Richard
But where you (I believe) start to confuse the picture is by selecting
an example of an 'emergent' system that is a special case. Hopfield
nets are barely complex enough to have any emergent properties: in
fact, they were pretty much engineered so that they could be analysed
using known laws of statistical physics. So it is no surprise that
the behavior of the attractors are subject to some predicatble laws.
Generalizing from Hopfield Nets to the case of a general complex
system with emergent properties is just a sleight of hand. HNs are a
freak case, in that larger context.
I chose HN's because they were the simplest system I could think of that
can fairly be said to involve emergence.
If you look at more complex ANN's as described e.g. in Daniel Amit's
book "Modeling Brain Function", then things get more and more subtle and
dramatic in terms of the kinds of emergence that are possible.... (Here
we have strange attractors, strange transients, and all sorts of fun
things happen...)
Amit reviews a series of more and more complex NN models, starting with
simple HN's and ending up with networks that are complex enough to carry
out arbitrary Turing computations in a purely emergent way (although he
doesn't phrase it this way). [I.e., once you have an ANN with an
arbitrarily complex strange attractor, then you can consider the
different "wings" of the attractor as symbols if you wish to, and view
the transition of the dynamics through the attractor as carrying out an
arbitrarily complex computation.]
My own view is that the brain utilizes a combination of emergent
representations/dynamics, with representations/dynamics that are more
directly and obviously tied to the neural level. The Novamente design
also has two levels of representation, with ways to communicate/convert
between the two.
One feature of my perspective is that it allows me to annoy both the
people who like emergence, and the people who dislike it ;-)
-- Ben
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