RogerL

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...

The video didn't make this clear, but it is answering real questions. Its used in the study of geometrical optics, celestial navigation, etc. Ie set up a 'toy' problem that gives you insights into rather more complicated dynamical systems.

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.

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.

IMO not enough talk about ordering. LLMs seem to have no understanding of e.g. the 5 Ws of journalism. Yes, they "know it", they just rarely use it. Nearly every programming response I get starts with the most lowest level fact "m_foo is [wall of text elided] hence the file format is wrong".

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.

It's a very simple question - is this act statistically likely to improve the results? If the answer is yes, and either it is within the rules, or unlikely to be detected, then it will happen. There are billions on the table, reputations and careers on the line; if you don't pick them up, someone else will.

"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).

MC is used because there is no analytic solution. Only some likelihood functions have a conjugate prior. You have to rework the analytic solution for every model change (where most changes would result it in being non-analytic anyway), and they don't work well for high dimensional problems. Restricting the tool to analytic would mostly result in a toy app that just does Gaussians.

individuals can blow in the wind, but if you are a company who bought a thousand seats and spent a ton of time training people up, establishing policies, vetting which extensions are allowed, the transition cost is much higher.

You want me to enter my api key into a website?

Yes, I see the message about it staying local. No, I don't trust the message or that you will never be hacked.

7 trivial prompts, and at 100% limit, using sonnet, not Opus this morning. Basically everyone at our company reporting the same use pattern. Support agent refuses to connect me to a human and terminated the conversation, I can't even get any other support because when I click "get help" (in Claude Desktop) it just takes me back to the agent and that conversation where fin refuses to respond any more.

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.

It's an AI generated article; don't trust anything in it unless you verify it.

it was light gathering. the D5 they brought is a very old camera tech wise, but it was ideal for the low light photos of the eclipse. they also brought a Z9 for much higher resolution photos.

I've purposely eaten insects while traveling. for me it is hard to get over the fact that they are not 'cleaned' - you eat everything in their digestive tracts. I intellectually understand that is safe, but my conditioning makes it hard to handle. taste and texture can be challenging once you get past grasshoppers and ants (for my palate of course).

yes, the correct sub for this is r/truespotify, and there are a dozen discussions on the problem.

Claude does these things even though you have explicit instructions not to do them, this isn't a tool for you asking it to delete files.

Just today Claude decided to do a git restore on me, blowing away local changes, despite having strict instructions to do nothing with git except to use it to look at history and branches.

Why jump to the conclusion that the person is so incompetent with no evidence?

I was just about to say the same thing. This is bad code/documentation. Single letter variable names is almost always wrong if it isn't i for an index or such (and even then, would typing 'idx' kill you?). And as parameters, so much worse. Don't make me guess how to call your function please.

You assume they were talking about a single product. at my job there is essentially endless amounts of small tasks. We have many products and clients we have many internal needs, but can't really justify the human capital. Like I might write 20 to 50 Python scripts in a week just to visualize the output of my code. Dead boring stuff like making yet another matplotlib plot, simple stats, etc. Sometimes some simple animations. there is no monstrosity being built, this is not evidence of tagging on features or whatever you think must be happening, it's just a lot of work that doesn't justify paying a bay area principal engineer salary to do in the face of a board that thinks the path to riches is laying off the people actually making things and turning the screws on the remaining people struggling to keep up with the workflow.

Work is finite, but there can be vastly more available than there are employees to do it for many reasons, not just my personal case.

I grew up in the 70s. The hand wringing then was calculators. No one was going to be able to do math anymore! And then wrist watches with calculators came out. Everyone is going to cheat on exams, oh no!

Everything turned out fine. Turns out you don't really need to be able to perform long division by hand. Sure, you should still understand the algorithm at some level, esp. if you work in STEM, but otherwise, not so much.

There were losses. I recall my AP physics professors was one of the old school types (retired from industry to teach). He could find the answer to essentially any problem to about 1-2 digits of precision in his head nearly instantly. Sometimes he'd have to reach for his slide rule for harder things or to get a few more digits. Ain't no one that can do that now (for reasonable values of "no one"). And, it is a loss, in that he could catch errors nearly instantly. Good skill to have. A better skill is to be able to set up a problem for finite element analysis, write kernels for operations, find an analytic solution using Mathematica (we don't need to do integrals by hand anymore for the mot part), unleash R to validate your statistics, and so on. The latter are more valuable than the former, and so we willingly pay the cost. Our ability to crank out integrals isn't what it was, but our ability to crank out better jet engines, efficient cars, computer vision models has exploded. Worth the trade off.

