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Infinitesimal (Englisch) Gebundene Ausgabe – 1. Mai 2014

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Produktinformation

Produktbeschreibungen

Pressestimmen

You probably don't think of the development of calculus as ripe material for a political thriller, but Amir Alexander has given us just that in "Infinitesimal." "Jordan Ellenberg, The Wall Street Journal"

Packed with vivid detail and founded on solid scholarship, ["Infinitesimal"] is both a rich history and a gripping page turner. "Jennifer Ouellette, The New York Times Book Review"

[A] finely detailed, dramatic story. "John Allen Paulos, The New York Times"

Alexander pulls off the impressive feat of putting a subtle mathematical concept centre stage in a ripping historical narrative . . . this is a complex story told with skill and verve, and overall Alexander does an excellent job . . . There is much in this fascinating book. "Times Higher Education"

A triumph. "Nature"

Every page of this book displays Alexander's passionate love of the history of mathematics. He helps readers refigure problems from over the centuries with him, creating pleasurable excursions through Euclid, Archimedes, Galileo, Cavalieri, Torricelli, Hobbes, and Wallis while explaining how seemingly timeless and abstract problems were deeply rooted in different worldviews. "Infinitesimal "captures beautifully a world on the cusp of inventing calculus but not quite there, struggling with what might be lost in the process of rendering mathematics less certain and familiar. "Paula E. Findlen, The Chronicle of Higher Education"

With a sure hand, Mr. Alexander links mathematical principles to seminal events in Western cultural history, and has produced a vibrant account of a disputatious era of human thought, propelled in no small part by the smallest part there is. "Alan Hirshfeld, The Wall Street Journal"

"Infinitesimal" is a gripping and thorough history of the ultimate triumph of [a] mathematical tool . . . If you are fascinated by numbers, "Infinitesimal "will inspire you to dig deeper into the implications of the philosophy of mathematics and of knowledge. "New Scientist"

Brilliantly documented . . . Alexander shines . . . the story of the infinitesimals is fascinating. "Owen Gingerich, The American Scholar"

Back in the 17th century, the unorthodox idea [of infinitesimals], which dared to suggest the universe was an imperfect place full of mathematical paradoxes, was considered dangerous and even heretical . . . Alexander puts readers in the middle of European intellectuals' public and widespread battles over the theory, filling the book's pages with both formulas and juicy character development. "Bill Andrews, Discover"

In "Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World," Amir Alexander successfully weaves a gripping narrative of the historical struggle over the seemingly innocuous topic of infinitesimals. He does an excellent job exploring the links between the contrasting religious and political motivations that lead to acceptance or refusal of the mathematical theory, skillfully breathing life into a potentially dry subject. "Infinitesimal "will certainly leave its readers with a newfound appreciation for the simple line, occasion for such controversy in the emergence of modern Europe. "Emilie Robert Wong, The Harvard Book Review"

Fluent and richly informative "Jonathan Ree, Literary Review (UK)"

Alexander tells this story of intellectual strife with the high drama and thrilling tension it deserves, weaving a history of mathematics through the social and religious upheavals that marked much of the era . . .The author navigates even the most abstract mathematical concepts as deftly as he does the layered social history, and the result is a book about math that is actually fun to read. A fast-paced history of the singular idea that shaped a multitude of modern achievements. "Kirkus (starred review)"

[Infinitesimal] gives readers insight into a real-world Da Vinci Code like intrigue with this look at the history of a simple, yet pivotal, mathematical concept . . . Alexander explores [a] war of ideas in the context of a world seething with political and social unrest. This in-depth history offers a unique view into the mathematical idea that became the foundation of our open, modern world. "Publishers Weekly"

A bracing reminder of the human drama behind mathematical formulas. "Bryce Christensen, Booklist"

A gripping account of the power of a mathematical idea to change the world. Amir Alexander writes with elegance and verve about how passion, politics, and the pursuit of knowledge collided in the arena of mathematics to shape the face of modernity. A page-turner full of fascinating stories about remarkable individuals and ideas, Infinitesimal will help you understand the world at a deeper level. "Edward Frenkel, Professor of Mathematics, University of California, Berkeley, and author of Love and Math"

In this fascinating book, Amir Alexander vividly re-creates a wonderfully strange chapter of scientific history, when fine-grained arguments about the foundations of mathematical analysis were literally matters of life and death, and fanatical Jesuits and English philosophers battled over the nature of geometry, with the fate of their societies hanging in the balance. You will never look at calculus the same way again. "Jordan Ellenberg, Professor of Mathematics, University of Wisconsin Madison, and author of How Not to Be Wrong"

You may find it hard to believe that illustrious mathematicians, philosophers, and religious thinkers would engage in a bitter dispute over infinitely small quantities. Yet this is precisely what happened in the seventeenth century. In Infinitesimal, Amir Alexander puts this fascinating battle in historical and intellectual context. "Mario Livio, astrophysicist, Space Telescope Science Institute, and author of Brilliant Blunders"

