There are ways to make it work, but it requires using it only supplementary and with strict discipline. And it will look different for a 6-year old than a 13-year old.
But think of this trick we use about turning a tricky research paper in maths/science into something more tangible by making an LLM whip up an interactive version. That works at every level of education, and it means that you can completely tailor a piece of educational material to the kid
Tiny example: one kid was introduced to fractions and found it abstract that it was both about partitioning stuff and about numbers on a number line. So while we were practicing, I had an LLM make https://fuglede.codeberg.page/broeklegeplads/ to make it more hands-on.
Obviously for the small kids, this has to be an experience guided by teachers and parents, but for bright older kids with sufficient discipline that ought to be a useful trick for enhancing education.
Of course when we were kids, we would just write such educational programs ourselves and get the same effect /and/ learn to program (before getting banned from the computer room for putting spooky /binaries/ on the computers anyway), so maybe that's better for older kids. And maybe these kids will never have to do any maths or programming because the AI overlords have taken over when they grow up.
I've reached for this solution many times too; it's certainly convenient.
What I don't like is that all the resulting pages look the same. It's so easy to tell when a page is authored by Claude, and by now, I get the same “ugh another one” feeling as Dall-E generated images would give when they were completely overdone.
Maybe it's just be, but if not, maybe HTML generated outputs will also end up being dialed down from where they're at now.
But maybe not, since it's obviously a useful thing to be able to do. I wonder if there's a way out. To be able to introduce some natural entropy so not everything ends up looking the same. I guess not, since we're using machines whose natural mode of behavior is regression toward the mean. And maybe having it be harder to tell the author wouldn't even be desirable anyway.
It would be very helpful to know in understanding the capabilities of the models; and in getting intuition about where they are best applicable.
If the reason it was able to output the proof is that it happened to be included in an in-house university report written in Georgian, then that would make it less useful for research than if it's new entirely.
The XOR swap trick also features in the compilation/synthesis of quantum algorithms, where the XOR instruction (in the form of a CNOT gate) is fundamental in many architectures, and where native swapping need not be available.
One extension that I ran into, and which I think forms a nice problem is the following:
Just like the XOR swap trick can be used to swap to variables (and let's just say that they're bools), it can be extended to implement any permutation of the variables: suppose that the permutation is written as a composition of n transpositions (i.e., swaps of pairs), and that is the minimal number of transpositions that let's you do that. Each transposition can be implemented by 3 XORs, by the XOR swap trick for pairs, and so the full permutation can be implemented by 3n XORs. Now here's the question: Is it possible to come up with a way of doing it with less than 3n, or can we find a permutation that has a shortcut through XOR-land (not allowing any other kinds of instructions)? In other words, is XOR-swapping XOR-optimal?
I'm not going to spoil it, but only last year a paper was published in the quantum information literature that contains an answer [0]. I ended up making a little game where you get to play around with XOR-optimizing not only permutations, but general linear reversible circuits. [1]
Just to not feed the witch hunt further, note that human 30 second solve times can be entirely possible for the easiest puzzles, with enough experience, practice, and a bit of risk-taking; see e.g. https://adventofcode.com/2021/leaderboard/day/1 part 1. But the 4 second solution times we saw last year are not, no matter how you look at it.
But yes, you would have people openly share repositories for automatically ingesting the puzzle text, solving the puzzles, and submitting the results the moment the puzzles opened, leading to inhuman solution times. So, despite the rules stating that you can't do that, the result is that whenever the puzzles were easy enough for an LLM to solve them with high probability – and most of them are – the leaderboards would be overrun with such solutions.
In 2023, the LLMs would still struggle enough that the overall leaderboard (taking all 25 ⋅ 2 puzzles into account) would still be dominated by ordinary people (many of them recording their solutions), in 2024 that was no longer the case. Personally I would go from being able to top 100 regularly, to almost never being able to. I'm going to miss the thrill, and think it's a bit saddening that we can't have nice things, but also ultimately think that getting rid of it is the best option.
Hm, yeah, tested it down to about 500 px width, and the low-resolution devices in Chromium but that was too optimistic then. The modals should of course be closeable, and both game boards simultaneously visible. Played around with the modals a bit, so maybe it works better now?
Yeah, the problem is in a sense solved asymptotically by the optimal construction in https://arxiv.org/abs/quant-ph/0302002, but that one tends to lead to long solutions in practice, so there's plenty of room to try to come up with solutions that give shorter solutions for concrete instances.