>2. Self-enhancement: It seems likely to me that there is
>an optimal strategy of intelligence increase which
>cannot be bettered except by luck or by working solely
>within a particular problem domain, and that this
>strategy is in some way isomorphic to calculating
>successive approximations to Chaitin's halting
>probability for a Turing machine given random
>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
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.
What I don't know yet is the most rapid way of
approximating Omega. Chaitin says somewhere that
you cannot know how rapidly you are converging,
it's another aspect of the noncomputability.
I think the Resource Bounded Probability method
of induction (http://world.std.com/~rjs/isis96.html)
might amount to an Omega approximation strategy,
but I'm not sure yet.
>I'm not as certain as you are that there exists an
>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.
Even if you decide to approximate Omega by blind
simulation, you still have decisions to make - you can't
let all the nonterminating programs run forever. If
there's no free lunch, that might mean even if you cull
them randomly, you'll still be converging on Omega as
fast as possible.
> > 3. If this is so, then once this strategy is
> > winning the intelligence race may after all boil
> > to hardware issues of speed and size (and possibly
> > issues of physics, if there are physical processes
> > which can act as oracles that compute trans-Turing
> > functions).
>What if this strategy is hard to compute
>efficiently, and different
>choices in initial conditions will produce
>noticeable differences in
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).
> > 5. Initial conditions: For an entity with goals or
> > intelligence is just another tool for the
> > of goals. It seems that a self-enhancing
> > could still reach superintelligence having started
> > almost *any* set of goals; the only constraint is
> > the pursuit of those goals should not hinder the
> > of self-enhancement.
>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
Ben Goertzel said
>My intuition is that there's going to be a huge diversity of possible ways
>to achieve intelligence increase by self-enhancement, each one with its own
>advantages and disadvantages in various environments.
This is surely true. Assuming that calculating Omega
really is a meta-solution to all problems, the real
question is then: What's more important - solving
environment-specific problems which Approximate Omega
can't yet solve for you, by domain-specific methods,
or continuing to calculate Omega? My guess is that in
most environments, even such a stupid process as
approximating Omega by blind simulation and random
culling always deserves its share of CPU time.
(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.)
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