Thanks for the concrete example. I do still think though that there is something of value in the quote that may be worth salvaging, perhaps by restricting it to solvable problems of the sort that we care about most (such as scientific and mathematical advances) and emphasizing not that everything is obvious to some conceivable intelligence but that most of what is currently not obvious to us and that we perceive as difficult is not obvious and is perceived as difficult not because it is intrinsically so but because we are so limited.
The heart of the quote for me is that instead of hardness being a function of one argument (in Haskell notation):
difficulty :: Problem → PositiveReal
it is a function of two arguments:
difficulty :: Mind → Problem → PositiveReal
And that most of the interesting real-world Problem instances that map to very large numbers for us (i.e. the difficult ones that we will eventually solve if we survive long enough) are problems that would be deemed obvious to sufficiently intelligent minds.
And that is a worthwhile insight, even if the function is not defined for all problems, even if there are solvable problems for which there are no physically possible minds that would yield “difficulty p m” (or “difficulty(p, m)” in Python syntax) being a small enough number to fall below the threshold of obviousness, and even if for any possible mind we can find solvable problems that have arbitrarily high difficulty.
Thanks for the concrete example. I do still think though that there is something of value in the quote that may be worth salvaging, perhaps by restricting it to solvable problems of the sort that we care about most (such as scientific and mathematical advances) and emphasizing not that everything is obvious to some conceivable intelligence but that most of what is currently not obvious to us and that we perceive as difficult is not obvious and is perceived as difficult not because it is intrinsically so but because we are so limited.
The heart of the quote for me is that instead of hardness being a function of one argument (in Haskell notation):
it is a function of two arguments:
And that most of the interesting real-world Problem instances that map to very large numbers for us (i.e. the difficult ones that we will eventually solve if we survive long enough) are problems that would be deemed obvious to sufficiently intelligent minds.
And that is a worthwhile insight, even if the function is not defined for all problems, even if there are solvable problems for which there are no physically possible minds that would yield “difficulty p m” (or “difficulty(p, m)” in Python syntax) being a small enough number to fall below the threshold of obviousness, and even if for any possible mind we can find solvable problems that have arbitrarily high difficulty.