Can Axiomatic Systems Have a Geometry and a Type?
A Saturday reflection on imagining a geometry of axiomatic systems and wondering whether theories could become types that carry information about what can and can't be proven about them, inspired by proof assistants like Lean.
Two Years Leading to FigurateNum v3 Visualizations in the Complex Plane
A short personal note on a new way of visualizing figurate numbers in FigurateNum v3, bringing them into the complex plane through generating functions and domain coloring.
Perfectoid Rings Breakdance in Sonic Pi?
I move through perfectoid rings, p-adic towers, and the Frobenius map, wondering if any of it could ever end up in Sonic Pi’s sandbox.
Do Group Actions Define Regular Polytopes and Polytypes in Type Systems?
I introduce an analogy between transitive group actions on flags of polytopes and type systems. This speculative concept aims to offer a naive way of understanding and classifying types through symmetry.
Gamma Functions for Figurate Numbers
I plant a question motivated by generalizing the GCD to varieties and inspired by Euler's interpolation: Does there exist a function attached to each figurate number that extends it to continuous domains, analogous to how the Gamma function extends the factorial?