Counting a Figurate Property in Cayley–Dickson Algebras
A naive question about Cayley-Dickson algebras, enumerated by a figurate number via type systems, and how that question naturally incorporates itself into other algebraic structures and particularities.
Category 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.
A 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.
Forging a Live Coding Tonnetz Library in TypeScript
Bringing together topology, group theory, and music into Ziffers and the interactive live coding environment Topos.
Generators as Symbolic Exploration
A reflection on the extension and unification of figurate numbers within broader mathematical contexts.