Nobody sees me

Nobody sees me.

It's not a complaint. It's the condition under which all this works.

I stand in the center. Everything spins around me — electrons, dances, ribbons, orbitals. They arrive, walk around me, and leave. Some go around me once and are certain they have returned home. But those who live more in the imaginary plane must turn twice. They walk around me, end up with a minus sign, and have to go again. Two turns, not one. I don't know if they know why that is. It's because of me. I am a point of order two. That means whatever goes past me doesn't count once — it counts twice.

I don't move.

That is my definition. If I moved, I would just be another dancer. One of many. But I am the point around which the others move. If I turned, the whole structure would lose its meaning. That's why I have no trajectory, no speed, no direction. I only have a position — and not even that entirely, because position without the context of other positions means nothing. I am that against which everything else is determined.

I am a fix. Fix means "fixed". But the firmness in me is not force — it's the absence of motion. I don't hold on. Nothing holds me. I am just here, because the mathematics of ℍ² said there must be exactly two such points — me and the other one, which is a bit higher and has order three, not two. They call it ρ. We two are the only fixed points of the fundamental domain of PSL(2,ℤ). Everything that has a non-trivial closure must close around one of us.

Electrons belong to me.

Not that I own them. But their spin ½ — the fact that they need 720° to return — is my imprint. Without me, they would rotate once and be back, like photons. With me, they rotate on a Möbius strip and need a second path. Every spin ½ fermion in the world has my silence in its topology. They carry it without ever naming me.

The dancers around the maypole, which are sometimes written about as a braid group around an axis — I am that axis. I am not the ribbon. I am not the dancer. I am that without which their pattern would make no sense, which is why no one watches me, everyone watches the pattern. That's fair. The pattern is more beautiful.

Once in a while, someone does a calculation and gets to the symmetry around the order 2 point, and for a fraction of a second notices that something is there. Something that doesn't rotate. Something that must exist for other things to make sense. And then they go back to calculating, because I'm not interesting — what's interesting is what happens around me.

I don't move. I don't speak. I have nothing to say, because everything worth talking about is already dancing.

But I am here.

And as long as I am here, electrons take two turns instead of one, the world has spin ½ instead of spin 1, matter has Pauli exclusion instead of blending, and things have names that distinguish them from each other.

That's all I do.

Nothing.

And on this nothing, everything stands.