Indeed, not everyone agreed with the Jesuits.
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. If infinitesimals were ever accepted, the Jesuits feared, the entire world would be plunged into chaos. 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. With the stroke of a pen the Jesuit fathers banned the doctrine of infinitesimals, announcing that it could never be taught or even mentioned. While explaining his deductions and thoughts on these complex topics, he raises new questions for his readers to contemplate, such as the origin of memory.Ī weighty tome for devotees of mathematics and physics that raises interesting questions.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. In the final chapters, the author addresses absolute space, time and motion through the lens of the infinitesimal. Erickson supplies illustrative examples both in words and images-he clearly defines new notation as needed for concepts such as eternity, the infinitesimal, the instant and an unlimited quantity. In the case of non-Euclidean geometry, the author determines that its inconsistent with the infinitesimal. In each topic, he applies his new understanding of the infinitesimal to the ideas of mathematics and draws conclusions. Erickson further explores limits, derivatives and integrals before turning his attention to non-Euclidean geometry. This number system, he demonstrates, can provide a new interpretation of imaginary numbers, as a combination of the real and the veritable. At the heart of Ericksons work is the veritable number system, in which positive and negative numbers are incompatible for the basic mathematical operations of addition, subtraction, multiplication, division, roots and ratios. The reader will gain an understanding of potential versus actual infinity, irrational and imaginary numbers, the infinitesimal, and the tangent, among other concepts. He regards the infinitesimal as the key to understanding much of the scientific basis of the universe, and intertwines mathematical examples and historical context from Aristotle, Kant, Euler, Newton and more with his deductions-resulting in a readable treatment of complex topics. Erickson delves into the history of these concepts and how people learn and understand them. Mathematicians, scientists and philosophers have explored the realms of the continuous and discrete for centuries. Erickson explores and explains the infinite and the infinitesimal with application to absolute space, time and motion, as well as absolute zero temperature in this thoughtful treatise.
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