Infinitesimal

How a Dangerous Mathematical Theory Shaped the Modern World
Narrated by: Ira Rosenberg
Length: 12 hrs and 15 mins
Categories: History, European
4 out of 5 stars (101 ratings)

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Publisher's Summary

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.

©2014 Amir Alexander (P)2014 Audible Inc.

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  • Overall
    5 out of 5 stars
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    5 out of 5 stars

An Amazing Listen to intrigue and history. Highly recommended.

A fantastic review of political - mathematical - religious history. Presented so the layperson can understand and follow. The two concepts need to be clearly outlined or perhaps I need to review the text again.

Definitely worth listening to. The book brings sense to some of histories extreme views. It also provides understanding for the great advances in the scientific, political and religious areas.

Highly recommended.

3 people found this helpful

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    5 out of 5 stars

An intriguing and underappreciated bit of history

What made the experience of listening to Infinitesimal the most enjoyable?

The best part of any historical work is learning about the parts of history which are normally occluded by time.

What did you like best about this story?

The most fascinating part of the story was certainly its focus on lesser known, yet significant, people of history.

What three words best describe Ira Rosenberg’s voice?

Clear and well-enunciated

If you were to make a film of this book, what would the tag line be?

Sometimes the very small can have a very big effect.

4 people found this helpful

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Great Story

We always hear that Newton and Leibnitz invented calculus and that's a big over-simplification, although they deserve a lot of credit. This book tells the a big part of the story behind why it's not that simple in an entertaining way.

1 person found this helpful

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Good Math History

Infinitesimal may tell you more than you want to know. I suspect that the reviews give the book less than a 5.0 rating is that the book gives the Jesuits a very hard time for holding back math in Italy for at least 100 years by burning one person at the stake and confining Galileo to house arrest for the end of the life for believing that math could progress by considering small units of measurement that had no width. They intimidated many other mathematicians to silence less they suffer the same fate.

Had they stuck to religious matters, calculus may have been discovered a century earlier and in Italy.

The book is filled with an immense amount of detail. It tells of the problems of using geometric solutions as analogous to political solutions to political problems.

1 person found this helpful

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    1 out of 5 stars

Very little math but a lot right wing politics

The author has nothing nice to say about Levelers, Diggers, etc.... Its all violent anarchism and mobs. The English Revolution and Protestant reformation are just violent and dangerous interruptions of existing idyllic paradises. Neither the Catholic Church or the Anglican English King had any responsibility for the consequential revolutionary era, according to the Amir! Amir, which means King in Hebrew, pours almost half the book in the historical reconstruction of one of the most authoritarian criminal organizations in Human history the Jesuits. Not a word condemning their crimes both in the sciences and the masses they grievously injured.

It is no coincidence that the Nazi Propaganda Minister Joseph Goebbels had been a student of the Jesuits, and Heinrich Himmler was impressed by the Order's organisational structure.[5] Hitler wrote favourably of their influence on architecture and on himself in Mein Kampf. Not that this flavor of authoritarianism was NOT the only peddled by Amir. He went into a nauseating detail into the diseased mind of Thomas Hobbes, a second rate philosopher and first order misanthrope.

If Amir had spent the 80% book his wasted politely describing the repression of Infinitesimal instead on a purely mathematical discourse he could have achieved his thesis of showing how the Infinitesimal impacted the modern World positively. He does so only at the end of his book. with some paltry references. I am grateful that he did spend a little time on Wallace, by far the only part of this book that is worth anything.

However his mealy mouth objectivity regarding what are crimes in any historical context i.e. the repression of science and of free thinkers in all classes is unforgivable. Amir did not mention a word about the most virulent exposition of criminality by the Catholic Church in its systematic program in the repression of Human reasoning, i.e its burning alive of the great scientist Giordano Bruno.

Amir Alexander or King Alexander his name's sake writes like Hobbes for the benefit of his powerful and rich benefactors. There is no more profitable business then the business of lickspittling!!

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    5 out of 5 stars

much more than a history of mathematics

I was surprised by how quickly the narrative pulled me in. This was in no way a dry read/listen.

It not only does a fantastic job of clearly placing the fight over infinitesimals in the politics and turmoil of the day and the outcome of that fight in shaping the future of the western world, but was also an outstanding and enjoyable history lesson.

I definitely finished the book with a feeling of having been enriched by it, and went so far as to order a used copy in print for future reference.

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    4 out of 5 stars

A sprawling historic account of...

A sprawling historic account of an inflection point in the history of science and mathematics.

Amir Alexander tells the story of how the concept of the infinitesimal became a flash point for opposing personalities in the Catholic Church, then the English parliament. He does so in great detail, sometimes going on circumlocutious tangents to set the scene. The book is more for historians than for philosophers of science and mathematics. Still, if you have the patience, the stories he tells will leave you with a very different perspective on how powerful and contentious mathematical debates can be.

He contends that this conflict over infinitesimals helped to determine the cultural and technological fates of England and Italy. I am unsure about this hard to verify assertion. Still, there is no doubt for me that analysis is a deeply philosophical and not just logicomathematical concept.

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much more than mere math history

I wanted to learn about math history, but this was much more. it gave very good background for understanding that everything is entangeled relugion history politics power games and shamefully petty men.
worth listening even if you are not mathematically inclined. A must for math teachers.

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needs pictures

needs pictures to understand the diagrams that the author uses to describe the concepts. the second half is easier to understand.