Symbols ask us to think. Icons ask us to look.

The symbol 5 tells us nothing about five. The icon ••••• is five.


Iconic Arithmetic Volume I

Volume I describes ensemble arithmetic and James Algebra, two boundary forms that greatly simplify common arithmetic.


Iconic Arithmetic Volume II

Eliminating sets, logic and functions leads to postsymbolic thinking. Volume II provides formal foundations.


Iconic Arithmetic Volume III

Volume III is now available (3/2021). It includes a plethora of innovations to our arithmetic of numbers.


Iconic Arithmetic Videos

Links to narrated videos that show the dynamic structure of the two postsymbolic forms of arithmetic explored in the books.


The Iconic Math Site

Symbols make common math too difficult. Icons make math easy.


Distinction is Sufficient

Logic is one distinction. The article shows how to cross the chasm between symbolic and postsymbolic form.


Iconic Arithmetic

Iconic arithmetic uses the Additive Principle: a sum looks like its parts.


LoF50 Presentation

Implementation of the LoF algebra in both software and hardware.


Iconic Algebra

Icons and manipulatives are both formal and friendly.


Binary Calculator

In binary mode, the Iconic Calculator adds and subtracts by grouping units and merging boundaries.


Decimal Unit Calculator

In decimal unit mode, the Iconic Calculator uses the Additive Principle rather than the Rules of Arithmetic.


Decimal Digit Calculator

In decimal digit mode, the Iconic Calculator uses depth-value notation to add and subtract in parallel.



Unit ensembles add by being put together in the same container.


Depth-value Notation

Depth-value eliminates the stepwise linear sequence of place-value.


Parens Notation

Parens express spatial and temporal structure as typographic strings.


Container Numbers

Animated container numbers add by merging boundaries and multiply by substitution.


Network Numbers

Animated network numbers add by being placed side-to-side and multiply by being placed top-to-bottom.


Block Numbers

Iconic form comes in linear, planar and spatial versions. Manipulatives provide physical meaning.


Container Algebra

The formal algebra of containers is simpler than the algebra of groups.


Spatial Algebra

Spatial algebra adds by sharing space and multiplies by touching.


James Algebra

James algebra uses three types of boundaries to express all the operations of arithmetic.


Iconic Logic

Iconic logic provides entirely new ways to think logically.


Boundary Logic

Boundary logic eliminates duality, converts deduction into deletion, and simplifies critical thinking.


James Imaginary

i (the square root of –1) is the multiplicative imaginary. J (the logarithm of –1) is the additive imaginary.


Boolean Cubes

Boolean logic can be expressed by configurations of cubes in space.


Laws of Form

Spencer Brown’s Laws of Form shows us the structure of unary logic.


Semiconductor Logic

Boundary logic provides powerful tools for the optimization of semiconductor circuits.



Iconic math is expressed physically by enclosures, blocks, paths, maps, rooms, trees and graphs.


Iconic Principles

The Principles of Iconic Math apply to many conceptual domains.


Educational Theory

By making mathematics humane, iconic math solves some of our problems with math education.