Is geometric algebra in physics different than in programming or game development?
No, they are exactly the same, that’s one of the benefits of the subject. When you learn it once, you can apply it anywhere. It is sort of a transition language; you can take techniques in one place and immediately apply them elsewhere.
At Geomerics, you developed software called Enlighted which is used in the videogame industry to compute light. How did you apply geometric algebra while you were developing it?
The original idea of the company was to commercialise a package of computing tools for engineering.
During the period of the Playstation 3 and the Xbox 360, one of the big improvements game studios had to work on was calculating lighting. One of the biggest challenges was to calculate lighting that bounced off of other areas. Companies used to precalculate the reflections and one of our goals was to be able to compute it dynamically. We did that using geometric algebra.
On a hardware level, is geometric algebra more efficient to compute tasks ?
That depends on the problem, i.e.: for the interpolation between two rotations, the correct mathematical way to do that is really expensive. Geometric algebra offers mathematical shortcuts to do that more efficiently. But there are some operations where vector algebra is and always will be more efficient.
There is no competition between these two languages. Vector algebra is a subset of geometric algebra, we have to use both.