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.

### LoF50 Presentation

Implementation of the LoF algebra in both software and hardware.

### The Iconic Math Site

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

### Distinction is Sufficient

NEW as of 4/18! Logic is one distinction. The article shows how to cross the chasm between symbolic and postsymbolic form.

Future content.

### Iconic Arithmetic

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

### 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

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.

### Varieties

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.