> There's a physical challenge which operates on *one* AIXI-tl and breaks
> it, even though it involves diagonalizing the AIXI-tl as part of the
> challenge.

OK, I see what you mean by calling it a "physical challenge."  You mean
that, as part of the challenge, the external agent posing the challenge is
allowed to clone the AIXI-tl.

>  > An intuitively fair, physically realizable challenge, with important
>  > real-world analogues, formalizable as a computation which can be fed
>  > either a tl-bounded uploaded human or an AIXI-tl, for which the human
>  > enjoys greater success measured strictly by total reward over time, due
>  > to the superior strategy employed by that human as the result of
>  > rational reasoning of a type not accessible to AIXI-tl.
> It's really the formalizability of the challenge as a computation which
> can be fed either a *single* AIXI-tl or a *single* tl-bounded uploaded
> human that makes the whole thing interesting at all... I'm sorry I didn't
> succeed in making clear the general class of real-world analogues for
> which this is a special case.

OK....  I don't see how the challenge you've described is
"formalizable as a computation which can be fed either a tl-bounded uploaded
human or an AIXI-tl."

The challenge involves cloning the agent being challenged.  Thus it is not a
computation feedable to the agent, unless you assume the agent is supplied
with a cloning machine...

> If I were to take a very rough stab at it, it would be that the
> cooperation case with your own clone is an extreme case of many scenarios
> where superintelligences can cooperate with each other on the one-shot
> Prisoner's Dilemna provided they have *loosely similar* reflective goal
> systems and that they can probabilistically estimate that enough loose
> similarity exists.

Yah, but the definition of a superintelligence is relative to the agent
being challenged.

For any fixed superintelligent agent A, there are AIXItl's big enough to
succeed against it in any cooperative game.

To "break" AIXI-tl, the challenge needs to be posed in a way that refers to
AIXItl's own size, i.e. one has to say something like "Playing a cooperative
game with other intelligences of intelligence at least f(t,l)"  where if is
some increasing function....

If the intelligence of the opponents is fixed, then one can always make an
AIXItl win by increasing t and l ...

So your challenges are all of the form:

* For any fixed AIXItl, here is a challenge that will defeat it

ForAll AIXItl's A(t,l), ThereExists a challenge C(t,l) so that fails_at(A,C)

or alternatively

ForAll AIXItl's A(t,l), ThereExists a challenge C(A(t,l)) so that

rather than of the form

* Here is a challenge that will defeat any AIXItl

ThereExists a challenge C so that ForAll AIXItl's A(t,l), fails_at(A,C)

The point is that the challenge C is a function C(t,l) rather than being
independent of t and l

This of course is why your challenge doesn't break Hutter's theorem.  But
it's a distinction that your initial verbal formulation didn't make very
clearly (and I understand, the distinction is not that easy to make in

Of course, it's also true that

ForAll uploaded humans H, ThereExists a challenge C(H) so that fails_at(H,C)

What you've shown that's interesting is that

ThereExists a challenge C, so that:
-- ForAll AIXItl's A(t,l), fails_at(A,C(A))
-- for many uploaded humans H, succeeds_at(H,C(H))

(Where, were one to try to actually prove this, one would substitute
"uploaded humans" with "other AI programs" or something).

>  The interesting part is that these little
> natural breakages in the formalism create an inability to take part in
> what I think might be a fundamental SI social idiom, conducting binding
> negotiations by convergence to goal processes that are guaranteed to have
> a correlated output, which relies on (a) Bayesian-inferred initial
> similarity between goal systems, and (b) the ability to create a
> top-level
> reflective choice that wasn't there before, that (c) was abstracted over
> an infinite recursion in your top-level predictive process.

I think part of what you're saying here is that AIXItl's are not designed to
be able to participate in a community of equals....  This is certainly true.

--- Ben G

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