="Warren Smith" <warren.wds@gmail.com> ... basically just random ravings.
OK then, as a longtime amateur fan of RWG's work I'll supply some of these!
only the tiniest fraction of it has yet been explored.
Yes, beyond strip mining, perhaps terraforming?
"path invariance" PaIn
Perhaps PaIn acts like a sort of "generalized commutativity" constraint in the vastly more general matrix setting?
what about in the "continuum limit" as the grid side --> 0? Wouldn't that be a whole new kind of analysis? ... This really could be the missing setting people have been wanting to do theoretical physics, and heaven knows what else.
I've long wondered this too, but I know even less of physics than of math. Anyway it motivated me to look more into product integrals (aka "prodigals") a subject I suspect deserves more attention, even in the non-matrix world. The analog of u*dt I write u^qt, q being for "quotient" like how d is for "difference". But alas in matrix-land the inverse of exponentiation seems bogglingly multi-valued. Physically we might visualize particles traveling in "fields" that instead of giving them little incremental nudges give them infinitesimal directional scalings (or, in matrix land, twisty little wedgies). It would be interesting to see how the classic laws look through this transformation. I wouldn't be surprised to learn some physicists already use such models. After all, Albert Einstein apocryphally said the most powerful force in the universe was compound interest. Doubling down on raving: it would also be very interesting to see what sort of physical models would result when expressed as "analytic flow fields" (to borrow RCS's elegant term from HAKMEM) wherein we'd use functional iteration instead of integration or productization.