From Geometry to Algebra and Back Again: 4000 Years of Papers
summary
Claim: replace our patchwork vector/matrix machinery with Geometric Algebra because one uniform algebraic system captures scalars, vectors, bivectors and volumes and makes rotations and physics concise. Evidence: historical math from 4000-year-old tablet to complex numbers as a bivector, Gibbs/Heaviside reformulation of Maxwell, and modern libraries like the ganja.js playground and a tiny Clojure live demo that runs a 2D box, a 3D cube and even a tesseract by changing one parameter. Tools: wedge and dot products, the geometric product, projective/conformal metrics; demos work and cut boilerplate.
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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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