Groups Become Walkable Geometries When Multiplication Is Drawn as Movement
burny_tech · x · 2026-11-14
@mathemetica visualizes abstract algebra: encoding edges as multiplication by generators turns groups into walkable structures.
- C₃ closes in three steps (e → a → a² → e), the shortest non-trivial cycle.
- S₃ interlaces order-2 and order-3 generators into a directed hexagon, making the smallest non-abelian group visible.
- Direct products tile the plane and cube: C₃×C₃ forms a 3×3 torus; C₂³ forms the binary cube.
Takeaway: algebra and geometry coincide the moment multiplication is drawn as movement.
More from Fun
- Distilling all of Claude Monet's works into a single painting — vincesitzmann · 2026-11-14
- Why do we say "tokens" instead of "words" for human reading? Plus the 15-token attention rule — sergeykarayev · 2026-11-14
- Viral meme: Jensen Huang inspecting a NVIDIA box beside Elon Musk — EngineeringInsd · 2026-11-14
- Dev records 2 hours of manual Neovim coding to get PRs accepted — yacineMTB · 2026-11-14
- Dev shares film photo holding an actual Cerebras wafer-scale chip — flavioAd · 2026-11-14
- Gary Marcus mocks United's chatbot telling him he's 'valued' while refusing help — GaryMarcus · 2026-11-14