Dual numbers (the surreals) are at least as exciting and useful as imaginary ones if not moreso, but far less widely known.

Source

• URL: https://x.com/eshear/status/2011549317119803830
• Author: Emmett Shear (@eshear)
• Posted: 2026-01-14 21:21:44

Thread

1/ @eshear

Dual numbers (the surreals) are at least as exciting and useful as imaginary ones if not moreso, but far less widely known. I wonder why?

2/ @EricLengyel

@eshear

I think you’d find the hyperreals to be more useful than the surreals. As for dual numbers, they show up everywhere in projective geometric algebra (PGA) and represent homogeneous magnitudes. See the following for a small taste of PGA over spacetime:
https://terathon.com/blog/relativistic-quaternions.html