Bivectors and higher show up a lot in the math of 4D+ geometry, too. There's a fascinating SIGRAPH 2020 talk [0] (with a paper [1]) by the maker of 4D Toys [2] and Miegakure (a 4D game in the works, [3]) explaining 4D geometry collision physics (with a good bivector intro in addition to the collision math). It's a great read and/or watch that smoothly covers everything from building basic intuitions to the gritty technical math of extending standard physics models to N-D spaces.