(Sorry about the double comment, but several responses were posted while I was typing.)
“It’s one thing to say that any implementation of an algorithm (or mind) has some physical basis, which is pretty obviously true and hence not very interesting, but if those implementations have nothing physical in common, then your reduction hasn’t actually accomplished very much.”
The reduction of a software system is just as difficult as the reduction of a physical system, and perhaps even more so. I believe there’s a theorem which states that the problem of producing a Turing machine which will give output Y for input X is uncomputable in the general case.
“That suggests that the algorithm itself is not a physical thing, but something else.”
Algorithms are made from math; math was originally abstracted from physical matter in exactly the way that you describe. You can implement “two” on completely different physical systems- two apples, two computers, two Space Shuttles, and so on.
“Your conjecture seems to be that the Problem of Chess requires intelligence.”
It’s just an example of how complex behaviors can arise from simple parts that don’t exhibit the behaviors themselves. Chess-playing, although not equivalent to general intelligence, does require several complex behaviors which are also used by general intelligence.
“I also don’t see how you can claim that understanding utility functions helps you understand the brain. Do you think that such functions are explicitly represented in the brain?”
Utility functions are general enough to apply to any optimization process which can state a clear preference over outcomes.
(Sorry about the double comment, but several responses were posted while I was typing.)
“It’s one thing to say that any implementation of an algorithm (or mind) has some physical basis, which is pretty obviously true and hence not very interesting, but if those implementations have nothing physical in common, then your reduction hasn’t actually accomplished very much.”
The reduction of a software system is just as difficult as the reduction of a physical system, and perhaps even more so. I believe there’s a theorem which states that the problem of producing a Turing machine which will give output Y for input X is uncomputable in the general case.
“That suggests that the algorithm itself is not a physical thing, but something else.”
Algorithms are made from math; math was originally abstracted from physical matter in exactly the way that you describe. You can implement “two” on completely different physical systems- two apples, two computers, two Space Shuttles, and so on.
“Your conjecture seems to be that the Problem of Chess requires intelligence.”
It’s just an example of how complex behaviors can arise from simple parts that don’t exhibit the behaviors themselves. Chess-playing, although not equivalent to general intelligence, does require several complex behaviors which are also used by general intelligence.
“I also don’t see how you can claim that understanding utility functions helps you understand the brain. Do you think that such functions are explicitly represented in the brain?”
Utility functions are general enough to apply to any optimization process which can state a clear preference over outcomes.