Abram Demski wrote:
I'm still not really satisfied, though, because I would personally
stop at the stage when the heuristic started to get messy, and say,
"The problem is starting to become AI-complete, so at this point I
should include a meta-level search to find a good heuristic for me,
rather than trying to hard-code one..."
And at that point, your lab and my lab are essentially starting to do
the same thing. You need to start searching the space of possible
heuristics in a systematic way, rather than just pick a hunch and go
with it.
The problem, though, is that you might already have gotten yourself into
a You Can't Get There By Starting From Here situation. Suppose your
choice of basic logical formalism, and knowledge representation format
(and the knowledge acquisition methods that MUST come along with that
formalism) has boxed you into a corner in which there does not exist any
choice of heuristic control mechanism that will get your system up into
human-level intelligence territory?
If the underlying search space was sufficiently general, we are OK,
there is no way to get boxed in except by the heuristic.
Wait: we are not talking about the same thing here.
Analogous situation. Imagine that John Horton Conway is trying to
invent a cellular automaton with particular characteristics - say, he
has already decided that the basic rules MUST show the global
characteristic of having a thing like a glider and a thing like a glider
gun. (This is equivalent to us saying that we want to build a system
that has the particular characteristics that we colloquially call
'intelligence', and we will do it with a system that is complex).
But now Conway boxes himself into a corner: he decides, a priori, that
the cellular automaton MUST have three sexes, instead of the two sexes
that we are familiar with in Game of Life. So three states for every
cell. But now (we will suppose, for the sake of the argument), it just
happens to be the case that there do not exist ANY 3-sex cellular
automata in which there are emergent patterns equivalent to the glider
and glider gun. Now, alas, Conway is up poop creek without an
instrument of propulsion - he can search through the entire space of
3-sex automata until the end of the universe, and he will never build a
system that satisfies his requirement.
This is the boxed-in corner that I am talking about. We decide that
intelligence must be built with some choice of logical formalism, plus
heuristics, and we assume that we can always keep jiggling the
heuristics until the system as a whole shows a significant degree of
intelligence. But there is nothing in the world that says that this is
possible. We could be in exactly the same system as our hypothetical
Conway, trying to find a solution in a part of the space of all possible
systems in which there do not exist any solutions.
The real killer is that, unlike the example you mention below,
mathematics cannot possibly tell you that this part of the space does
not contain any solutions. That is the whole point of complex systems,
n'est pas? No analysis will let you know what the global properties are
without doing a brute force exploration of (simulations of) the system.
Richard Loosemore
This is what the mathematics is good for. An experiment, I think, will
not tell you this, since a formalism can cover almost everything but
not everything. For example, is a given notation for functions
Turing-complete, or merely primitive recursive? Primitive recursion is
amazingly expressive, so I think it would be easy to be fooled. But a
proof of Turing-completeness will suffice.
-------------------------------------------
agi
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