From Geometry to Algebra and Back Again: 4000 Years of Papers
summary
The claim is concrete: replace our ad hoc vector/matrix toolkit with Geometric Algebra so rotations, areas and volumes share one algebraic protocol. The talk shows the actual operations — geometric product, wedge and dot — applied to Maxwell equations and to graphics via ganja.js, where a three‑line physics engine makes a box bounce (and scales to a cube and even a tesseract) live on stage, arguing the approach simplifies proofs and code after 4,000 years of papers.
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chapters (16)
- 0:00Introduction
- 3:54Math notation as thought tool
- 6:21Mesopotamian numerical computing
- 8:28Babylonian math achievements
- 10:16Greek math and irrational numbers
- 10:58Math progress across cultures
- 12:41Negative numbers geometrically
- 13:43Complex numbers and Bombelli
- 15:30Electromagnetism and telegraphy
- 17:35Grassmann and Clifford's algebra
- 21:47Geometric algebra vs matrices
- 24:12K-vectors and higher geometry
- 25:57Metrics in geometric algebras
- 27:00Live coding demo
- 29:33Hestenes and math notation
- 30:35Closing remarks
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