With considerable wit and unusual energy, Amir Alexander charts the great debate about whether mathematics could be reduced to a rigorous pattern of logical and orderly deductions or whether, instead, it could be an open-ended and exciting endeavor to explore the world's mysteries. Infinitesimal shows why the lessons of mathematics count so much in the modern world. "Simon Schaffer, Professor of the History of Science, University of Cambridge"

In Infinitesimal, Amir Alexander offers a new reading of the beginning of the modern period in which mathematics plays a starring role. He brings to life the protagonists of the battle over infinitesimals as if they were our contemporaries, while preserving historical authenticity. The result is a seamless synthesis of cultural history and storytelling in which mathematical concepts and personalities emerge in parallel. The history of mathematics has rarely been so readable. "Michael Harris, Professor of Mathematics, Columbia University and Universite Paris Diderot"

We thought we knew the whole story: Copernicus, Galileo, the sun in the center, the Church rushing to condemn. Now this remarkable book puts the deeply subversive doctrine of atomism and its accompanying mathematics at the heart of modern science. "Margaret C. Jacob, Distinguished Professor of History, University of California, Los Angeles""

-You probably don't think of the development of calculus as ripe material for a political thriller, but Amir Alexander has given us just that in Infinitesimal.- --Jordan Ellenberg, The Wall Street Journal

-Packed with vivid detail and founded on solid scholarship, [Infinitesimal] is both a rich history and a gripping page turner.- --Jennifer Ouellette, The New York Times Book Review

-[A] finely detailed, dramatic story.- --John Allen Paulos, The New York Times

-Alexander pulls off the impressive feat of putting a subtle mathematical concept centre stage in a ripping historical narrative . . . this is a complex story told with skill and verve, and overall Alexander does an excellent job . . . There is much in this fascinating book.- --Times Higher Education

-A triumph.- --Nature

-Every page of this book displays Alexander's passionate love of the history of mathematics. He helps readers refigure problems from over the centuries with him, creating pleasurable excursions through Euclid, Archimedes, Galileo, Cavalieri, Torricelli, Hobbes, and Wallis while explaining how seemingly timeless and abstract problems were deeply rooted in different worldviews. Infinitesimal captures beautifully a world on the cusp of inventing calculus but not quite there, struggling with what might be lost in the process of rendering mathematics less certain and familiar.- --Paula E. Findlen, The Chronicle of Higher Education

-With a sure hand, Mr. Alexander links mathematical principles to seminal events in Western cultural history, and has produced a vibrant account of a disputatious era of human thought, propelled in no small part by the smallest part there is.- --Alan Hirshfeld, The Wall Street Journal

-Infinitesimal is a gripping and thorough history of the ultimate triumph of [a] mathematical tool . . . If you are fascinated by numbers, Infinitesimal will inspire you to dig deeper into the implications of the philosophy of mathematics and of knowledge.- --New Scientist

-Brilliantly documented . . . Alexander shines . . . the story of the infinitesimals is fascinating.- --Owen Gingerich, The American Scholar

-Back in the 17th century, the unorthodox idea [of infinitesimals], which dared to suggest the universe was an imperfect place full of mathematical paradoxes, was considered dangerous and even heretical . . . Alexander puts readers in the middle of European intellectuals' public and widespread battles over the theory, filling the book's pages with both formulas and juicy character development.- --Bill Andrews, Discover

-In Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World, Amir Alexander successfully weaves a gripping narrative of the historical struggle over the seemingly innocuous topic of infinitesimals. He does an excellent job exploring the links between the contrasting religious and political motivations that lead to acceptance or refusal of the mathematical theory, skillfully breathing life into a potentially dry subject. Infinitesimal will certainly leave its readers with a newfound appreciation for the simple line, occasion for such controversy in the emergence of modern Europe.- --Emilie Robert Wong, The Harvard Book Review

-Fluent and richly informative- --Jonathan Ree, Literary Review (UK)

-Alexander tells this story of intellectual strife with the high drama and thrilling tension it deserves, weaving a history of mathematics through the social and religious upheavals that marked much of the era . . .The author navigates even the most abstract mathematical concepts as deftly as he does the layered social history, and the result is a book about math that is actually fun to read. A fast-paced history of the singular idea that shaped a multitude of modern achievements.- --Kirkus (starred review)

-[Infinitesimal] gives readers insight into a real-world Da Vinci Code-like intrigue with this look at the history of a simple, yet pivotal, mathematical concept . . . Alexander explores [a] war of ideas in the context of a world seething with political and social unrest. This in-depth history offers a unique view into the mathematical idea that became the foundation of our open, modern world.- --Publishers Weekly

