gukoff

Interesting, thank you for sharing.

Yes, and the standalone formal proof and independent review will follow.

By the way, I'd like to note that it will likely be a formalization of not the last result in that conversation, but of one of the initial proofs that relied on the Langford sequences and theorems of their existence.

Apologies for the confusion - the playground had a typo (7 instead of 8) which is fixed now. Now it works as you would expect, and zeroed potentials correspond to a zeroed hexagon.

The "wide ring" gadget is an interesting idea. I think it will be linear pyramids and not gaussian. A set of these gadgets can also form a basis, and in such a different basis the potential fields may look very different - almost flat, perhaps?..

Thank you, I'm glad you found it readable on mobile!

Thanks a lot for the detailed perspective!

The potential fields are a curious phenomenon. I feel like - and I haven't verified this in any way yet - the smoothness is dictated by the fact that all values are within a not-so-broad range. Then as you "peel" the hexagon from the outer layer using those 6-rings, building the potential field, each next layer inwards shouldn't changed too much.

I had also explored a case of n->inf where the sums turn into integrals, and consecutiveness turns into the uniform distribution. Then it's not so hard to find a solution. It's not in the article, because it turned out to be a dead end for solving the discrete case, and I didn't want to make the article too heavy - but if I remember correctly, there I also observed the smoothness.

You're absolutely right, technically the title should have said "every order other than 2" or "every order larger than 2". The case for 2 is impossible, because it immediately forces equal numbers on the outer layer.

Interesting observation. That's simply part of the usual definition of a magic square, and it does indeed feel arbitrary once you compare it with the hexagon case, which is very symmetrical. I first learned about magic squares from math books as a kid, about 25 years ago, and just accepted those rules as given.

Upon a quick research, there are many variations, and the closest to what you're describing is the "pandiagonal" magic square, where additional diagonals are considered (except they wrap around the edges of the square in a slightly funny way, so that every diagonal still contains exactly N numbers): https://en.wikipedia.org/wiki/Pandiagonal_magic_square

How do you run these models on AMD GPUs?

Timestamps are conversation metadata and don't need to be fed to the LLM and require tokens.

Draw.io already allows creating editable PNGs and SVGs: it embeds the diagram definition in the image metadata. You can then import this image like you would import any other .drawio diagram

The VSCode integration is the cherry on top. All files with the correct extension (such as xxx.drawio.png) will automatically open for edit in the draw.io UI embedded in the IDE.

I use this feature often to build on top of the previously made diagrams.

> Prof Penadés' said the tool had in fact done more than successfully replicating his research.

> "It's not just that the top hypothesis they provide was the right one," he said.

> "It's that they provide another four, and all of them made sense.

> "And for one of them, we never thought about it, and we're now working on that."

The Google's co-scientist still seems to make a useful assistant.

That's very impressive - how do you do this? I also see an IDE screen with the debugger in your other article about telegram - presumably also HTML/CSS

Thank you, this is very interesting

This really depends on the pure strategies that you choose.

The initial set of strategies wasn't very diverse and compensated for the binary search "weaknesses" on the ends of the spectrum by sometimes guessing 1 and 98.

But after adding some more pure strategies to the set, we've got a far better mixed strategy that prefers the numbers between 28-70 as the first pick: https://github.com/gukoff/ballmer_puzzle#winning-strategy

Interesting! What about the worst case? And which kinds of strategies did you pick?

I don't view the original problem this way, but let's think about it!

> the spread on that surely goes over the 0 line.

Do you imagine starting with $1 or $1000? :)

Let's add a condition that Ballmer has infinite money, we start with a specific budget, and we can't continue playing if we exceed budget randomly changes after each game,

In the game where you start with $N, win $1 with probability p > 0.5 and lose $1 otherwise, the chance of eventually losing all your money is (p/(1-p))^N. [1]

So, the ruin chance actually becomes exponentially lower the more money you have at the start.

The steps in the random walk above belong to a simple, Bernoulli-like random distribution. Meanwhile the mixed strategy is a more complex discrete random variable because it can do more steps than just +1 and -1.

However, I believe that the same principle applies for the mixed strategy.

If you zoom out and consider "batches" of steps, you can apply the Central limit theorem and see that all these random walks work roughly the same. The caveat being that you need a large enough starting budget to "zoom out" :)

Granted, the standard deviation for the mixed strategy is ~$1. I would guesstimate that if you start with ~$1000, there's no way you will ever lose your money.

> What would be more interesting is to monte carlo simulate this strategy and look at the win/loss distribution. Presumably the choice is then not so clear cut.

Agree, this would be a nice demonstration! I will think about doing this next time I get a couple of hours of free time.

[1] https://math.stackexchange.com/a/153141/65143

Thanks for spotting it! Exactly right, I fixed the text.

You can actually do well combining different flavors of binary search! I commented a solution on the parent post if you're curious.

You forget that the quick guesses bring you more than $1!

As the original article says, on average you can win $0.20. But that's indeed the upper bound if we speak of the adversarial number picking.

Yes, you can counter the adversarial choices and win at least 7 cents per game :)

https://gukov.dev/puzzles/math/2024/09/05/steve-ballmer-was-...

He means the last examples about Nintendo.com

Can you adjust vector magnitude prior to the normalization? If the max coordinate C is close enough to 0, divide all coordinates by C.

From your experience, where does it bring value?

What is the idea of "data push"?

Exactly. And stretching may lead to the further injuries if your muscles are weak and can't support the safe movement during the full range of motion. Especially if you already have hypermobility.

The author should talk to a knowledgeable physiotherapist, not a chiropractor...

The only habit you need are the regular strength exercises, especially for the stability of the back muscles.

Please, please forget about the stretches or "ergonomics" if you don't excersise. It will not help you in the long run.

Mind to share? I'd like to try this out

I just finished the first chapter, and so far I think it's really worth reading.

After years of Python development, I encountered all the same problems and reached all the same conclusions. I wish I read this at the beginning of my career.

Can I somehow get the list of all shows available on Netflix in country X but not in country Y?

I see that many see the apology as innocent and sincere.

To me, this apology screams narcissism and abuse. The author cares only about his public image and tailors the article accordingly. He knows what he's doing there. And I really, really don't envy those who work for him.

I wish I could think otherwise. But once you deal with a narcissist and see them abuse people, you know it.