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.
ReadTowards 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?
ReadCategory of Modules and Type-Level Programming with Figurate Numbers
I invite you to explore the intersection of figurate numbers and module theory, where type-level programming unlocks new possibilities for math and live coding music.
ReadA Field Extension Perspective on Formal Languages
This post explores an analogy between formal languages and field extensions, using ideas from Galois theory to reframe truth, interpretation, and metalanguage hierarchies in logic.
ReadForging a Live Coding Tonnetz Library in TypeScript
Bringing together topology, group theory, and music into Ziffers and the interactive live coding environment Topos.
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