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

*generalized inverse*, a single operator that achieves all of the common inverse operations (subtraction, division, root).