elon musk's obsession with the tic tac toe of video games
https://awful.systems/post/3388357
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I just want to focus on this extremely ridiculous quote as if one understands how unfathomably silly it is - it becomes impossible to take anything elmo says seriously (not that you should need more proof)
What elmo is trying to talk about is called game-tree complexity - the number of possible games based on the number of possible moves.
For checkers this is 10^54 - massive but obviously computable (took 18 years and finished in 2007)
For chess this is 10^120 - called the Shannon number is unimaginably massive - like if we counted it in Planck times (smallest unit of time) - checkers’ number would convert to about 300 years - chess on the other hand comes out to around 10^58 universe ages
What’s more - there’s about 10^80 atoms in the universe - so it’s physically impossible to store that many game states in a usable manner to compute a full solution of chess.
Even giving him the biggest benefit of the doubt and turning the whole observable universe into a black hole (the most information dense object imaginable) the Bekenstein bound still dictates you only have 10^96 bits to work with so it appears it’s physically impossible to compute and store a full solution of chess.
Overall this proves the point of this post - elmo literally does not believe he lives in the real world and any proof otherwise will get rejected by his solipsistic brain.
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I’m splitting hairs here, but wouldn’t the 10^96 number just need to be a bound on the Kolmogorov complexity, whose value would be uncomputable? I don’t think you can conclude solution storage is impossible, it’s possible the Kolmogorov complexity is astonishingly low and there’s an algorithm that could be stored on a drive today, it would just require brilliant insight to find it and no one is going to devote time to that for a variety of reasons.
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That’s fair - I guess that’s why I said “it appears” as I can’t confidently state something whose unknowns I don’t fully understand.
But yeah theoretically there might be a way to compress the final output into a physically possible form. Still considering the magnitude of the numbers we’re talking - this would still be a mind boggling undertaking.
I guess my point was more around elmo confidently stating that chess is solvable and using the actual complexity of the task as a way to highlight how being that confident in such a statement is absurd.
Then again maybe I feel in a similar trap so thanks for pointing it out!
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Still considering the magnitude of the numbers we’re talking about - this would still be a mind boggling undertaking.
Nowhere near to the degree you seem to think, although it will tell you something about the maximum possible Kolmogorov complexity. Let’s say you’ve got a weird computer that can read, store, and compute with the English alphabet as symbols. If you want your computer to output a word that has 10^96 letters, it sounds completely impossible, but if every letter in the word is ‘A’, then a computer program to generate that word will take up virtually no space at all relative to storing each letter directly.
More generally, a massive amount of strings with 10^96 letters will have some pattern a program requiring relatively minimal storage can exploit, but finding that program for your string could be a herculean task.
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if I’ve followed the comment chain here correctly, the problem remains that you first need to compute all possible game states, which is probably impractical, right?
and you still need to save the data for computing the numbers’ compressed version, or is there a way to compress the numbers on-the-fly that i haven’t heard of?
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You don’t necessarily need to. There’s a possibility of defining instructions for winning without that. The idea may just be hard to imagine because chess is complicated.
You can make up stupid examples of games that defy this. Maybe we dream up a game with an ungodly number of states that has an action X that is an available option every turn. If the winning strategy is just “player 1 chooses action X every turn”, you can imagine there may be a way to show that’s true without needing to simulate every single state, and there’s certainly a way to easily store and communicate this strategy.
For a ludicrously dumb win condition, maybe the first playet to press X 10,000,000 times wins. You should be able to show that pressing X every turn is a winning strategy without computing every potential state. This can be true of more complicated games too, it would just be much less obvious. Just because no one has conceived of a way to do that yet with a game such as chess doesn’t mean no one ever will.
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the first playet to press X 10,000,000 times wins
Hey look, you found another one of Elon’s favourite games.
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