From: Ben Goertzel (ben@goertzel.org)
Date: Mon Oct 25 2004 - 07:33:57 MDT
Well, I think the comparison btw the Riemann Hypothesis and FAI is not very
apt!
The Riemann Hypothesis is a hard math problem. It's possible that it's
undecidable according to the axioms of ZFC, but frankly I doubt it. I guess
it'll be solved in the next 50 years (even if the Singularity doesn't come
in that time-frame) by some clever human or a combination of a human and an
automated theorem-prover or by some AI. Just like the Fermat problem
recently succumbed.
The FAI problem may end up not being pragmatically formalizable as a pure
math problem. I can imagine proving theorems like "In any society of minds
fulfilling property P, an AI satisfying property Q will be Friendly with
probability p after time period T." But then the verification that human
minds fulfill property P is going to be intuitive rather than purely
mathematical -- unless it's based on a really detailed theory of human brain
dynamics.... The thing is we don't even know if theorems like I've outlined
above exist. The odds that the FAI problem is unsolvable seem to me,
intuitively, a lot higher than the odds that the Riemann Hypothesis is
undecidable.
-- Ben G
> -----Original Message-----
> From: owner-sl4@sl4.org [mailto:owner-sl4@sl4.org]On Behalf Of Marc
> Geddes
> Sent: Monday, October 25, 2004 3:09 AM
> To: sl4@sl4.org
> Subject: RE: A funding suggestion: Solve The Riemann hypothesis ;)
>
>
> --- Ben Goertzel <ben@goertzel.org> wrote:
> >
> > I believe I know how to define quantum chaos; see
> > Section 3 of
> >
> > http://www.goertzel.org/papers/ChaoQM.htm
> >
> > [which is an intuitive discussion -- I have not
> > worked out all the math by
> > any means]
> >
> > However, I do not understand the relationship
> > between this and the Riemann
> > Hypothesis.
> >
> > -- Ben G
> >
> > p.s. If someone wants to rule this off-topic for
> > SL4, I don't mind
> >
>
> Thanks for the link Ben. I'll have a read. Be
> assured that there is a strong connection between
> quantum chaos and the Riemann Hypothesis.
>
> Now I just need a way to calculate the probability of
> clearing the desk in the card game Klondike ;)
>
> PS I do not seriously think I can solve Riemann. But
> since I've started looking into FAI theory, I figured
> what the heck I may as well look into a second
> impossibly hard problem as well. FAI theory and
> Riemann are really just hobbies for me though ;)
>
> I suspect that the sort of *horribly hard* maths
> behind Riemann is of a comparable level of difficulty
> to the formal maths behind FAI theory. So if I can't
> solve Riemann, I can forget about FAI ;)
>
> Regarding FAI, I suspect that we are now at about the
> point that Einstein was regarding Relativity at the
> trun of the 20th century, or the founders of QM were
> regarding QM theory circa 1910. We have a good idea
> of the fundamental principles behind FAI, but now the
> principles need to be formalized into hard maths. I
> note that the process of working out the maths seems
> to take around 15-20, once the fundamental principles
> are known. For instance, it took Einstein from 1900
> to 1916 for Relativity, and the founders of QM from
> 1910 to around 1930 for QM. This suggests that at a
> minimum, we are still 15-20 years away from
> Singularity.
>
>
>
>
>
> =====
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> - Gen. John Stark
>
> "The Universe...or nothing!"
> -H.G.Wells
>
>
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>
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