The numga library compiles simulations expressed in geometric algebra into GPU accelerated programs. Why is this important?
Consider this single geometric algebra equation that compresses Maxwell’s Equations*:
or even more parsimoniously in terms of the “quasi-vector-ish-four-potential A”:
Such simple and elegant expressive power is the sine qua non of science. Bridging the distance between such expressions and computational models of the real world chews up vast programming resources. But perhaps even worse is the resulting barrier to wide-spread adoption of such parsimonious expressive power. Even scientists fail to surmount this barrier, let alone engineers. I mean how many academies have geometric algebra as a prerequisite for engineering or even physics?
- Caveat: These expressions presume gauge invariance, which some alternative (“crackpot” to some) theories of EM violate.