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Comment by brador | Hacker News Reader

This is math junk food. Pretty though.

The video contains no equations, but it cites original, ongoing, research that has been going on since the 50s. Sure, you could rip a bong and go "woah, cool colors", or you could follow the links and read, say, Tabachnikov's book.

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.

p.s. From Schwartz' paper "Unbounded Orbits for Outer Billiards":

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 would call it art, not junk food.

How so? I think applied mathematics is the exception.

It made me reconsider what I think about mathematics in general. So, if it was junk food, it was a nutritious one at that.

Entire math is junk food. Real animals don't touch that.

That’s not entirely true. There are parts of mathematics that have useful real world applications. Sometimes even the parts we thought were esoteric and abstract turn out to have applications that were not conceived of yet at the time of discovery.

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