From: Anders Sandberg (asa@nada.kth.se)
Date: Fri Oct 04 2002 - 09:06:01 MDT
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.
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;
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.
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).
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. 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. 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 detailled behavior of a human.
That still leaves a lot to understand. But we have to remember
that "anything" will be inside a certain domain.
"The unreasonable effectiveness of mathematics" seems to suggest
that there exists a domain encompassing much of physics amenable
to understanding of mathematical type, and this understanding
seems to fit human brains well (possibly augmented with pen and
paper to extend working memory). This domain runs into problems
when dealing with complex systems (i.e. everything interesting),
some of which may be principal problems like uncomputability and
chaos. The real question is whether there are some qualitative
barriers here that are not principal but actually reflect
limitations of cognitive systems.
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.
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
isomorphies between different regions, essentially connecting
them with cognitive "wormholes" into fewer isolated regions.
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).
-- ----------------------------------------------------------------------- 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
This archive was generated by hypermail 2.1.5 : Sat Nov 02 2002 - 09:17:25 MST