Re: large search spaces don't mean magic

From: Daniel Radetsky (
Date: Tue Aug 02 2005 - 03:29:54 MDT

On Tue, 2 Aug 2005 02:44:43 -0400
"Ben Goertzel" <> wrote:

> For instance, quantum physics can be derived from the assumption that
> uncertainty should be quantified using complex-valued probabilities (cf Saul
> Yousseff's work). Mathematically it seems consistent that there are more
> general physics theories that use quaternionic and octonionic
> probabilities>

Okay, so you have probabilities coming from "larger" fields than the reals. Do
you think you have evidence that those would provide box-exploits, or are you
just saying that you now have a larger universe of physical theories in which
box-exploits might be? The first disjunct is just another possibility, which
means it isn't an argument for magic. The second disjunct requires that you
answer my earlier objections. Pick a disjunct and start swinging.

> So you're right. The argument from the known (empirical and conceptual)
> incompleteness of physics is only PART of my reason for believing a
> superhuman AI could find a box-exploit.

But my point is that the incompleteness of physics provides next to no support
for the existence of exploits.

> The other part is the part you don't agree with, which is a general argument
> that if X is a lot smarter than Y, then X can probably find a way out of any
> box that Y creates.

That's only true if there really *is* a way out, given the circumstances X
finds himself in. It may simply be impossible for X to get out. To believe that
X can probably find a way out, you must first believe that X has a reasonable
way out. What makes you believe he has a way?

> It occurs to me now that it might be possible to prove a mathematical
> theorem to this effect. One could look at an average over all possible
> physical universes (assuming some probability distribution on them), and
> over all pairs of organisms X and Y within them, then try to prove that "If
> X is much smarter than Y, then X can escape from most boxes Y could create."

This sounds mighty specious to me, but I can't really say for sure until I know
exactly what it would mean. What is the probability distribution a distribution
of? Which of the universes is most likely? If so, it would have to work for
*any* probability distribution, since you don't know what the real one is,
including the distribution in which there is a probability of 1 that we end up
in a universe where most boxes are unbreakable (or it is ridiculously easy to
make an unbreakable box).

> Now, turning the previous paragraph into a real theorem would involve
> formalizing "intelligence" and "organism" and "box" in useful ways (which we
> have currently only made limited progress towards), and then proving a
> possibly very hard theorem. But I submit that if we did prove something
> like this, it would be decent evidence for the "other part" of my reason for
> believing a superhuman Ai could find a box-exploit.

You'd also need a good working definition of "possible," and other nasty
things like that. I doubt it would work. In any case, the evidence would only
be as strong as your definitions of all of the terms are uncontroversial. Good


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