Delightful video on the lambda calculus and other compution concepts https://www.youtube.com/watch?v=RcVA8Nj6HEo
Reminds me of a Pynchon novel or my favorite lyrics from The Dismemberment Plan.
"So in the end, whatever, we die, we dissolve / Equations unbalanced, riddles unsolved / And we were never connected or involved / Except for the intersections and crazy mathematics / With no time and no space and no schedule and no place."
BRB going to go make hyperbolic outer billards art
From Tabachnikov's book Geometry and Billiards:
Classical mechanics and geometrical optics, discussed in this chapter, are intimately related. The configuration trajectories of mechanical systems are extremals of a variational principle, similar to the trajectories of light. In fact, mechanics can be described as akind of geometrical optics; this was Hamilton’s approach to mechanics(see [3] for details). The brachistochrone problem is a good example of this optics-mechanics analogy.
Personally I found that the videos instantly made some group theory aspects of this stand out. Maybe I'm completely off, and that's not really how this is approached, but now I have a question/idea as a foil which I can use to look a bit deeper. In any case, the animation SW came from a researcher in the field, I don't think they are doing this to generate junk food, but to solve actual problems in their field.
Outer billiards is a basic dymamical system which serves as a toy model for celestial mechanics....
I tried as hard as possible to write a proof that is independent from Billiard King [the visualization SW], but still the reader of this paper would get a much greater appreciation for what is going on by learning to use Billiard King. A few minutes playing with Billiard King is worth hours of reading the paper.
https://arxiv.org/pdf/math/0702073
edit:
ah, and here is a Dogru & Tabachnikov paper where they make the connection between this problem and celestial mechanics clear. Very readable!
https://drive.google.com/file/d/1sm47vPUwDqfcY-IGEKSoKIBqyqr...
I was curious what they used to generate the graphic's and it's their own tool:
Could also be the Stars of David (1m46s) and swastikas (2m24s) that end up drawn by the repeating patterns.
However, my best rank was 12. That’s twelve, in case you misunderstand the numbers. I was literally the worst player in the entire league.
I don’t think that there’s anyone out there who is much worse than I am.
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