Roger Penrose thinks the human brain can do things a Turing machine
cannot. (Note: I don't say 'computer'.) He claims it's due to some
quantum-physical effects used by the brain. I doubt his ideas are
correct, but he did have a few interesting chess-positions to support
his theory. Typically, they would contain a completely locked
position, say a V-shaped pawn position and bishops on the wrong color
to pass the pawn-ranks. These types of positions are very easily
analyzed by even mediocre players, yet a computer never gets the right
answer.
Basically what it shows is that the human brain is able to
conceptualize certain things that enable it to reason about situations
that cannot be calculated by brute force. I don't claim that a Turing
machine cannot do such things as well if programmed well, but it's
very easy to see that there could be barriers to computers, no matter
how much computing power you give them, if they solely rely on a
simple method with brute force.
Mark
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