Guess

I just found out that Gromov got the Abel Prize. I figure he must know a thing or two. I am just starting to study symplectic geometry. Here there is a guess:

The minus sign in Hamilton´s equations points toward a geometric reason for energy conservation. Something like we live in the universe we do, because three dimensional rotations are non-commutative, and then the universe is stable, i.e., it conserves energy.

Complex numbers don't quite cut the cake, quaternions are there in between, and Gromov saw that something in between in symplectic geometry was the subtle solution to the complex, quaternion, nature of the physical and geometrical space we happen to live in.

I know this is a messy set of ideas. At this stage this is all I can report.

The mystery for me is: What does the minus sign in Hamilton's equations have to do with the orientability of surfaces in our neck of the woods, and vice versa?

I'll like an answer like. Only in three dimensional space and one time there can be a stable Universe.

What about Geometric Anthropic Principle, for a name to this wished for answer?