Mathematical posts

Feynman diagrams without any physics

Feynman diagrams are associated with complicated physics, but they can also be found hiding in relatively simple questions about Gaussian random variables.

Basic general relativity with Julia

A minimal implementation of differential geometry calculations in Julia.

Defining Entropy with a Composition Law

My favourite characterisation of (information) entropy in terms of a natural composition law, complete with a uniqueness proof.

Daylight Hours: A spherical geometry problem

How many hours are there between sunrise and sunset? The Earth’s tilt makes this a fun geometry problem…

A Simple Example of a Connection With Torsion

A minimal example of a connection on the plane which exhibits torsion.

Explicit Baker–Campbell–Hausdorff–Dynkin formula for Spacetime via Geometric Algebra

A paper on composing Lorentz transformations in terms of their bivector generators using the geometric algebra of spacetime, submitted to the International Journal of Geometric Methods in Modern Physics.

Mathematical One-liners

A collection of succinct but wonderfully satisfying mathematical results.

Van Gogh’s Starry Night as a phase portrait

My Dynamical Systems course had a competition to make the most creative phase portrait…