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PDF Download Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World
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Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World
PDF Download Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World
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Audible Audiobook
Listening Length: 12 hours and 15 minutes
Program Type: Audiobook
Version: Unabridged
Publisher: Audible Studios
Audible.com Release Date: September 2, 2014
Whispersync for Voice: Ready
Language: English, English
ASIN: B00M4LU9UY
Amazon Best Sellers Rank:
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.
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 “proofâ€.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.
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.
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.
I sincerely loved the deep analysis of the conflict between Wallace and Hobbes. Even in the politics and culture wars in the US today, we can see this conflict between somewhat authoritarian, conservative factions and forward looking modern thinkers.
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