-A bracing reminder of the human drama behind mathematical formulas.- --Bryce Christensen, Booklist

-A gripping account of the power of a mathematical idea to change the world. Amir Alexander writes with elegance and verve about how passion, politics, and the pursuit of knowledge collided in the arena of mathematics to shape the face of modernity. A page-turner full of fascinating stories about remarkable individuals and ideas, Infinitesimal will help you understand the world at a deeper level.- --Edward Frenkel, Professor of Mathematics, University of California, Berkeley, and author of Love and Math

-In this fascinating book, Amir Alexander vividly re-creates a wonderfully strange chapter of scientific history, when fine-grained arguments about the foundations of mathematical analysis were literally matters of life and death, and fanatical Jesuits and English philosophers battled over the nature of geometry, with the fate of their societies hanging in the balance. You will never look at calculus the same way again.- --Jordan Ellenberg, Professor of Mathematics, University of Wisconsin-Madison, and author of How Not to Be Wrong

-You may find it hard to believe that illustrious mathematicians, philosophers, and religious thinkers would engage in a bitter dispute over infinitely small quantities. Yet this is precisely what happened in the seventeenth century. In Infinitesimal, Amir Alexander puts this fascinating battle in historical and intellectual context.- --Mario Livio, astrophysicist, Space Telescope Science Institute, and author of Brilliant Blunders

-With considerable wit and unusual energy, Amir Alexander charts the great debate about whether mathematics could be reduced to a rigorous pattern of logical and orderly deductions or whether, instead, it could be an open-ended and exciting endeavor to explore the world's mysteries. Infinitesimal shows why the lessons of mathematics count so much in the modern world.- --Simon Schaffer, Professor of the History of Science, University of Cambridge

-In Infinitesimal, Amir Alexander offers a new reading of the beginning of the modern period in which mathematics plays a starring role. He brings to life the protagonists of the battle over infinitesimals as if they were our contemporaries, while preserving historical authenticity. The result is a seamless synthesis of cultural history and storytelling in which mathematical concepts and personalities emerge in parallel. The history of mathematics has rarely been so readable.- --Michael Harris, Professor of Mathematics, Columbia University and Universite Paris Diderot

-We thought we knew the whole story: Copernicus, Galileo, the sun in the center, the Church rushing to condemn. Now this remarkable book puts the deeply subversive doctrine of atomism and its accompanying mathematics at the heart of modern science.- --Margaret C. Jacob, Distinguished Professor of History, University of California, Los Angeles

Über den Autor und weitere Mitwirkende

Amir Alexander teaches history at UCLA. He is the author of Geometrical Landscapes and Duel at Dawn. His work has been featured in Nature, The Guardian, and other publications. He lives in Los Angeles, California.

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9 von 9 Kunden fanden die folgende Rezension hilfreich
4.0 von 5 Sternen A Deeply Divisive Debate about Reality 31. August 2014
Von H. J. Spencer PhD, renegade-Physicist - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe Verifizierter Kauf
This book is much more than an esoteric history of an area of mathematics. It tracks the ancient rivalry between ‘rationalists’ and ‘empiricists’. The dominant rationalists have always believed that human minds (at least those possessed by educated intellectuals) are capable of understanding the world purely by thought alone. The empiricists acknowledge that reality is far too complicated for humans to just guess its detailed structures. This is not simply an esoteric philosophical distinction but the difference in fundamental world-views that have deeply influenced the evolution of western civilization. In fact, rationalist intellectuals have usually looked to the logical perfection of mathematics as a justification for the preservation of religion and hierarchical social structures. In particular, the rationalists have raised the timeless, unchanging mathematical knowledge, represented by Euclidean geometry, as not just the only valid form of symbolic knowledge but as the only valid model of the logic of “proof”.

In particular, this book focuses on the battle between the reactionaries (e.g. Jesuits and Hobbes), who needed a model of timeless perfection to preserve their class-based religious and social privileges and reality-driven modernists, like Galileo and Bacon. The core of the disagreement was over the nature of the continuum, which was based on Euclid’s definition of a line as an infinite number of points. This intellectual argument implicitly links back to reality: is matter made of distinct atoms with empty space between them or are there no gaps between continuous matter? Although the model of the reactionaries was always Euclid's geometry, they never recognized they were only dealing with unreal definitions, as they faked out their arguments with appeals to 'real' lines etc. As such, they vigorously rejected the new concept of "indivisibles" (or "infinitesimals", the roots of calculus) and all ideas that were grounded in empirical studies of reality (like physics and the atomic hypothesis). Failure to admit debate about reality led Italy back into the Dark Ages while Northern Europe set off on the course of modernism.

