**Stephen P. King** (*stephenk1@home.com*)

*Wed, 31 Mar 1999 22:23:48 -0500*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Stephen P. King: "[time 88] Re: [time 85] Re: [time 82] discrete models, QM vs. GR"**Previous message:**Ben Goertzel: "[time 86]"

Dear Ben,

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

Ben Goertzel wrote:

*>
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*> > Is this "Markovian patterns" related to the infamous Markov Chains?
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*>
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*> yes, it means the same thing.
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*>
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*> What I mean is, if you take a dynamical system and study its trajectory,
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*> you can compute the information in the trajectory using concepts like
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*> metric entropy, which look at the probabilities of transition from one part of
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*> state space to the other (Markov probabilities). The metric entropy is
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*> proportional to the algorithmic information of the trajectory for almost all
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*> dynamical systems, but not for the most interesting ones, the ones with
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*> intricate algorithmic structure.
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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
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*> >covers this, I think! :)
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*>
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*> It is very different,if my recollection serves. Fuzzy set theory is not
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*> the same as entropy or algorithmic information theory.
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*>
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*> It is based on the Min() and Max() operators which preserve distributivity
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*> but are not at all psychologically realistic. My preference is for probabilistic
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*> 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.
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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
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*> digressions will lead...
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:)

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

Later,

Stephen

**Next message:**Stephen P. King: "[time 88] Re: [time 85] Re: [time 82] discrete models, QM vs. GR"**Previous message:**Ben Goertzel: "[time 86]"

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