# Algebra

An algebra supplies general rules for arbitrary configurations of objects. This section shows several types of iconic algebra. The Image by Adam Hayes opened a July 28, 2012 article in The New York Times Sunday Review entitled “Is Algebra Necessary?”. It shows students drowning in a sea of algebraic symbols. Andrew Hacker, the author of the article, is an emeritus professor of political science at the City University of New York.

## Section Contents

Iconic Algebra presents the theory of iconic numbers expressed as equations that can be interpreted as physical instructions to act or as abstract algebraic structures..

Container Algebra presents the theory of iconic numbers expressed as equations that can be interpreted as physical instructions to act or as abstract algebraic structures.

Spatial Algebra provides a different type of iconic algebra expressed as physical blocks.  In spatial algebra addition is putting blocks into the same space, while multiplication is represented by putting blocks in contact.

James Algebra is an entirely different boundary-based algebra that incorporates three types of containers to represent real numbers as well as whole numbers.  James containers express exponential and logarithmic concepts in a very convenient manner.  Addition is putting into the same additive space, while multiplication is putting into the same logarithmic space.

The James Imaginary is a new type of imaginary number, the logarithm of –1. The common imaginary, i, is composed of two James imaginaries. This new concept leads to very new ideas such as the generalized inverse, a single operator that achieves all of the common inverse operations (subtraction, division, root).