[FOM] Re: Harvey Friedman's "hyperaliens"
Timothy Y. Chow
tchow at alum.mit.edu
Sun Mar 14 18:54:37 EST 2004
Harvey Friedman <friedman at math.ohio-state.edu> wrote:
> These experiments are done on the device as a "black box" with
> absolutely no understanding whatsoever of its internal mechanism.
> I claim that we would then obtain a "proof" that Goldbach conjecture is
> false, that is not as convincing as one would hope, but substantially
> more convincing than any knowledge that we presently have in the
> sciences and engineering outside mathematics.
I don't directly disagree with this, but I don't really see what this has
to do with hypercomputation per se. We have "proofs" of this kind already
of all kinds of mathematical statements---e.g., that such-and-such a
probabilistic prime is really a prime, that the next 10^10 zeroes of the
Riemann zeta function that we bother to compute will lie on the critical
line, that ZFC is consistent, and so on. The hyperaliens do not seem to
add anything qualitatively different to this situation.
Let me put it this way. Soon after Harvey Friedman's aliens show up,
another group of extraterrestrials arrives. Seeing the situation, the
ET's roll their eyes and tell us, "I see you've met the hyperaliens.
Don't believe a word they say; they're charlatans. They've monitored
your mathematical progress and they know exactly what you've proved so
far and all the things you're capable of verifying with your limited
resources, and have hardcoded the `right' answers into their black box.
We made the mistake of forking over lots of cash for one of their black
boxes, and our scientists analyzed it and found that it's no better than
snake oil. You'd be much better off using one of *our* computers, which
is just a conventional computer but 10^100 times more powerful than
yours. We don't claim to break the Church-Turing barrier, but your
confidence will be a lot better founded if you base it on our machine
rather than theirs."
I see no real difference between choosing to believe the aliens versus
choosing to believe the ET's. So this seems orthogonal to the issue of
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