hiremebecauseimsmart:

**Question.** Why do we live in a 3-dimensional universe?

**Tentative Answer.** Maybe because 3 dimensions is the most interesting number of dimensions? Maybe 3-D is the boundary between “too constrained” and “too free”.

The above link is to some mathematicians discussing other interesting dimensions besides 3 — because they already know 3-D is uniquely suited to complexity.

In other words, lots of “facts” are only facts in **ℝᵈ** when **d=3**. So by the anthropic principle…we live in 3-D.

Here’s one fact that’s unique to just the fourth dimension.

**Exotic ℝ⁴:** There are infinitely many non-diffeomorphic smooth structures on the topological space **ℝᵈ **if and only if **d=4**.

Otherwise there is only one diffeomorphism class.

**^** pictures of diffeomorphisms

**(A diffeomorphism preserves the relationships between neighbouring points.)**

(via isomorphismes)