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Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World (Anglais) Relié – 1 mai 2014

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On August 10, 1632, five leading Jesuits convened in a sombre 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 takes us from the bloody religious strife of the sixteenth century to the battlefields of the English civil war and the fierce confrontations between leading thinkers like Galileo and Hobbes. 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.

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Couverture | Copyright | Table des matières | Extrait | Index | Quatrième de couverture
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Commentaires client les plus utiles sur (beta) 70 commentaires
42 internautes sur 46 ont trouvé ce commentaire utile 
A Brief History of the Jesuits and Infinitesimals That Needs Editing 7 mai 2014
Par Steven R. Staton - Publié sur
Format: Format Kindle Achat vérifié
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.
30 internautes sur 32 ont trouvé ce commentaire utile 
Misleading... 4 juillet 2014
Par Timothy Haugh - Publié sur
Format: Relié
As a math teacher, I’m often on the lookout for books that will help my students make connections between math and its importance, whether that be practical or historical. As I was teaching AP Calculus this year, Prof. Alexander’s book drew my attention. I was hoping for something that would really make a strong case for the importance of infinitesimal mathematics. Unfortunately, this book turned out to be something other than what I was looking for.

Essentially, there was considerably less discussion of math than I expected. Though there are some nice forays into some important basics, the touches on the foundational ideas here are quite brief. Primarily, this is a book of history. And yet, even the focus of the history is not mainly on mathematical ideas. This is a history of conflict where mathematics played a small part.

Infinitesimal is divided into two parts, each of which covers a major historical conflict. Part I deals with the Reformation and Counter-reformation. Our primary characters here are the Galileans and the Jesuits. In fact, there is a rather extensive history of the Jesuits and Prof. Alexander does a nice job of showing their developing educational philosophy. He describes how the Jesuits rejected the concept of the infinitesimal in favor of Euclidean geometry more for reasons of philosophy than general mathematics. In describing this conflict, however, Prof. Alexander deserves credit for being less hostile towards the Jesuits than one often finds in these descriptions, even if he overreaches a bit at the end, claiming that this rejection of the new math held back the development of math and science in Italy for centuries whereas the Protestant areas of Europe made the great leaps forward. This is not quite as true or as simple as Prof. Alexander tries to make it out to be.

Part II deals with the English Civil War. Here, the focus is almost entirely on Thomas Hobbes (for Euclidean geometry) and John Wallis (for infinitesimals). Once again, these men’s difference in mathematical technique was somewhat of a sideshow in their political differences—Hobbes and his Leviathan for a strong monarchy and Wallis a beneficiary of the Commonwealth. Somehow, both men managed to survive the chaos of their time with heads intact, though it could be argued that both men’s mathematical development suffered because of the need to achieve political ends. Still, Prof. Alexander seems to argue that it is the rise of Wallis and the slow decline of Hobbes that leads to Newton and the rise of England as the birthplace of much of the new physics which, once again, is not quite as true or simple as may be implied in this book.

In the end, I felt a bit misled. Though there is some very nice biography and history here, the math seems really to be secondary to the conflicts presented, however much Prof. Alexander wants to bring them to the fore. And his overall arguments about this mathematical theory shaping the modern world; well, this theory might have played a small role in this world of high intellectual ferment but, as much as I believe in the importance of math, there’s a lot more going on here than that. Prof. Alexander seems to know that, if his thesis doesn’t quite allow him to admit it.
67 internautes sur 84 ont trouvé ce commentaire utile 
Not exactly war of all againts all, but still a very damaging fight 10 avril 2014
Par Mariano Apuya Jr - Publié sur
Format: Relié
The opening chapters of "Infinitesimal" are about a board of Jesuits in the 17th century ruling on legitimacy of a mathematical topic. That which would be binding on every university of the Jesuit order-the most prestigious of the time. So I thought this was a book about intolerant and unscientific clergy oppressing reason or a hagiography for secularism. Expect none of that.
I have had come across this topic somewhere but I can't recall chapter in a book I don't remember. The point of that passage was the hostility of clergy to science
Roughly the present book is the history of mathematical thought of the infinitesimal. Halfway through I had the suspicion that it was the history of the limit concept, it is but partly so. This book is in fact a history book. There is substantial coverage of topics on social and historical subjects such as the reformation, the formation and fortunes of the Jesuits, even an entire chapter that is a précis of Thomas Hobbes' philosophy. And all of this is related to the subject of how the concept of infinitesimals took hold in what I think is an original analysis. Up until halfway, I was skeptical of the various arguments and even doubted its veracity-I was looking for holes in Mr. Alexander's account of the whole thing.

