If the guesser wins routinely, this suggests that the thinker can access about 220≈1 million possible items in the few seconds allotted.
I’m not sure this premise is sound. Are there not infinitely more than 2^20 permutations of the game?
This would be true if the questions were preset, but the game, in reality, requires the guesser to make choices as the game progresses. These choices can be quite complex, relying on a well developed theory of mind and shared cultural context. Not all the information is internal to the mechanics of the game.
The unspoken rules of the game also require the thinker to pick something that can plausibly be solved. Picking something outlandishly obscure would be frowned upon. The game is partly cooperative in that sense.
If you were to reduce the game to “guess the number I’m thinking of between 0 and infinity”, then it wouldn’t be very fun, it would not persist across time and cultures, and you wouldn’t be studying it. But you might get close to a 0% win rate (or…maybe not?).
I’d guess that most of the “few seconds” the thinker spends is actually to reduce the number of candidates to something reasonable within the context of the game. If that’s true, it says nothing whatsoever about the upper bound of possibilities they are capable of considering.
Idea for further research: establish a “30 questions” game and compare win rates over time. Hypothesis: the win rate in 30 questions would fall to similar levels as with “20 questions” as players gained experience with the new mechanics and optimized their internal selection process.
our brain will never extract more than 10 bits/s
Aren’t there real recorded cases of eidetic memory? E.g. The Mind of a Mnemonist. I have not re-read that book with a mind toward information theory, so perhaps I am overestimating/misremembering the true information content of his memories.
I’m not sure this premise is sound. Are there not infinitely more than 2^20 permutations of the game?
This would be true if the questions were preset, but the game, in reality, requires the guesser to make choices as the game progresses. These choices can be quite complex, relying on a well developed theory of mind and shared cultural context. Not all the information is internal to the mechanics of the game.
The unspoken rules of the game also require the thinker to pick something that can plausibly be solved. Picking something outlandishly obscure would be frowned upon. The game is partly cooperative in that sense.
If you were to reduce the game to “guess the number I’m thinking of between 0 and infinity”, then it wouldn’t be very fun, it would not persist across time and cultures, and you wouldn’t be studying it. But you might get close to a 0% win rate (or…maybe not?).
I’d guess that most of the “few seconds” the thinker spends is actually to reduce the number of candidates to something reasonable within the context of the game. If that’s true, it says nothing whatsoever about the upper bound of possibilities they are capable of considering.
Idea for further research: establish a “30 questions” game and compare win rates over time. Hypothesis: the win rate in 30 questions would fall to similar levels as with “20 questions” as players gained experience with the new mechanics and optimized their internal selection process.
Aren’t there real recorded cases of eidetic memory? E.g. The Mind of a Mnemonist. I have not re-read that book with a mind toward information theory, so perhaps I am overestimating/misremembering the true information content of his memories.