Why three dimensions? There's so much deep math and physics and even philosophy around the abstractions of what's a measurement, what's an observation, what is information, what is communication, what is the direction of time, etc. I keep thinking that could eventually lead to a completion of an understanding of reality when proved deep enough. But why three dimensions? It seems so arbitrary in the context of everything else. But there has to be a reason.
Well, that's four, actually. This is what is needed for electrodynamics to work, and we being "electric creatures" only care about these. It's like different animals that are adapted to seeing different colors. (I don't know, some of them probably think they live in one dimension, why not?)