.... Hm: One chap at Uni came up with the concept that there's three dimensions of time, one for each of space, which in some way I can't remember simplified relativity equations. I don't know what became of him; perhaps he's gone into some obscure adjacent possible and closed the door behind him.

If you really want to bend your brain, start looking into quaternions. They can't be used as-is to describe spacetime*, but I've read recently that they can describe the sort of gyroscope which doesn't suffer gimbal lock.

* I once got lost in a book on relativity which used quaternions instead of tensors. I don't know what happened to that author either.