![]() 2Īt the same time, the mathematical achievements of earlier centuries would take man to the Moon. In his preface, he would say: We know today that mathematics does not possess the qualities that in the past earned for it universal respect and admiration. In 1980, a distinguished academic professor in that field had a book published by the Oxford University Press titled: Mathematics: The Loss of Certainty. The revolutionary attitude prevailed, not only in politics, psychology, physical theory, and advertising, but also in mathematics, long considered to be the very epitome of certainty. But that is the defect in the favorite imagery of the so-recently deceased century. Then it is supposed that the wheel stops, that it ceases to move on, no longer displacing that which is eminent and putting the vanquished back on top. 1Īn important characteristic of such a revolution is that what is lowermost becomes uppermost and vice versa. In a recent issue of The Wall Street Journal appeared the now commonplace headline: Home Depot’s CEO Led a Revolution, But Left Some Behind. ![]() Eventually, one grew to expect improved household products to bid for the prospective buyers’ approval with the claim that they were revolutionary. Everybody has heard about Marxism-Leninism, Freudian psychiatry, the Einstein theory, etc. If it had a reigning idea, it was revolution. ![]() No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the copyright owner.Ĭhapter II The Rejection In Behalf Of The FiniteĬhapter III In Defense Of The ImmeasurableĬhapter V The Conflation Of Actual And Potential InfinityĬhapter VIII On The Divisibility Of SpaceĬhapter X What Is Actual Infinity?Part 1-The ImmeasurableĬhapter XI What Is Actual Infinity?Part 2-EndlessnessĬhapter XV The Veritable Number System-The Solution To The Mystery Of √-1 Library of Congress Control Number: 2005906265Īll rights reserved. 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. 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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