Christian’s argument shows there are always problems that can’t be solved or shown to be unsolvable. But even if you ignore them and look at finitely solvable problems (or provable theorems in PA), there’s no upper bound on the time or processing power needed to solve a randomly chosen problem. Not even for the “smartest” intelligence allowed by the laws of physics (i.e. the one ideally optimized to solve the chosen problem).
Christian’s argument shows there are always problems that can’t be solved or shown to be unsolvable. But even if you ignore them and look at finitely solvable problems (or provable theorems in PA), there’s no upper bound on the time or processing power needed to solve a randomly chosen problem. Not even for the “smartest” intelligence allowed by the laws of physics (i.e. the one ideally optimized to solve the chosen problem).
Thanks for the clear explanation. My response below to Christian is relevant here also.