Re: Category Theory and Rosen - some clarifications (i hope 8-))

[Roger M. Burkhart]

>From Glen's message:

> Roger M. Burkhart writes:
>  > I agree that we need better formalizations, including "open," expandable
>  > ones that give a better chance of modeling life, thought, and complex
>  > dynamics, but the purpose is not to make them any more generally
>  > analyzable.  A likely outcome is to make them only more contextual and
>  > bound by culture and history, and so perhaps more ultimately interesting
>  > than those that don't even resist a simple compression.
> 
> Agreed.  I'm not suggesting that the purpose of formalization of Alife
> is to make Alife more analyzable.  But, I *do* want to be able to make
> statements about Alife systems.  Not only that, I want to be able to
> state *theorems* of Alife systems.  (Namely, theorems of
> controllability and observability. [grin])

Does your [grin] mean that you don't really expect these systems to submit
to your conditions of controllability and observability?  I don't see that
you can have any such expectation until you first narrow things down to
something more specific than "Alife systems."

The class of systems we're talking about is, literally and figuratively,
everything under the sun -- any sufficiently rich, self-organizing system
that is driven thermodynamically.  These systems can generate novelty
without limit.  For the totally general, unrestricted class of "Alife
systems" you can't rule out the ability of the system to outsmart or
confound any theorem you attempt to establish.

You who live out there in coyote-land ought to know about tricksters.
(For non-North Americans, Coyote is the trickster god of native American
mythology, and they're also the feral canines that yip and yelp during the
night around Santa Fe, especially in the foothills around the Institute.)
If a trickster happens to end up inside your system, none of the blunt
instruments at your disposal will be enough to pin it down.

To fast-forward the image beyond metaphor, Goedel showed that a trickster
lives in most any constructive system you care to pick.  There are
computability bounds on how quickly a system might calculate or develop a
response, but beyond that I question the feasibility of theorems on an
utterly unrestricted class of evolving, adaptive systems.  The first thing
you've got to do before you even start theorizing is to somehow be more
specific about the kind of system you've got.  (Maybe the No Free Lunch
theorem is enough to rescue us from General Systems Theory.)  We must
observe and theorize about specific classes of systems that we either
specify and build ourselves (literally as simulations or abstractly as
mathematics), or in which we actually live.

Roger Burkhart


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