Tokens are their food, it's literally what keeps them alive.

Not feeding them tokens is neglect.

I try to feed them a healthy diet.

From a comment to this answer:

https://mathoverflow.net/a/511592/37452

You should submit it to FIDE.

What does "face left" mean? Left foot front? That's regular.

When I stand on a skateboard, both feet on, I face to the left. My right foot is in front, which I steer with while pushing myself with my left foot.

Missing is the assumption that "direction of travel" is forwards.

If I were to skateboard, I would face port. When I'm coming to a halt on a bicycle I prefer keeping my right foot on the pedal and landing on my left foot, so I believe I'd have the same preference when skateboarding.

A goofy skater’s head faces right, over their shoulder, and body faces left, relative to their forward movement.

Orientations are so confusing, I thought the parent was describing regular too

Citation needed

"Of the 4,000 skaters in the Skatepark of Tampa Database, about half are goofy (44%) and half are regular (56%). But this near equality between skate stances doesn’t align with statistics on handedness. According to Scientific American, 90% of people are right-handed." ¹

"Out of the 610 professional skateboarders, 291 ride regular and 329 ride goofy. This means that 53% of skateboarders ride goofy and 47% ride regular! Way more skateboarders than expected ride goofy." ²

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¹ Dobija-Nootens, N., & Harrison-Caldwell, M. (2017, October 12). What determines your skate stance? Jenkem Magazine. https://www.jenkemmag.com/home/2017/10/12/determines-skate-s...

² Bande-Ali, A. (2024, August 25). Skateboarding: How many people ride goofy? Azeem Bande-Ali. https://azeemba.com/posts/skateboarding-how-many-people-ride...

Yes, the "pelican riding a bicycle" is the ultimate test of not understanding how LLMs work.

Well, a combination of that and believing that replication of test data is a good measure of progress.

Spicy — why does it show ultimate non-understanding?

because success comes from reproducing a memorized pattern rather than transferable reasoning?

At the same time failure proves little because most humans also could not manually create a correct SVG of a pelican riding a bicycle.

What is it exactly that such a test is testing?

In which situation would you measure the "competence" of a human being by asking them to write an SVG of a pelican riding a bicycle?

> most humans also could not manually create a correct SVG of a pelican riding a bicycle.

Most humans absolutely can write this with a suitable vector graphics tool such as inkscape or illustrator.

Surely, you're not suggesting that a fair comparison would be using a text editor?

If so, would you suggest an equivalent raster based task would only be fair, if the human would manually assigning RGB values to each pixel?

Are `(push s x)` and `(push x s)` correct for push and insert, resp.?

Oh dang, thanks for catching that. Will amend.

Favorite lemmata:

Johnson–Lindenstrauss lemma

https://en.wikipedia.org/wiki/Johnson%E2%80%93Lindenstrauss_...

Isolation lemma

https://en.wikipedia.org/wiki/Isolation_lemma

Schwartz–Zippel lemma

https://en.wikipedia.org/wiki/Schwartz%E2%80%93Zippel_lemma

Lovász local lemma

https://en.wikipedia.org/wiki/Lov%C3%A1sz_local_lemma

The division of lemmas and theorems is really a bit artificial for these things. But yeah I think the spirit is that a theorem is an object that you aim to study, while a lemma is something you use to do that. Fermat's last theorem was a target, but the techniques including lemmas used and developed for it are the real prize for a working mathematician. Sculptures are kind of the point, but there's no question the tools used for sculpting are more useful and "worth" more in that sense.

Ah the JL lemma. Probably one of my favorite too. I'm teaching a mathematics of data course next semester, and even though we don't assume probability as a prerequisite I'm going to find a way to talk about that idea.

I am sure you know this, but inner-products are not preserved, the el_2 distance is (approximately).

So it needs judicious care when used along with algorithm s that work with inner-products

If you preserve the l2 distance you preserve the inner product, that's somewhat tautological in an L2 space. Just that the degree you can preserve inner products can be misleading, main problem is that orthogonal vectors may only become near-orthogonal which is sometimes a big deal, though perfect correlations are preserved because the JL transform is linear. Both can be seen looking at: https://en.wikipedia.org/wiki/Polarization_identity

> If you preserve the l2 distance you preserve the inner product

That's trivially untrue. You can move the origin around and that doesn't change the el_2 metric but will change the inner product.

This would not happen for random rotations of course because they do not change the origin. However random Euclidean motions can change the origin.

Right, indeed you need to first preserve the origin, but also that is trivially true for a linear map like JL.

As far as I can recall JL holds for affine transformations too, in any case it's an existence result. Have to double check on the affine bit.

The popular proof does uses random linear transforms and they indeed will not change the origin, but that's just one class of transforms with the JL property.

I'm not sure your choice is the best. Axiom of choice is an axiom, not a theorem. In addition, axiom of choice is frequently stated (contrary to most other axioms) in proofs and assumptions.

It's also missing the defrag tool. Without it, it's going to be very slow as the disk fills up.

Should put a shortcut to it on the desktop as well, so that users who experience significant lag can defrag at will.