DanArmak comments on LW/OB Quotes - Fall 2009 - Less Wrong
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Does your 2nd sentence hold recursively? And could you explain why that is the case?
I can easily imagine mathematical problems that are non-obviously not answerable for me or for human beings much smarter than I am, just as the Continuum Hypothesis was for human beings before Godel and Cohen, but I can also easily imagine an intelligence that would, for example, nearly instantly notice Godel's incompleteness theorems as obvious consequences of the Peano axioms.
That is not literally what the original quote says, but an intelligence that could, for example, 'learn' our next century of discoveries in mathematics and theoretical physics in an afternoon seems to me to justify the weaker position that there are possible intelligences that would regard every problem we have yet solved or shown to be unsolvable as obvious and not hard.
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.