High-logic stuff here. I don’t claim to understand all but the ‘gist’.
The gist: HoTT is attempting to become THE foundation for mathematics via Logic. Like… THE. There’s been other attempts in the past and likely to be others in the future, but HoTT is.. hot stuff in this particular field.
Since Theoretical Physics is founded upon mathematics (to hopefully find confirmation in reality), a reformulation of the foundations (universals of logic) of the foundation (mathematics, which is really founded on geometry but then again, geometry is founded on the axiom/proof system, which goes back to logic) of the foundation (Theoretical Physics) of Physics, which is supposed to be the foundation all physical systems WHICH is supposed to be the foundations of Reality itself…. the effort is worth it.
So foundation. Much reductive everythingness.
I love this article for the Title more than anything else and knowing what they’re attempting to do. Personally? I think they’ll end up chasing complicated tails around and still be missing the cheese and the maze, but we’ll definitely learn a LOT in the process of going through it all.
Above my head? Yup. I couldn’t do it. But I’ve got an intuition for accuracy without the refinements of precision. I’d rather be accurate than overly precise because too much precision towards the wrong bulleye can lead you to be perfect and perfectly wrong at the same time. So, I try to avoid that. Gives me headaches.
But I admire those who strive for precision with all my admirative abilities BECAUSE they’re doing what I can’t or won’t, and I cheer them all, while also maintaining my own ignorance of things-very-precise. For me, they’d be mazes I’d have trouble getting out of.