Iconic Arithmetic Volume I

Iconic Arithmetic Volume I

The Image is the cover of Iconic Arithmetic Volume I: The Design of Mathematics for Human Understanding, the book version of some of the content on this website.
This book is the first of three volumes and is available on Amazon (ISBN 978-1-7324851-3-6).
The first part of Iconic Arithmetic describes ensemble arithmetic, an iconic system based on tallies, the unary arithmetic in use since the dawn of civilization. Hilbert considered this arithmetic to be so simple that it does not need any axioms. Add and multiply integers without cognitive effort!
The second part of Volume I describes James algebra, an iconic system that expresses the rules and operations of arithmetic, including rational, real and imaginary numbers, using one concept (containment) and three simple axioms.

Here is the text on the back cover:

Arithmetic evolves.
The Laws of Algebra are design choices made before the Internet, before computers, before electricity.
The arbitrary symbols we memorize and try to recall are abstract, one-dimensional, sequential, detached.
Iconic arithmetic is physical, sensual, natural.
Tangible mathematics connects us to our cultural and biological heritage, to the authentic world of experience.
Icons look and feel like what they mean: embodied, multidimensional, concurrent, inclusive.
Iconic arithmetic is a form of experience.


The second volume of this series, Iconic Arithmetic Volume II: Symbolic and Postsymbolic Formal Foundations, is available from Amazon (ISBN 978-1-7324851-4-3).
Iconic Arithmetic Volume III: The Structure of Imaginary and Infinite Forms is also available on Amazon (ISBN 978-1-7324851-5-0).

A PDF sample of Iconic Arithmetic Volume One 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 I Sample includes the contents, preface, bibliography and index of Volume I, as well as Chapters 1, 5, 6 and 15. Chapter 5 includes the axiomatic basis of all systems described in the three volumes. Chapter 6 outlines the perspective of iconic and void-based thinking about arithmetic.



Chapters 2-4 include the structure of ensemble arithmetic, depth-value notation and many multidimensional dialects.
Chapters 7-14 introduce the structure of James arithmetic as it applies to thinking, counting, computing and the deconstruction of the arithmetic and algebra of numbers. Several multidimensional and interactive dialects are described.



The softcover physical book Iconic Arithmetic Volume One can be purchased directly from Amazon ($30), ISBN 978-1-7324851-3-6.
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