Things to Make and Do in the Fourth Dimension

by Matt Parker

I find it fascinating that regular shapes can go from there being infinitely many in 2D, to five and six options in 3D and 4D respectively, and then suddenly only three for all other dimensions. The problem with 2D is that there aren’t enough options to place any significant constraints on regular shapes: they’re allowed to run wild. 2D is too limited to have any nuanced behaviour. 3D and 4D are the sweet-spot for enough freedom to build something interesting but there not being too many options to ruin everything. From 5D onwards, there’s too much freedom to be able to lock anything down. For me, this explains why we live in a universe with around three to four dimensions: it’s enough to make the options interesting, but not too many that any attempt at anything too complex falls apart. Throw in the lack of knots and orbits in 4D and it tips the scales to why we experience a 3D reality.