Recently watched an Alan Guth interview, and he made a throwaway comment, paraphrased: "I proved X in this book, well, Mathematica proved...". The point being that the proof was multiple pages per step, and while he could keep track of all the sub/superscripts and perform the Einstein sums on all the tensors correctly, why??? I'd rather he use his brain to think up new solutions to problems, not manipulate GR equations by hand.

I'm ignoring AGI/singularity type events, just opining about the current tooling.

Yah, the transition will be bumpy. But we will learn the skills we need for the new tools, and the old skills just won't matter as much. When they do, yah, it'll be a bit more painful, but so what, we gained so much efficiency we can afford the losses.

The article and the press release it was derived from says nothing about "more efficient", just smaller.

https://yasa.com/news/yasa-smashes-own-unofficial-power-dens...

I'm not a physicist but every definition of dark matter that I read says it does not interact with electromagnetic radiation hence it is invisible, and rocks are not that dark matter (wiki. NASA, etc)

Hire, then train them for a long period of time? That is an apprenticeship. It's what they do in the trades already. There aren't enough slots (union or not).

e.g. http://www.calapprenticeship.org/programs/electrician_appren...

You need a diploma, a smattering of algebra, a driver's license, and the physical ability to do the work. Everything else you will be taught on the job, while being paid.

The oil can coat the pasta, reducing the ability of the sauce to penetrate the pasta when you cook them together.

Hard water will boil at a higher temperature, but it's only a degree or two.

Or because their kid or dog is in the car. Or because they have difficulty walking. Or because they just want to decompress and scroll their phone or listen to the news for 10 minutes. Or they hate crowds. Or they are immune compromised and don't want to be mingling with a bunch of people around a counter. Or they have social anxiety. Or they have a cold and just don't feel like getting out of their car. Or they are expecting a call from the baby sitter. Or they are having a fight with their spouse which they don't want to export into the public.

IMO, drive throughs are great, I hate crowds and queues (yes, the car line is a queue, you know what I mean), and it is much kinder to my bad discs in my back (transitions from sitting/standing is just murder, steady state is much better). It would take a egregious queue to get me to go in in most cases. But sure, I'm lazy or just reaaally bad at math. edit: I also find it hard to hear in high volume rooms with lots of reflections (like an in-n-out), and yes, the drive through can have it's own sonic issues, but it is generally smoother for me.

Sorry, but I get tired when people take the most uncharitable read, especially when they blanket apply it to everyone.

Go check out VxWorks or the like. only 20K a seat, build tools at a similar price, and then oh joy, runtime licenses required to deploy the sw you wrote.

Which are reasonable prices when lives are at risk.

Yes, I know RTOS are not general purpose, this is NOT apples to apples, but that is what that kind of reliability, testing, safety certification, etc. costs.

My inbox is filled with never asked for sales pitches, most having no concept of what we do or what pain points we have. And I'm a principal IC, but still IC, so mostly wasted effort on their part. Every last email gets deleted unread after I report it as spam to our spam filters. I'm sure I've deleted at least one email that could have actually been something worth investigating, but who has the time for all that? And realistically, I know what my pain points are, we talk about them all the time and actively search for solutions, but budget, reluctance of decision makers, etc often gets in the way, or the solution is too expensive compared to the actual difficulties. Not that something revolutionary can't come along, but ya, its essentially all spam.

I also do the same with anyone that cold emails or calls me - 99% look to be a waste of time. When we still worked in an office you'd hear the telephones ring across the office one by one, as the robocaller worked through the extensions. Many ended up turning the ringer off, because otherwise it is an onslaught that is far more disruptive than whatever pain point they might actually be able to solve. So "Get in front" of someone sounds good, but I would guess it is hard.

> really hard to convince yourself to work 60 hour weeks

Good!

It's a life endeavor that you will never master. start at age 4 playing minuet in G, at age of 90 you'll still be learning new things. The music is beyond us, yet ourselves, to paraphrase Wallace Stevens. All we can do is enjoy the ride.

You also need selection, not just mutation (I know you are being silly, so am I)

That's not the point, the point is the ordering is inverted, not that history shouldn't be learned.

The tiniest amount of vacuum stops sound as abruptly as non transparent matter stops light. furthermore, there was no amount of sound which can overcome the vacuum, whereas enough photons at enough energy will destroy the matter in its path.

edit: yes, an explosion will expel matter through a vacuum, so in some sense enough noise will travel through a vacuum, but you are probably not going to be complaining about the "noise" if you are showered with enough matter to hear it from a massive explosion as your sudden disassembly will (briefly) capture your full attention. Whereas light trivially crosses the universe, as well as through some matter.