David, I would categorize this under the heading of “trying to measure how much effort something takes”. I’m just trying to integrate over a measure, not describe the structure of the space relative to a particular way of searching for solutions. One kind of search might bog down where another would succeed immediately—the neighborhood of a problem space as seen by a human is not like the neighborhood of DNA strands seen by natural selection. One mind’s cheap problem that can be solved by a short program like water running downhill is another mind’s stumper—to a transhuman mind, for example, chess might appear as a pointless exercise because you can solve it by a simple Deep-Blue like program.
Indeed, there was recently developed a program that plays provably correct checkers from the canonical starting position—so it is now clear that playing checkers requires no optimization power, since you can solve it as deterministically as water running downhill. At least that’s where this argument seems to me to lead.
I think you just have to construct “impressiveness” in a more complex way than “optimization power”.
David, I would categorize this under the heading of “trying to measure how much effort something takes”. I’m just trying to integrate over a measure, not describe the structure of the space relative to a particular way of searching for solutions. One kind of search might bog down where another would succeed immediately—the neighborhood of a problem space as seen by a human is not like the neighborhood of DNA strands seen by natural selection. One mind’s cheap problem that can be solved by a short program like water running downhill is another mind’s stumper—to a transhuman mind, for example, chess might appear as a pointless exercise because you can solve it by a simple Deep-Blue like program.
Indeed, there was recently developed a program that plays provably correct checkers from the canonical starting position—so it is now clear that playing checkers requires no optimization power, since you can solve it as deterministically as water running downhill. At least that’s where this argument seems to me to lead.
I think you just have to construct “impressiveness” in a more complex way than “optimization power”.