And then there’s a link to questions, and there are ones that wasn’t mentioned in lecture. E.g. 3-rd says “What do mathematicians usually call the thing that Fong and Spivak call a poset?”, and you even said in lecture that you answered that question. But… you didn’t, if you enter word “math” in browser search, you won’t find an occurrence in the first lecture.

And in general, I’m surprised that lectures are soo tiny, did people succeed learning Category Theory from them?

]]>It may not be easy to follow, but my talk here describes the connection:

• John Baez, Props in network theory, Applied Category Theory 2018, May 4, 2018.

The category where morphisms are ‘open Petri nets’ is called RxNet in these slides, and the main category where morphisms are *drawn* as signal flow graphs is called LinRel. My student Jason Erbele and I have also studied the category SigFlow where morphisms *are* signal flow graphs. My talk slides contain links to papers on all these categories… but feel free to ask questions!

I have no idea why you think the two orbits should have the same area (or why you think one of them is circular). The two orbits have the same semi-major axis (as required) and different semi-minor axes, so they do not have the same area. You *could* choose the new position for the planet so that its orbit was circular, and then the dashed arc would overlay it, but that would make for a far more confusing image because the generality of the construction would not be apparent.

This is not correct according to the figure drawn. The four points shown are not at the same distance. All you have to do is draw a straight line from the Sun through the points on the ellipse, and you can clearly see that the points on the ellipse are much closer. Don’t worry though, the error is only in the drawing because they didn’t draw the ellipse and the circle with the same exact total area. At that point the dotted arc would overlay the circle and should be eliminated because it would be redundant. Sorry to be picky like that but … you know … it’s mathematics.

]]>Thanks! I think I read that reference, probably after writing the above stuff.

I still want to quantize thermodynamics and see what happens. If you want to help, that’d be great.

]]>• Eyal Subag, Symmetries of the hydrogen atom and algebraic families.

Abstract.We show how the Schrödinger equation for the hydrogen atom in two dimensions gives rise to an algebraic family of Harish-Chandra pairs that codifies hidden symmetries. The hidden symmetries vary continuously between SO(3), SO(2,1) and the Euclidean group O(2)⋉R2. We show that solutions of the Schrödinger equation may be organized into an algebraic family of Harish-Chandra modules. Furthermore, we use Jantzen filtration techniques to algebraically recover the spectrum of the Schrödinger operator. This is a first application to physics of the algebraic families of Harish-Chandra pairs and modules developed in the work of Bernstein et al. [Int. Math. Res. Notices, rny147 (2018); rny146 (2018)].

One interesting thing about this paper is that it constructs a ‘space of 2d hydrogen atom state’ for any *complex* energy. The physical meaning of these seems open for exploration.