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
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.