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Infinitesimal Amir Alexander

book Review

In this delightful book, you can follow the author’s rendition of the Mythos / Logos conflict from the standpoint of its infinitesimal mathematical turf. In the Alexander’s skillful hands Infinitesimal turns out to be a most important concept influencing, if not creating, the Reformation, Enlightenment, Industrial Revolution, and more. Whether cause or effect in logic, whether tradition and religion or belief or science, Alexander provides a page turner we could not put down.

Indeed it was the Five Pillars in full display in its many manifestations. We read about how idealism being grounded by the rawest of emotion as a backdrop for the finest new thinking in new directions, whether political, religious, or philosophical. Alexander is right on in describing how mathematics of infinity and the infinitesimal posed both threats and promises that led philosophers and their societies in new directions.

Readers schooled in math by rote, as we once were, may expect as we did, a prominent role for both Newton and Leibnitz. But they only appear in force in the epilog. Moreover, the fist eighty or so pages provide little clue as to what the book is really about—It is all the very-much needed social backdrop of the times. In this late Renaissance era, classical philosophies had been reborn. The geometry of Euclid became a pastime for the learned; arithmetic sufficed for business and provided precision for the geographers and allied endeavors. Geometry, with its deductive logic was still developing, but for the quick in mind, its purity seemed to hold out the possibility that a society could be developed via rules of the game similar to infallible geometry of the ancients. Geometric reasoning “proved” the ideal form of government was a strong central government led by a strong king who countenanced no sass.

All that changed with the advent of Galileo and others who rejected the idea that the ancients had answers for everything—and of course history confirmed his thinking. Galileo not only discovered four moons orbiting Jupiter, but demonstrated certain key laws of motion. Beyond that he reconsidered geometry, and in the process developed alternate means to discover new proofs by means of the infinitesimal. This of course challenged the thinking orthodoxy in vogue at the time. Geometry is pure and logical. Who could ever make use of the infinitesimal? Who can even define it? If geometry were not pure, then the very existence of humanity seemed at high risk. Religious circles like the Jesuits, in particular, felt threatened, as of course they were in fact.

Alexander artfully provides a vivid history of the next century and how Mythos won in Italy and Logos won in England and France. And at the same time how the discipline of science was born. There is more, much more we leave you to discover for yourself. This is a five star book.


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