How it could be that geometrical thinking suppressed the infinitesimal concept from taking hold is fascinating (not solely geometry). It also had a lot to do with groupthink between several groups and some of these groups can be thought of as coteries. Geometric thinking introduced to humanity the concept of the Proof, should there be differences between Geometric proof and the kind students study in a `transition to abstract mathematics' course today? "Infinitesimal" maps the course it took.
There is a joke in mathematics publishing that for every equation in a book, half the readers go away. There really are not a lot of equations in this book, mostly it is geometric figures with the accompanying explanations-my rough count is ten. My reading of the book confirms my disability to follow geometric arguments but for the vast majority of readers this would be welcome as they are clearly written by Mr. Alexander. I'm hesitant to give this book the full five stars, clicked on five stars anyways because the reduction is infinitesimal. Has a place in my book collection.
18 internautes sur 22 ont trouvé ce commentaire utile 
The battle between hierarchical and egalitarian worldviews 24 avril 2014
Par Fred Erling Wenstøp - Publié sur
Format: Format Kindle Achat vérifié
This is one of the most interesting books I have read. It gives an insight into the battle of world views -- hierarchical versus egalitarian. And if it really is true that a sophisticated mathematical question could be a key point in this battle, it is really remarkable. The author makes you believe it with his lucid and entertaining style which makes you read the book without interruption.
5 internautes sur 5 ont trouvé ce commentaire utile 
A learned and detailed description of the controversial (at that time) development of the Calculus. 24 juillet 2014
Par Big Daddy - Publié sur
Format: Format Kindle Achat vérifié
I am enjoying reading this book, although I still have about the last 25% to finish. The book is a scholarly history of Mathematical (and, to a lesser extent, Physics) developments from roughly the time of Galileo through to (I am anticipating) the 17th or 18th Century. For those who have studied the Calculus, the general discussions will be riveting as a narration of the historical developments (and controversies) that led up to the concept of the infinitesimal, accepted in the modern notation as, for example, "dx". Entwined with the somewhat clumsy and rambling development preceding the Calculus is the politicized environment fostered by the Jesuit Order of the Church. The Jesuits, as it turned out, were on the wrong side of developments.

People today tend to be critical of the Church as having hindered scientific and mathematical developments in the roughly 1300 to 1700 time frame, but one should keep in mind that the Church was the dominant and most extensive learned community, at least in the European theatre, at that time. There really was no other comparable organization to play the role of cultural integrator. True, there were individuals (such as Galileo) who illuminated the way, but then, as now, organized progress was the off-spring of large organizations.

The Jesuits were on the wrong side of the philosophy of the infinitesimal, which later was developed by Leibnitz (in Germany) and Newton (in England) to create the most powerful mathematical philosophy known to date. If the resulting Calculus had been known, for example, to Edmund Halley, his tour de force of demonstrating the periodicity of his comet's orbit would have been enormously less tedious. Incidentally, Newton's and Leibnits' work, although very similar, were not identical to each other ... but each accused the other of plagiarism!

We tend to think of historical developments as being linear. But for those who live those developments, they are not. This book illustrates the often meandering and error filled missteps associated with human progress, and how human pride, obstinacy, and sometimes, downright dishonesty and raw politics play a role.

The Calculus was a concept whose time had come, we recognize today, but we sometimes fail to realize that the development was via human stumbling, intrigue, politics, pride and even, it seems, stubborn orneriness at times! Human affairs do not follow clean and neat orderliness: the point is very clearly illustrated by this book.

If you take the time to read this book, your patience will be richly rewarded.
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