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David,
I can't say I'd
really thought about this specific situation previously, so my remarks were
rather off-the-cuff. As to who else I've read that speak of these things in
these terms, other than Rosen (and to some extent, Kampis) I really haven't. Of
course, with respect to catastrophes and bifurcations, Rene Thom's
Structural Stability and Morphogenesis was a profound
eye-opener for me.
Regards,
Tim
Tim,
You wrote...
TG: As I think I understand it,
flexible state spaces would - like the state spaces described in Ch. 4 of
Life Itself - still suffer from the inability to encode impredicative
entailments (the latter which I take as a necessity for encoding
anticipation). I think that as long as the state spaces (that is, the
original state space is "flexed" in multiple and various ways) can be
transformed into each other mathematically, then there would be a
largest model, a largest state space representation. If, on the other hand,
the state spaces were incommensurable, then this could be a way to encode
impredicative entailments (EL p. 294-295). I'm not sure if this kind of
incommensurability falls under the heading of what you mean by 'flexible state
spaces' or not, since I imagine such incommensurable state spaces would not be
as if one state space were "flexed" into the other, unless such a flexing
meant it went through some kind of a bifurcation
point.
Well, whether or not you have the formal
training, what you have said here seems like a state of the art filet of the
problem. It's roughly where I've been with the problem for a little
while now. Few have I read that come even close to stating the problem
this way. Who else have you read that speak of these things in
these terms? Flexible state space by way of bifurcations, nice.
Very nice. You may have visualizations that are quite different
than mine. How long have you been stating the problem this way?
Top notch Tim, thank you.
David
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