This section includes several notations that incorporate the Additive and Multiplicative Principles of Iconic Arithmetic. The image shows a Numerical Pocket Piece from 1753. It shows the Table for Multiplication and Division (a modern times table) from 3 to 9 and is inscribed as “a new and short method.” The times table for 2 is not included because doubling was taught as a necessary math skill, and was included in the algorithm for achieving multiplication and division.
Iconic arithmetic defines addition and multiplication as physical activities.
Unit-ensembles are collections of identical sticks, pebbles, marks, tokens, or fingers.
Depth-value notation provides a convenient and simple way to group larger collections of units.
Container numbers illustrate unit-ensembles and depth-value working in concert.
Parens notation permits containers to be expressed by a string of typographical characters.
Network numbers express iconic arithmetic as composable networks.
Block numbers express iconic arithmetic as physical constructions using blocks.
Spencer-Brown numbers have units that act both as numbers and as operations.