Paul Almond's site has many philosophically deep articles on theoretical rationality along LessWrongish assumptions, including but not limited to some great atheology, an attempt to solve the problem of arbitrary UTM choice, a possible anthropic explanation why space is 3D, a thorough defense of Occam's Razor, a lot of AI theory that I haven't tried to understand, and an attempt to explain what it means for minds to be implemented (related in approach to this and this).
I do not find the article on 3D space terribly convincing either - and I am the author of it - so I would have to be understanding if you don't. It is generally my policy, though, that my articles reflect how I think of things at the time I wrote them and I don't remove them if my views change - though I might occasionally add notes after. I do think that an anthropic explanation still works for this: I just don't think mine was a particularly good one.
It's a difficult topic. Life (e.g. self-replicating CA) exist fine in 2, 3 and 4 dimensions, though there is still the issue of evolving intelligence. Some say that three dimensions is the only number that permits you to tie knots, though the significance of knots is unclear. I am not convinced that 3 is terribly special - and I'm not sure we know enough about physics and biology to coherently address the issue yet.