Functional Probability

A visual introduction to probability theory, inspired by the type-theoretic framing developed by Bart Jacobs, Fabio Zanasi, Kenta Cho, and others.

Their representation is elegant, and makes it easy to talk about the theory’s features as being kinds of mathematical functions, or their compositions. I tried to leverage that, and create a unified set of diagrams that would serve as concrete visual examples for the features being explained.

I conceived and began writing this during the pandemic. I intended there to be about 6 parts, covering Bayes’ theorem, d-separation, and other central concepts.

However, maintaining the diagramming system (Jinja-templated TikZ) and using it to manually write all the increasingly complex diagrams for the series became a costly and unpalatable dev experience. So I bracketed the project, and only the first two parts are more or less complete.

I might pick it up again. Repetitive coding tasks are no longer a barrier.

Started: 11 December 2023
Updated: 12 April 2026
Status: unfinished
Epistemic status: synthesis
probabilitymathematics