The relevant value of K here is something like the total number of bits of information embodied in, and available to, the whole human race, including whatever other bits of the universe we may happen to recruit for our use. So K might be extremely large.
Now let me remind you that the size and (in ordinary informal terms) complexity, and indeed the speed, of a hypothetical Thinking Device scarcely influence its Kolmogorov complexity. If it takes some number of bits to specify a machine with 3^^^3 bits of memory or 3^^^3 artificial neurons, it takes only a few bits more to replace 3^^^3 with 3^^^^3.
So I’m going to go with “option 1, for all practical purposes”. All it requires is that there be a recipe for How To Think that can be stated in (let’s say) not too many orders of magnitude more space than the entire intellectual output of the human race to date, given that we’re allowed to equip it with essentially-arbitrary amounts of actual hardware, such that other ways of thinking aren’t in principle more powerful in the sense that they do better no matter how much hardware one throws at ours. That seems pretty plausible to me.
The relevant value of K here is something like the total number of bits of information embodied in, and available to, the whole human race, including whatever other bits of the universe we may happen to recruit for our use. So K might be extremely large.
Now let me remind you that the size and (in ordinary informal terms) complexity, and indeed the speed, of a hypothetical Thinking Device scarcely influence its Kolmogorov complexity. If it takes some number of bits to specify a machine with 3^^^3 bits of memory or 3^^^3 artificial neurons, it takes only a few bits more to replace 3^^^3 with 3^^^^3.
So I’m going to go with “option 1, for all practical purposes”. All it requires is that there be a recipe for How To Think that can be stated in (let’s say) not too many orders of magnitude more space than the entire intellectual output of the human race to date, given that we’re allowed to equip it with essentially-arbitrary amounts of actual hardware, such that other ways of thinking aren’t in principle more powerful in the sense that they do better no matter how much hardware one throws at ours. That seems pretty plausible to me.