Symplectic group Updated +Created
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.
The best films of all time Updated +Created
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.
Discrete logarithm Updated +Created
Super Mario 64 Updated +Created
And as a result, adult Ciro really enjoys tool-assisted speedruns of the game.
Super Mario Bros. Updated +Created
The Man From Earth (2007) Updated +Created
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)
TwinsUK Updated +Created
jq Updated +Created
Yet another awk-like domain-specific language to do things from the CLI in a ridiculously short humber of character? Oh yes.
Los Alamos National Laboratory Updated +Created
Video 1.
Historic Manhattan Project Sites at Los Alamos by Los Alamos National Lab
. Source.
Historian Alan B. Carr:
Slow neutron Updated +Created
Synthetic virus Updated +Created
Tangent space Updated +Created
TODO what's the point of it.
Bibliography:
Karlsruhe Institute of Technology Updated +Created
Tax the rich Updated +Created
Video 1.
How the rich avoid paying taxes by Vox (2021)
Source. Features interview with Morris Pearl, a rich dude that is campaigning to tax the rich. He also participates in an association called "Patriotic Millionaires" to further this agenda.
Video 2.
What Eating the Rich Did For Japan by Asianometry (2021)
Source.
New Testament part Updated +Created
Telephone Updated +Created
We are at a point in history where the electrical telegraph is well established.
But people don't want to press letters one by one on a switch. They want to talk!
The first phones appear to have used telegraph lines directly.
Also wired phones don't require modulation, which likely made their development much easier than wireless voice transmission. You just send the signal as a voltage differential directly obtained from the air pressure: how the telephone works.
Wizards of the Coast Updated +Created
Basic Linear Algebra Subprograms Updated +Created
Domain hack Updated +Created
Some cool ones:
  • playinside.me

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