Ben: analogy is mathematically a matter of finding mappings that match certain
constraints. The traditional AI approach to this would be to search the
constrained space of mappings using some search heuristic. A complex systems
approach is to embed the constraints into a dynamical system and let the
dynamical system evolve into a configuration that embodies a mapping matching
the constraints.
Ben,
If you are to arrive at a surprising analogy or solution to a creative problem,
the first task is to find out a new domain that "maps" on to or is relevant to
the given domain, and by definition you have no rules for where to search. If
for example you had to solve Kauffman's practical problem - how do I
hide/protect a loose computer cord so that no one trips over it? - which
domains do you start with (that connect to computer cords), and where do you
end? Books? Bricks? Tubes? Cellotape? Warning signs? There are actually an
infinity (or practically endless set) of possibilities. And there are no
pre-applicable rules about which domains to search, or what constitutes
"hiding/protecting" - and therefore the "constraints" of the problem, or indeed
how much evidence to consider, and what constitutes evidence.And "hiding
computer cords and other household objects" is not a part of any formal subject
or branch of reasoning.
Ditto if you, say, are an adman and have to find a new analogy for your beer
being "as cool as a --- " (must be new/surprising aka cabbages and kings, and
preferably in form as well as content, e.g. as cool as a tool in a pool as a
rule [1st attempt] ).
Doesn't complexity only apply when you have some formulae or rules to start
with? But you don't with analogy. That's the very nature of the problem
That's why I asked you to give me a problem example. {Can you remember a
problem example of analogy or otherwise crossing domains from your book - just
one? )
Nor can I see how maths applies to problems such as these, or any crossing of
domains, other than to prove that there are infinite possibilities. Which
branch of maths actually deals with analogies?
And the statement:
"it is provable that complex systems methods can solve **any** analogy problem,
given appropriate data"
seems outrageous. You can prove mathematically that you can solve the creative
problem of the "engram" (how info. is laid down in the brain)? That you can
solve any of the problems of discovery and invention currently being faced by
science and technology? A mind-reading machine, say? Or did you mean problems
where you are given "appropriate data", i.e. "the answers/clues/rules"? Those
aren't problems of analogy or creativity.
I don't know about you, but a lot of computer guys don't actually understand
what analogy is. Hofstadter's oft-cited "xyy is to xyz as abb is to a--?" for
example is NOT an analogy. It is logic.
And if you look at your "brief answer" para, you will find that while you talk
of mappings and constraints, (which are not necessarily AGI at all), you make
no mention in any form of how complexity applies to the crossing of hitherto
unconnected "domains" [or matrices, frames etc], which, of course, are.
.
Ben,
Ben: the reason AGI is so hard has to do with Santa Fe Institute style
complexity ...
Intelligence is not fundamentally grounded in any particular mechanism but
rather in emergent structures
and dynamics that arise in certain complex systems coupled with their
environments
Characterizing what these emergent structures/dynamics are is hard,
Ben,
Maybe you could indicate how complexity might help solve any aspect of
*general* intelligence - how it will help in any form of crossing domains, such
as analogy, metaphor, creativity, any form of resourcefulness etc.- giving
some example.
Personally, I don't think it has any connection - and it doesn't sound
from your last sentence, as if you actually see a connection :).
You certainly draw some odd conclusions from the wording of peoples'
sentences. I not only see a connection, I wrote a book on this subject,
published by Plenum Press in 1997: "From Complexity to Creativity."
Characterizing these things at the conceptual and even mathematical level is
not as hard at realizing them at the software level... my 1997 book was
concerned with the former.
I don't have time today to cut and paste extensively from there to satisfy
your curiosity, but you're free to read the thing ;-) ... I still agree with
most of it ...
To give a brief answer to one of your questions: analogy is mathematically a
matter of finding mappings that match certain constraints. The traditional AI
approach to this would be to search the constrained space of mappings using
some search heuristic. A complex systems approach is to embed the constraints
into a dynamical system and let the dynamical system evolve into a
configuration that embodies a mapping matching the constraints. Based on this,
it is provable that complex systems methods can solve **any** analogy problem,
given appropriate data, and using for example asymmetric Hopfield nets (as
described in Amit's book on Attractor Neural Networks back in the 80's).
Whether they are the most resource-efficient way to solve such problems is
another issue. OpenCog and the NCE seek to hybridize complex-systems methods
with probabilistic-logic methods, thus alienating almost everybody ;=>
-- Ben G
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