The Densities

[Moine]

That session quote didn't like the spider web traps of large Lie groups but did think Lie groups are useful if careful. It mentioned Geometric algebra as useful too. You can get small Lie groups from geometric algebra and that is probably better than getting small Lie groups from large Lie groups. Large numbers of people do get trapped in things like string theory and smaller numbers of individuals do make progress but it will be slower since there are fewer people.

Quite. Although I do think that too many people are experimenting with novel, and rather abstract, constructions that may have little to no basis in whatever reality they are trying to elucidate. A careful selection of your tool-set will thus provide a better result. So with your geometric algebras, you've got different flavors of interpolation.

Wikipedia: Geometric Algebra

In more detail, there have been three approaches to geometric algebra: quaternionic analysis, initiated by Hamilton in 1843 and geometrized as rotors by Clifford in 1878; geometric algebra, initiated by Grassmann in 1844; and vector analysis, developed out of quaternionic analysis in the late 19th century by Gibbs and Heaviside. The legacy of quaternionic analysis in vector analysis can be seen in the use of ⁠i

⁠, ⁠j

⁠, ⁠k

⁠ to indicate the basis vectors of ⁠R3⁠: it is being thought of as the purely imaginary quaternions. From the perspective of geometric algebra, the even subalgebra of the Space Time Algebra is isomorphic to the GA of 3D Euclidean space and quaternions are isomorphic to the even subalgebra of the GA of 3D Euclidean space, which unifies the three approaches.