As other reviewers have noted, this book would have benefitted quite a bit by including the story of the rivalry between Leibniz and Newton, who are usually credited with the invention of the calculus. As this book shows, this 17th Century rivalry had much older roots. Indeed, the book could also have been improved by establishing this acrimonious debate back in Classical Greece, where the atomic model, first proposed by Democritus, was immediately seen as an atheistic proposal that threatened traditional religion. The modern reader might assume that science has now firmly voted for the atomic model but the extensive use of the calculus embedded in Quantum Physics has preserved the conceptual features of the continuum advocates, so that we are now faced with the paradox of waves and particles. None-the-less, even readers with minimal competence in mathematics will enjoy discovering how this tiny idea of the infinitely small punctured an ancient dream: that the world is a perfectly rational place that is governed by strict mathematical rules.
4 von 4 Kunden fanden die folgende Rezension hilfreich
4.0 von 5 Sternen Fascinating but overdrawn 23. Juni 2016
Von Matt Young - Veröffentlicht auf Amazon.com
Format: Kindle Edition Verifizierter Kauf
I like the book, though I found it a bit overlong and sometimes redundant. Further, I suspect that the author may have the cart before the horse in thinking that failure to study infinitesimals stultified Italy, rather than the other way round. Also, I sometimes found the going hard because the author failed to distinguish between an infinitesimal and an indivisible. Nevertheless, it was fascinating to learn that the Jesuits opposed the study of infinitesimals on theological grounds whereas in northern Europe – Protestant countries – the concept was generally accepted and led to development of calculus. I had no idea that Thomas (nasty, brutish, and short) Hobbes had so vigorously opposed the concept of infinitesimals, and perhaps more surprisingly I had never heard of John Wallis, who was sort of the hero of the book and vigorously defended the concept of infinitesimals in England (and invented the symbol for infinity). Indeed, unless Alexander is exaggerating, it appears that without Wallis, Newton would not have developed the calculus. Nevertheless, I find it very hard to believe that England prospered and Italy stagnated simply because England developed mathematics and Italy did not.
57 von 63 Kunden fanden die folgende Rezension hilfreich
3.0 von 5 Sternen A Brief History of the Jesuits and Infinitesimals That Needs Editing 7. Mai 2014
Von Steven R. Staton - Veröffentlicht auf Amazon.com
Format: Kindle Edition Verifizierter Kauf
This book is a quick read, and it seriously could be pared down with some editing. I found the repetition of the thesis to be tedious (e.g. the Jesuits suppressed the mathematics of the Infinitesimal because it clashed with their dogma) and really wish this book be edited to get to the point (pun intended) without having to circle around and repeat ideas that were introduced and examined with a fine tooth comb already. The details are fine, but the reiteration of the information was really off-putting.

I was also surprised that the story ends abruptly *before* Newton, when the mathematical world really took off thanks to the math of the infinite and continuous (i.e. the Calculus). There is a lot of mathematical history that would have added meat to this story starting in the late 1670's that simply isn't there (never mind the epic battle between Newton and Leibniz).

This story is richer than the book eludes to and I would strongly recommend that the author consider a second edition that had less repetition of plot and more history (especially post 1660) of this branch of mathematics. It's a shame that the e-book cannot include interactive diagrams of the key geometric proofs from Hobbes and the Italians, too.
2 von 2 Kunden fanden die folgende Rezension hilfreich
4.0 von 5 Sternen The intersection of mathematics, religion, the scientific method and philosophy 28. Juni 2014
Von Richard - Veröffentlicht auf Amazon.com
Format: Kindle Edition Verifizierter Kauf
The author has succeeded in writing a compelling account of how the work of brilliant 17th century mathematicians provoked conflicts of great cultural significance within the Catholic Church. He also explains with clarity how these conflicts had relevance to the reformation and the evolution of European political entities. The profiles of individual actors in mathematics and the Church are fascinating although it can be challenging to follow the large number of Italian names and places.

The underlying mathematical theory of indivisibles, which was the cornerstone of the conflict, the forerunner of calculus and perhaps even atomic physics, is explained with enough clarity that most readers without a background in math will readily understand it. I enjoyed reading Infinitesimal as a brilliant history of religion, science and philosophy as they interacted 350 years ago, a glimpse of mathematical genius and a multifaceted biography of extraordinary people.
3.0 von 5 Sternen Interesting…so far as it goes 18. Dezember 2016
Von Nicholas Wheeler - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe Verifizierter Kauf
The author writes very interestingly about the religious and political positions with regard to---of all things!--the nature of the continuum that in 17th century Italy and England impeded the development of the calculus, and about the oddly-motivated positions taken by Gallileo and John Wallis that ultimately broke that barrier. But, though a portrait of Newton adorns the dust jacket, he has strangely little to say about the final chapter (Fermat, Newton, Leibniz) of his story, or about any of the other important mathematics that was gong on during the centuries in question. Promotes the view that mathematical developments are culturally determined, which is surely only part of the story.
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