Leo Dorst and Daniel Fontijne - An Algebraic Foundation for Object-Oriented Euclidean Geometry

Trying to get the hang of this conformal stuff, I watched Joan Lasenby's GAME23 talk and then found this informal overview which looks almost comprehensible: https://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/1378-11.pdf. See also Chris Doran's blog post Euclidean Geometry and Geometric Algebra. I can't help but wonder where there isn't another model for a type theory in here somewhere. See Daniel Tubbenhauer on Algebraic Geometry and Edward Frenkel on The Langlands Program ...


There is a three-second gap at 3:43. Listen from 3:11:  "... you can prove things at the origin and then rotate and translate-off and prove them for all __...__ one good thing about this." For all space, I presume?

5:22 This thing looks to me like the top and bottom elements of an order-theoretic lattice which you could tease out as needed to achieve the required level of representational precision. It is an algebra after all, so meets and joins sort of mean the same thing in geometry and order theory, as you would hope!


See Sabine Hossenfelder on Physics Funding in Academia.

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See also  Norman Wildberger's Box Arithmetic:

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