From: Lee Corbin (lcorbin@tsoft.com)
Date: Fri Oct 04 2002 - 10:22:33 MDT
Anders writes (in addition to cogent comments by Eliezer, Avatar,
and Eugen)
> On Fri, Oct 04, 2002 at 12:55:51AM -0700, Lee Corbin wrote:
> > People seem smart enough that most adults lie on the
> > positive side of an interesting watershed: I think
> > it likely that most adults and some children have
> > reached the threshold of universal intelligence.
> >
> > I will call an entity universally intelligent if it
> > is possible for that entity to understand *anything*
> > if provided enough time.
>
> This is an interesting issue.
I forgot to mention the *absolutely* key role of language.
Without the ability to linguistically chunk previous results
(and to write them down, of course, as someone charitably
noted), yes, this would be impossible.
> With understanding X I usually mean that a being can represent X
> in such a way that it can predict X and how it would interact
> with other things at some suitable level of resolution;
Very well put.
> understanding is nearly always relative to a level of resolution
> and domain. A rabbit understands carrots to the extent that it
> can dig them up and eat them. A human might understand how the
> carrot plant grows and can be farmed, as well as how carrots can
> be prepared as food and behaves as physical objects. A biologist
> might have an understanding on a deeper level of what is going
> on ecologically, evolutionarily, chemically and genetically.
Of course, one should not distinguish "human" from "biologist"
here since I contend that any normal adult from the former
set can emulate one of the latter.
> Universal understanding would mean that a being could gain an
> understanding at any given level of resolution or domain of an
> arbitrary thing, given enough information. It seems equivalent
> to the creation of an internal simulation that is an emulation
> within a certain level of resolution (one could talk about
> probabilistic understanding: conclusions are right with a finite
> probability, useful understanding occurs when this probability
> is high).
I think that *emulation* is too strong. For a model of
what I have in mind, consider an extremely complicated
mathematics proof that one has "understood". This hardly
means either that one has memorized it, nor that one could
readily reproduce it, nor that one even now could answer
any question about. All that was achieved is that the
mathematician *at some point* while he was studying the
proof *could have* attended to that question---all the
mathematician has left are notes to the effect that he
or she has verified the calculations. For that matter,
extremely few children *know* in the sense that you and
Eliezer have talked about that 56144*983 = 55189552.
All they know is that they verified by algorithm each
step leading to that result. And that's all that matters.
> As Eliezer neatly showed, finite beings cannot of course achieve
> this since there are always non-compressible objects that cannot
> fit into their mental hardware.
As someone also charitably pointed out, however, the
assumption was that we have unlimited pencils and paper.
> There are also limits in the form of Gödel/Turing/Chaitin
> uncomputability or anti-predictability where there is
> actually no structure to understand or no way of understanding it.
Yes, a qualification that I meant to add was that the
results lying within human reach are only those lying
within the reach of any finite intelligence, no matter
how more "advanced" (i.e. quick) than humans.
> There are also systems where certain levels of resolution
> requires infinite or impractical amounts of information,
> like "understanding" the output of a chaotic system or the
> detailed behavior of a human.
Eliezer's comparison with the Chinese room is very apt
here, and I will deal with it when I have more time.
At the end of a trillion-year calculation that the
human finally succeeded in performing, the end result
would be like talking to a librarian who knew, or could
figure out, where any intermediate result is stored.
The key point however, is that the human, unlike the
busy little guy in the Chinese room, knows the meanings
of the final result and a huge number of intermediate
results. The word "knows" perhaps should even be in
quotes because asking him about the results determined
during the 701st of the billion years comprising the
trillion, may send him off on another two million year
quest.
> The real question is whether there are some qualitative
> barriers here that are not principal but actually reflect
> limitations of cognitive systems.
Yes, that's the key question, to which I answer No.
> As I see it there is likely no universal understanding because
> the boundary between domains where understanding is possible is
> a kind of fractal mess of undecidable, information limited and
> mental resource limited systems that cannot be understood or
> mapped in general. It is not just that we cannot understand
> every object, we cannot easily predict if certain objects are
> amenable to understanding.
This sounds as though you are referring to systems unanalyzable
by any intelligence of any organization whatsoever. I mean to
exclude such projects. My claim, to put it in the most graphic
terms, is that no alien race, nor any SI, is *smarter* than
humans except for time and speed, when the potentially immortal
human is not handicapped by health, poverty, or death.
> It should be noted that separation in this space of objects *
> domains of action * levels of precision is extremely
> non-trivial: understanding often acts by demonstrating
> isomorphisms between different regions, essentially connecting
> them with cognitive "wormholes" into fewer isolated regions.
Could you possibly provide examples of what you are talking
about here? I can think of several nice interpretation, but
they might be mine and not yours! ;-)
> Mathematics proved to be a region that could map itself nicely
> onto a lot of other regions, uniting them into a simpler region.
>
> The better understanding, the more the entire space has been
> reduced into a minimal set of "primitive" regions. So maybe a
> better question than whether there exists universal
> understanding is the structure of the set of primitive regions,
> and if it is unique. If there are non-unique sets of primitive
> regions there would exist different *kinds* of understanding
> (which may be differently useful in different environments).
I read "The better [the] understanding, the more the entire
space has been reduced into a minimal set of "primitive"
regions" as referring to *chunking*: in my examples, the
human at the end of his trillion year computation or mastery
of some proof, has possibly before him one final sentence:
A is true because of B, C, D, and E, even though E implies
some very other interesting things.
Sorry, I'm baffled by your last sentence, but will have more
time later to study it.
Thanks,
Lee
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