[time 87] Re: [time 83] Re: [time 81] Entropy, wholeness, dialogue,algebras

Stephen P. King (stephenk1@home.com)
Wed, 31 Mar 1999 22:23:48 -0500

Dear Ben,

        I hope its ok to forward this to the Time list. :)

Ben Goertzel wrote:
> > Is this "Markovian patterns" related to the infamous Markov Chains?
> yes, it means the same thing.
> What I mean is, if you take a dynamical system and study its trajectory,
> you can compute the information in the trajectory using concepts like
> metric entropy, which look at the probabilities of transition from one part of
> state space to the other (Markov probabilities). The metric entropy is
> proportional to the algorithmic information of the trajectory for almost all
> dynamical systems, but not for the most interesting ones, the ones with
> intricate algorithmic structure.

        Are you thinking of this in terms of Kolmogorov complexity? I am not
familiar with "metric entropy". :( It look like metric entropy needs to
be generalized to deal with intricate algorithmic structure. I need more
info on it. I have a text on Kalmogorov complexity, I'll take a look...
it'll probably be a few days...
> >I think we should look at Kosko's subsethood theorem, it
> >covers this, I think! :)
> It is very different,if my recollection serves. Fuzzy set theory is not
> the same as entropy or algorithmic information theory.
> It is based on the Min() and Max() operators which preserve distributivity
> but are not at all psychologically realistic. My preference is for probabilistic
> logic. So I agree that fuzziness is needed, but the min/max algebra on fuzzy sets I have always steered > away from in my AI work.

        I hope we can get into this in more detail. Could you explain how the
operators are not realistic. I am missing something... :(

> Anyway these are all digressions, but of course you never know where
> digressions will lead...

> > I have found Tony et al's discussions very interesting. I wonder if
> >they would be interesting in joining us? :)
> Maybe. I have not heard from Tony for a while, I will drop him a line...
> http://www.innerx.net/personal/tsmith/TShome.html
> Yikes!!! I hadn't seen that...
> ben

        I hope everything is ok for Tony...



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