Anders Sandberg wrote:
> "Mitchell Porter" <mitchtemporarily@hotmail.com> writes:
>
> > Anders said
> >
> > >Why is this isomorphic to Chaitin approximations? I
> > >might have had too
> > >little sleep for the last nights, but it doesn't
> > >seem clear to me.
> >
> > If you know the halting probability for a Turing
> > machine, you can solve the halting problem for
> > any program on that machine. ("... knowing Omega_N
> > [first N bits of the halting probability] enables
> > one to solve the halting problem for all N-bit
> > programs" --http://www.cs.umaine.edu/~chaitin/nv.html)
>
> Aha!
>
> > The idea is that a superintelligence would have
> > a 'computational core' which spends its time
> > approximating Omega, and modules which take general
> > problems, encode them as halting problems, and look
> > them up in Approximate Omega.
>
> Ah, that's where the rub is: how do you convert a general problem into
> a halting problem in an efficient way? For example, how does "What
> actions will give me the largest probability of having more than one
> million dollars within ten years?" or "How do I build a
> nanoassembler?" convert into halting problems?
>
> I would guess that the sum of work often remains constant in the
> general case: the amount of work needed to encode a problem into a
> form solvable by an algorithm and the amount of work in using the
> algorithm tend to be fairly constant. Intelligence is about finding
> ways of getting around this by exploiting patterns that make the
> problem non-general, such as in mathematical tricks where a simple
> transformation makes a hard problem simple.
>
> > >I'm not as certain as you are that there exists an
> > >unique optimal
> > >strategy. Without working within a certain problem
> > >domain the no free
> > >lunch theorems get you. Taking the problem domain to
> > >be 'the entire
> > >physical universe' doesn't really help, since you
> > >also have to include
> > >the probability distribution of the environment, and
> > >this will be very
> > >dependent not just on the interests but also actions
> > >of the being.
> >
> > I think approximating Omega is precisely the sort of
> > task where a no-free-lunch theorem is likely to apply.
> > The optimal strategy probably involves nothing more
> > intelligent than simulating all possible programs, and
> > incrementing Approximate Omega appropriately when one
> > is seen to terminate. The no-free-lunch theorem might
> > be: even if you have an approximation strategy which
> > outperforms blind simulation in calculating some finite
> > number of Omega bits, its asymptotic performance can't
> > beat blind simulation.
>
> Sounds possible.
>
> > >What if this strategy is hard to compute
> > >efficiently, and different
> > >choices in initial conditions will produce
> > >noticeable differences in
> > >performance?
> >
> > If the No-Free-Omega Hypothesis :) is correct, then
> > such differences in performance will disappear
> > asymptotically (assuming hardware equality, and assuming
> > no-one pursues a *sub*optimal strategy).
>
> Ah, egalitarian transcendence! I wonder what we libertarians on the
> list should make of it :-)
>
> > >Some goals are not much helped by intelligence
> > >beyond a certain level
> > >(like, say, gardening), so the self-enhancement
> > >process would peter
> > >out before it reached any strong limits.
> >
> > Only if self-enhancement was strictly a subgoal of
> > the gardening goal. But perhaps this is more precise:
> > self-enhancement will not be hindered if it is a
> > subgoal of an open-ended goal, or a co-goal of just
> > about anything.
>
> Beings with closed goals will eventually run out of expansion, I
> think. Only beings with open-ended goals will be motivated to grow and
> persist indefinitely. Playing Carse's "infinite games" might be a
> survival trait for posthumans.
>
> > (Okay, that's a retreat from 'You don't have to do
> > anything *but* approximate Omega!' But this is what
> > I want a general theory of self-enhancement to tell me -
> > in what sort of environments will you *always* need
> > domain-specific modules that do something more than
> > consult the Omega module? Maybe this will even prove
> > to be true in the majority of environments.)
>
> A very interesting question. I'll have to think hard on that one, it
> seems to relate to some of my own issues with how to set learning
> parameters dependent on the information learned from the environment.
>
> --
> -----------------------------------------------------------------------
> Anders Sandberg Towards Ascension!
> asa@nada.kth.se http://www.nada.kth.se/~asa/
> GCS/M/S/O d++ -p+ c++++ !l u+ e++ m++ s+/+ n--- h+/* f+ g+ w++ t+ r+ !y
I was thinking about it, and having hundreds of thousands of free
processors waiting for you to cast them a thread, in a physical computer
of the future. The processors are very fast.
Ross
This archive was generated by hypermail 2b30 : Mon May 28 2001 - 09:56:38 MDT