Author: william brickenPublisher: Unary Press
ISBN: 9781732485136
Category :
Languages : en
Pages : 446
Book Description
Arithmetic evolves. Iconic arithmetic is built from icons that look and feel like what they mean, rather than from strings of symbols that must be memorized. The book explores the formal structure of two types of postsymbolic boundary arithmetic. Ensemble arithmetic modernizes tallies to provide forms that add together by being placed together and multiply by being placed inside one another. James algebra defines the concepts and operations of arithmetic as different ways of arranging containers. Three simple axioms are sufficient. Features of iconic arithmetic include (1) a void with no representation and no properties instead of the symbol zero; (2) void-equivalent forms that can be freely deleted; (3) meaning based on existence of structure rather than truth or numerical value; (4) only one relation (containment) to represent all forms; and (5) construction and deletion to implement all transformations. Iconic forms and transformations can be represented as two and three dimensional structures that can be directly viewed, manipulated, and even inhabited. Many different spatial interactive dialects are described. The author explores this new kind of arithmetic from the perspectives of historical evolution, formal mathematics, computer science and mathematics education. The overall objective is to provide proof of principle that our current universal approach to the arithmetic of numbers is a design choice rather than a truth embedded in numbers themselves. Iconic Arithmetic recognizes that knowledge is embodied, multidimensional, sensual, simple. It helps us to transition into a postsymbolic world of interactive information.