[Closi]

Why would we teach kids maths then, when they can use a calculator? It's much easier and faster for them.

I believe it's because having a foundational understanding of maths and logic is important when solving other problems, and if you are looking to create an AI that can generally solve all problems it should probably have some intuitive understanding of maths too.

i.e. if we want an LLM to be able to solve unsolved theorems in the future, this requires a level of understanding of maths that is more than 'teach it to use a calculator'.

More broadly, I can imagine a world where LLM training is a bit more 'interactive' - right now if you ask it to play a game of chess with you it fails, but it has only ever read about chess and past games and guesses the next token based on that. What if it could actually play a game of chess - would it get a deeper appreciation for the game? How would this change it's internal model for other questions (e.g. would this make it answer better at questions about other games, or even game theory?)

[ChatGTP]

It's also fun to use your brain I guess, I think we've truly forgotten that life should be about fun.

Watching my kids grow up, they just have fun doing things like trying to crawl, walk or drink. It's not about being the best at it, or the most efficient, it's just about the experience.

Now maths is taught in a boring way, but knowing it can help us lead more enjoable lives. When math is taught in an enjoyable way AND people get results out of it. Well that's glorious.

[smeej]

> Why would we teach kids maths then, when they can use a calculator? It's much easier and faster for them.

I am five years older than my brother, and we happened to land just on opposite sides of when children were still being taught mental arithmetic and when it was assumed they would, in fact, have calculators in their pockets.

It drives him crazy that I can do basic day-to-day arithmetic in my head faster than he can get out his calculator to do it. He feels like he really did get cheated out of something useful because of the proliferation of technology.

[wegfawefgawefg]

Skull has limited volume. What room is unused by one capacity may be used by another.

[smeej]

Even if that were true, I can count on one hand the number of times I've needed to use anything more than basic algebra (which is basically arithmetic with a placeholder) in my adult life. I think I'd genuinely rather keep arithmetic in my head than calculator use.

[Jeff_Brown]

Is this intuition scientifically supported? I've read that people who remember every detail of their lives tend not to have spectacular intelligence, but outside of that extreme I'm unaware of having seen the tradeoff actually bite. And there are certainly complementarities in knowledge -- knowing physics helps with chemistry, knowing math and drama both help with music, etc.

[wegfawefgawefg]

Chimps have a much better working memory than humans. They can also count 100 times faster than humans. However, the area of their brain responsible for this faculty is used for language in humans... The theory is that the prior working memory and counting ability may have been optimized out at some point to make physical room, assuming human ancestors could do it too.

Lookup the chimp test. the videos of the best chimp are really quite incredible.

There is also the measured inflation of map traversing parts of the brain in pro tetris players and taxi drivers. I vaguely remember an explanation about atrophy in nearby areas of the brain, potentially to make room.

[comex]

Judging by some YouTube videos I’ve seen, ChatGPT with GPT-4 can get pretty far through a game of chess. (Certainly much farther than GPT-3.5.) For that duration it makes reasonably strategic moves, though eventually it seems to inevitably lose track of the board state and start making illegal moves. I don’t know if that counts as being able to “actually play a game”, but it does have some ability, and that may have already influenced its answers about the other topics you mentioned.

[vczf]

What if you encoded the whole game state into a one-shot completion that fits into the context window every turn? It would likely not make those illegal moves. I suspect it's an artifact of the context window management that is designed to summarize lengthy chat conversations, rather than an actual limitation of GPT4's internal model of chess.

[actionfromafar]

I am sorry, but I thought it was a bold assumption it has an internal model of chess?

[vidarh]

Having an internal model of chess and maintaining an internal model of the game state of a specific given game when it's unable to see the board are two very different things.

EDIT: On re-reading I think I misunderstood you. No, I don't think it's a bold assumption to think it has an internal model of it at all. It may not be a sophisticated model, but it's fairly clear that LLM training builds world models.

[PoignardAzur]

Not that bold, given the results from OthelloGPT.

We know with reasonable certainty that an LLM fed on enough chess games will eventually develop an internal chess model. The only question is whether GPT4 got that far.

[tedajax]

Doesn't really seem like an internal chess model if it's still probabalistic in nature. Seems like it could still produce illegal moves.

[vidarh]

So can humans. And nothing stops probabilities in a probabilistic model from approaching or reaching 0 or 1 unless your architecture explicitly prevents that.

[baq]

Why?

Or, given https://thegradient.pub/othello/, why wouldn't it have an internal model of chess? It probably saw more than enough example games and quite a few chess books during training.

[vidarh]

> More broadly, I can imagine a world where LLM training is a bit more 'interactive'

Well, yes, assume that every conversation you have with ChatGPT without turning off history makes it into the training set.