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Algebraicness

tsvibt.github.io · 489 words · saved by 1 readers

There's a dimension of task-sets that's something like: how much is it the case that solving tasks like this basically boils down to "crunching the numbers"? We could call this "combinatoricness" or "algebraicness". Algebraic things are soulless, calculative. More to the point, compared to more structure-rich tasks, it's less the case that being a mind implies being good at algebraic tasks, or vice versa. Examples: Humans tend to find it fun when there's a continuum of combinatorics/algebra in a domain. In chess, very crudely speaking, you could look one move ahead, two moves ahead, etc. (That's not really how it works, but there's a similar spirit that does hold true. Stronger players will tend to deal with longer, more complex, more contingent, more counterintuitive combinations. Even Karpov would, I assume without knowing, be playing strategically/positionally in response to an environment with such calculating opponents, tuned to shut down such tactics.) We can ask different things

Algebraicness There's a dimension of task-sets that's something like: how much is it the case that solving tasks like this basically boils down to "crunching the numbers"? We could call this "combinatoricness" or "algebraicness". Algebraic things are soulless, calculative. More to the point, compared to more structure-rich tasks, it's less the case that being a mind implies being good at algebraic tasks, or vice versa. Examples: Small-world games tend to be algebraic. E.g. chess, Go, etc. Think of a Zachtronics game like SpaceChem. Or tetris. Similarly, a lot of problems in number theory or an

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