Ciro Santilli @cirosantilli 37

Intuition, please? Example? mathoverflow.net/questions/278641/intuition-for-symplectic-groups The key motivation seems to be related to Hamiltonian mechanics. The two arguments of the bilinear form correspond to each set of variables in Hamiltonian mechanics: the generalized positions and generalized momentums, which appear in the same number each.

Seems to be set of matrices that preserve a skew-symmetric bilinear form, which is comparable to the orthogonal group, which preserves a symmetric bilinear form. More precisely, the orthogonal group has:and its generalization the indefinite orthogonal group has:where S is symmetric. So for the symplectic group we have matrices Y such as:where A is antisymmetric. This is explained at: www.ucl.ac.uk/~ucahad0/7302_handout_13.pdf They also explain there that unlike as in the analogous orthogonal group, that definition ends up excluding determinant -1 automatically.

Therefore, just like the special orthogonal group, the symplectic group is also a subgroup of the special linear group.

There is only a very fine difference between a very good film, and the best films of all time. Perhaps it is something to do on how epic the subject matter is? It is often very hard to tell, and switches between the categories are also possible.

Critique of Harvard by Sean Carroll. Applies to basically all universities.

Maybe they did try once though: Harvard Project Physics.

The best instrumental songs: Section "The best Chinese traditional instrumental music"

In the process of moving out of: cirosantilli.com/china-dictatorship/music

Bibliography:

Some free online collections:** collections.si.edu/search/results.htm?q=&fq=online_visual_material%3Atrue&fq=online_media_type%3A%22Images%22&fq=culture%3A%22Chinese%22&fq=object_type%3A%22Paintings%22&view=list&date.slider=300s%2C1800s

Unclear legality:

This is the classic result of formal language theory, but there is too much slack between context free and context sensitive, which is PSPACE (larger than NP!).

By Noam Chomsky.

A good summary table that opens up each category much more can be seen e.g. at the bottom of en.wikipedia.org/wiki/Automata_theory under the summary thingy at the bottom entitled "Automata theory: formal languages and formal grammars".

Ah, Ciro Santilli loved this one... games young Ciro Santilli played.

And as a result, adult Ciro really enjoys tool-assisted speedruns of the game.

Low budget.

Good theory of Jesus.

List of similar feeling films: www.youtube.com/watch?v=zwYwFoanrNg 11 Underrated Hard Sci-fi Movies by Marvelous Videos (2021)

Political division:

TODO what's the point of it.

Bibliography:

The original gangster.

Some cool ones: