Yeah, Penrose’s position that the human brain is a hypercomputer isn’t really supported by known physics, but there’s still enough unknown and poorly understood physics that it can’t be ruled out. His “proof” that human brains are hypercomputers based on applying Godel’s incompleteness theorem to human mathematical reasoning, however, missed the obvious loophole: Godel’s theorem only applies to consistent systems, and human reasoning is anything but consistent!
His “proof” that human brains are hypercomputers based on applying Godel’s incompleteness theorem to human mathematical reasoning, however, missed the obvious loophole: Godel’s theorem only applies to consistent systems, and human reasoning is anything but consistent!
I thought the obvious loophole was that brains aren’t formal systems.
I thought the obvious loophole was that one can construct statements of the form “Cyan’s brain can’t prove this statement is true”. (The statement is true, but you’ll have to prove it for yourself—you can’t take my word for it.)
Yeah, Penrose’s position that the human brain is a hypercomputer isn’t really supported by known physics, but there’s still enough unknown and poorly understood physics that it can’t be ruled out. His “proof” that human brains are hypercomputers based on applying Godel’s incompleteness theorem to human mathematical reasoning, however, missed the obvious loophole: Godel’s theorem only applies to consistent systems, and human reasoning is anything but consistent!
I thought the obvious loophole was that brains aren’t formal systems.
If you can simulate them in a Turing machine, then they might as well be.
I thought the obvious loophole was that one can construct statements of the form “Cyan’s brain can’t prove this statement is true”. (The statement is true, but you’ll have to prove it for yourself—you can’t take my word for it.)