This page links to three narrated videos that provide an introduction to the postsymbolic systems described in the Iconic Arithmetic books.

### Narrated Videos, May 2023

The 30 minute video * Unit Ensembles* presents the content of Chapters 2 through 4 in

*Iconic Arithmetic Volume I*. Description of the history of tally arithmetic and the design of depth-value notation is followed by dynamic demonstrations of the block, container and network dialects. The iconic calculator is briefly described and illustrated by dynamic examples of base-10 decimal, base-10 tally and base-2 addition and subtraction. The examples emphasize the separation of arithmetic operations from counting

*how many*, the unification of addition and subtraction, and the computational parallelism facilitated by iconic notation.

The 40 minute video * James Algebra* presents the content of Chapters 5 through 12 in

*Iconic Arithmetic Volume I*. After a brief outline of the concepts underlying iconic algebra and the importance of void-equivalence, the structural forms of the three James algebra axioms are described and illustrated dynamically. The structural principles of James frames and the correspondence to Spencer Brown’s

*Laws of Form*is followed by several dynamic examples of James arithmetic (+, –, x, ÷, ^, log), the generic inverse, and the mapping to conventional exponential and logarithmic operations. James algebra is illustrated by the solution to the general quadratic formula.

The 20 minute video * Surprises in James Algebra* describes results in

*Iconic Arithmetic Volume III*. The use of formal illusions and base-free exponents is briefly described and then applied to the rules for calculus derivatives. The imaginary

**J**(interpreted as the

*logarithm of –1*) is described. Fractions of J are then aligned with the roots of –1, with fractional polarity, and with rotation in the complex plane. These features are applied to the construction of a one-dimensional reflective trigonometry that defines cosine and sine without the use of the conventional constants π, i or e. Finally the non-numeric unit is used to organize infinite and indeterminate expressions.