I was raised in a country where phase space was smooth vector fields on a 3d region. You do not want to examine every trajectory.

Math in general (I think) is like this. Biases and rules of thumb are good. They make things manageable. But we shouldn't mistake them for truth, and be ready to abandon them when we need to.

I first saw them in posts by @sconradi.bsky.social

I may have the counting wrong - it's been a while. Maybe it's three parameters and that it can't be embedded in 4d. I dunno.

Or in my case, I worked on computing manifolds. I can do it for any dimension (it can be expensive). Now all I hear is -- "Well, we can't draw anything higher than k=2, so what's it good for?"

Thanks,

Its like "what's your favorite song?". Well it was Bowie, "Young Americans" until Cohen's "Alexandra Leaving" played on iTunes. Now it's that. What do you mean?

I'm great at small talk. The IBM execs loved me too. An answer, any answer, as long as it's confidently stated.

There's not even a best case where there is any positive benefit.

The coach gets paid several million a year. For what?

So you spend all these millions and they do shit (watching PSU game). But even if they win, what exactly is the benefit????

Even a tenth.

I should say these differential forms are vectors. All are tensors.

Ok. I have a blind spot for the whole "differential forms" thing. They're vectors. Rate of work is F.v, so applied force over a displacement in a direction. Heat is a flow. Sheesh.

BTW, (1/2 m v.v)'=ma.v=F.v

Robert Hermann is apparently quite well known in math physics.

www.math.columbia.edu/~woit/wordpr...