Amir Alexander A Note About the Author Copyright No continuous thing is divisible into things without parts. —ARISTOTLE Introduction A COURTIER ABROAD In the winter of 1663 the French courtier Samuel Sorbière was presented at a meeting of the newly founded scientific academy, the Royal Society of London.

For instance, if a line is composed of indivisibles, how many and how big are they? One possibility is that there is a very large number of such points in a line, say a billion billion indivisibles. In that case, the size of each indivisible is a billion-billionth of the original line, which is indeed a very small magnitude. The problem is that any positive magnitude, even a very small one, can always be divided. ” That means that our supposed indivisibles are, in fact, divisible after all, and our initial supposition that they are the irreducible atoms of the continuous line is false.

The reason was that much more was at stake than an obscure mathematical concept: The fight was over the face of the modern world. Two camps confronted each other over the infinitesimal. On the one side were ranged the forces of hierarchy and order—Jesuits, Hobbesians, French royal courtiers, and High Church Anglicans. They believed in a unified and fixed order in the world, both natural and human, and were fiercely opposed to infinitesimals. On the other side were comparative “liberalizers” such as Galileo, Wallis, and the Newtonians.

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Infinitesimal : how a dangerous mathematical theory shaped the modern world by Amir Alexander

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