A screenshot from Catecon, the Categorical Console, showing basic string shots. Here we start to see the colored chalkings of coherence.

# Math

# Catecon: Fibonacci

Let’s try to see the Fibonacci numbers. As you know, the Fibonacci number of n is the Fibonacci number of n-1 plus the Fibonacci number of n-2. Looks like a natural use of recursion so buckle up. Let’s start by having our own Fibonacci diagram. Drag the natural numbers onto the diagram. Control-drag to form…

# Catecon: Factorial

Prior video Catecon: Introduction. My first machine to play on beyond some sticks to rub together (a slide rule) was an Olivetti Programma 101 with magnetic cards. My first program, well, one with loops, was to compute factorials. Let’s do that here, with recursion. Given a natural number n, the factorial of n is n…

# V Is For Vortex – More Categorical Programming

Vortex, A Categorical Database In the early 90’s I led a product team of three folks to create Vortex, a database for electronic design automation (EDA). This work at Intergraph Electronics/Dazix/Veribest was based on the categorical programming technique previously developed for the Clipper microprocessor. As it happens the product was never released. The one remaining…

# Intro To Categorical Programming

Have You Shorts Or Opens? Categorical programming was applied to the building of the Clipper microprocessor. Read how part of it was done. Beginning work ’84 at Fairchild Semiconductor as a CAD engineer on the Clipper microprocessor, one of the early assignments was to look at a pen plotter. A pen plotter possesses a few…

# Saunders Mac Lane Geometrical Mechanics

“Kinetic Energy Is A Riemann Metric On Configuration Space” Saunders taught a course on Geometrical Mechanics around 1979-80 or so while I was there. The class was taught in the neighboring Ryerson physics building built with no ferrous metals, though not for that reason but for the metal ball he used to demonstrate spin modes.…

# Souslin’s Hypothesis

I found my only published math article here as an erratum in the Journal of Pure and Applied Algebra 14 (1979) 115-116. It refers to Marta Bunge’s article “Topos Theory and Souslin’s Hypothesis”, Journal of Pure and Applied Algebra 4 (1974) 159-187 as seen here. From the erratum: Harry Dole (Department of Mathematics, The University…