In article <CI4MtH.53M at carmen.logica.co.uk>,
Richard Wilson <WilsonR at LILHD.Logica.com> wrote:
>>In article <1993Dec16.015121.6208 at news.media.mit.edu> minsky at media.mit.edu (Marvin Minsky) writes:
>>In article <CI3Cwn.813 at carmen.logica.co.uk> WilsonR at LILHD.Logica.com (Richard Wilson) writes:
>>>>>>In article <1993Dec14.230227.9576 at news.media.mit.edu> minsky at media.mit.edu (Marvin Minsky) writes:
>>>>In article <CI1E7p.6qG at carmen.logica.co.uk> WilsonR at LILHD.Logica.com (Richard Wilson) writes:
>>>>>>>>I think this was first shown by Shepherdson. If you mean
>>>>nondeterministic is some unspecified sense, then your assertion is too
>>>>vague to refute, but you ought to offer something more than IMO.
>>>>Like, say, IMHO?
>>Why should I be humble about it? I've already admitted that it's an opinion
>which means I'm working on the the theory. My central example of non-
>deterministic behaviour is choice. An FSA cannot handle choice, not because
>it is finite, but because it's deterministic. The general idea is that there
>is a class of system of which the brain is an example which we don't
>have the theory for. "Chaos" theory won't do but has the right flavour in
>that it deals with non-linear behaviour.
>Choice is a bit more complex than just non-determinism. There are actually
three behavioral options open during most choice processes: go right, go
left, and dither (collect information). In games against nature, this
system generally has a stable strategy consisting of of two regions where
one or the other choice is correct and an intermediate region where the
collection of additional information is better. Dynamic programming is the
applicable field. In games against an intelligent opponent, things become
chaotic (in the theoretical sense). I have two or three papers that
address this, if you want them, but your comment above has led to a flash
of insight. I think I see a way of combining that earlier work with more
recent work on controlling chaos in the vicinity of hyperbolic points and
with work I've been doing on mass action models (Freeman Nets) to define a
Internet: herwin at cs.gmu.edu or erwin at trwacs.fp.trw.com
Working on Freeman nets....