Vignette

Ideals were covered earlier in the playlist. They are like multiplying by zero but without collapsing the whole algebra. Ideals are the things that multiplied by anything only get scaled. Ideals and nilpotents are related, nilpotents square to zero, ideals square to themselves.

Ideals are the algebra of the lightcone. Photons don't experience time, and yet we can see some travel farther than others. It's an operation you can't undo. You can't collapse all time to nothing and then ask how much of it there was.

Ladder operations seem to be about a discrete operation that makes something more. In discrete form the only way that makes sense to me is in number of dimensions. But it could connect to what floor you are on in the complex logarithmic spiral.

Creation and destruction operations, as quantum all or nothing changes to a quantum field, are still not totally clear to me. As far as I can tell it gets swept under the rug under the guise of some Hilbert space proxy for some infinite dimensional linear algebra.

But I'm pretty sure that if integers are coming back in after we have a continuum it's because of topology; making a full cycle or turning back. Returning to start having completed something or not.

Some kind of topological invariant.

I'd like to explain quantum mechanics in terms of geometry which may or may not be classical. I by no means want to explain it by deciding it is an axiom.