THE NATURE of INFINITESIMALS

About the Book

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. Mathematicians, scientists and philosophers have explored the realms of the continuous and discrete for centuries. Erickson delves into the history of these concepts and how people learn and understand them. 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. The reader will gain an understanding of potential versus actual infinity, irrational and imaginary numbers, the infinitesimal, and the tangent, among other concepts. At the heart of Erickson’s 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. This number system, he demonstrates, can provide a new interpretation of imaginary numbers, as a combination of the real and the veritable. Erickson further explores limits, derivatives and integrals before turning his attention to non-Euclidean geometry. In each topic, he applies his new understanding of the infinitesimal to the ideas of mathematics and draws conclusions. In the case of non-Euclidean geometry, the author determines that it’s inconsistent with 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 final chapters, the author addresses absolute space, time and motion through the lens of the infinitesimal. 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. A weighty tome for devotees of mathematics and physics that raises interesting questions.

About the Author

Peter F. Erickson graduated, Phi Beta Kappa, from Stanford University. In 1975, he wrote Introduction To The Tripartite System. Therein, a new monetary system was proposed, one designed to obviate the eventual doom of the U.S. dollar In 1997, there came forth The Stance of Atlas, a critical review of Ayn Rand’s philosophy, especially of her epistemology. The first paper on the veritable number system was copyrighted and distributed in 1999. Passport To Poverty: The 90’s Stock Market And What It can Still Do To You appeared in 2003. In 2006, the first form of the present work, titled Absolute Space, Absolute Time, and Absolute Motion, was published. In 2011, came The Nature of Negative Numbers.