Iconic Arithmetic Volume III

Iconic Arithmetic Volume III

The Image is the cover of Iconic Arithmetic Volume III: The Structure of Imaginary and Infinite Forms.
Volume III (ISBN 978-1-7324851-5-0) applies the tools developed in Volumes I and II to several areas of elementary mathematics. James arithmetic and void-based thinking are applied to imaginary and complex numbers, to the analysis of critical breakdowns in algebraic rules such as distribution of polarity across square roots, to calculus derivatives, to trigonometry on the real and complex planes, and to the organization and integration of infinite and indeterminate forms within arithmetic.

Here is the text on the back cover:

Arithmetic invites invention and exploration.
The way we record arithmetic obscures its simplicity.
Postsymbolism eliminates the artifacts of symbolic notation.
Iconic patterns provide space for more elegant concepts.
Void-based structure renders numeric illusions transparent.
Meaning is in existence rather than symbolic truth or numeric value.
Numbers are bipolar. Zero is self-contradictory.
Functions are opaque. Inverses reduce to one constant.
The multiplicative √–1 decomposes into the additive log –1.
Base-free logarithms, fractional polarity, angle-free trigonometry, one generic derivative, coalition of the Many with the One.
Iconic arithmetic is embodied cognition.


The first volume of this series, Iconic Arithmetic Volume I: The Design of Mathematics for Human Understanding, is available on Amazon (ISBN 978-1-7324851-3-6).

Iconic Arithmetic Volume II: Symbolic and Postsymbolic Formal Foundations is also available on Amazon (ISBN 978-1-7324851-4-3).

A PDF sample of Iconic Arithmetic Volume Three is available below. It has been designed for two-page layout, with a distinct right and left page format. Please set your PDF viewer (probably Acrobat) for View>PageDisplay>TwoPageView.



The Iconic Arithmetic Volume III Sample includes the contents, preface, bibliography and index of Volume III, as well as Chapters 31, 38 and 45. The first Chapter 31 introduces the objectives of the volume, particularly the introduction and use of an abandoned imaginary number J, the logarithm of –1. Chapter 38 describes how both the imaginary i and the imaginary J evolve from the structure of our number system. The final Chapter 45 summarizes the volume and briefly describes and critiques the innovations.



Chapters 32-36 describe the history and features of the imaginary constant log –1.
Chapter 37 applies James algebra to elementary calculus derivatives.
Chapters 39-40 apply James algebra to the complex plane and to real and imaginary trigonometry.
Chapters 41-43 integrate infinite and indeterminate forms into James algebra.
Chapter 44 returns to the experiential dialects of Volume I, applying them to the innovations in this volume.



The softcover physical book Iconic Arithmetic Volume Three can be purchased directly from Amazon ($30), ISBN 978-1-7324851-5-0.
The price is intended only to cover some of the development overhead. Thanks!



Your editorial comments and error corrections are most welcomed at william@iconicmath.com