RogerL
Joined 13 years ago
Joined 13 years ago
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.
Whereas any human would say "I think your file format is missing a key/value pair for foo'ing. Let's trace through the code, and see if/where m_foo is set...."
It happens everywhere. Docstring type comments for a function endlessly just lists information about specific variables, implementation details, etc, and often never really even says what the function does. Then maybe a comment in the body might actually describe what it is for.
These days I've learned when facing these walls of text to check the last sentence first; it is often enough to provide the context for the text dump.
I have instructions to this effect in my claude.md. It doesn't help much on responses, but it give me a way to quickly say "reread claude.md and then rewrite that last prompt" and that can tend to go better.
Someone else mentioned model of mind while writing. The LLM has no model of mind; it does not consider how to present information, what you might already know or not know. We work in a huge mono-repo - it'll blithely just start listing variable names and I have no idea what file that is in, what it is referring to, how it interacts with 5 other classes it hasn't mentioned, or mentions out of order. It doesn't matter to the LLM. It can hold millions of facts in 'mind' at once; humans stall out at 5-7. If I replay saying it is leaving out info, many times it turned out it did dump all the facts out, spread across multiple prompts, often with key facts interspersed with all the vagueisms. No human mind can cope.
"But the driver's head might get chopped off". Not sure why you bring that up, it is not part of the equation. Will we likely get more points, will we get caught? Those are the only metrics that matter.
I suppose I exaggerate, but not by much. Drivers didn't want the halo because they thought it would hinder their driving. The first season out Verstappen literally drove over the top of Lewis' helmet, leaving tire marks (he would have been dead w/o the halo).
Yes, I see the message about it staying local. No, I don't trust the message or that you will never be hacked.
And then on my personal account I had $150 in credits yesterday. This morning it is at $100, and no, I didn't use my personal account, just $50 gone.
Commenting here because this appears to be the only place that Anthropic responds. Sorry to the bored readers, but this is just terrible service.
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...