Re: Rosen & Ashby

["Tim Gwinn" <***>]

Hi Jamie,

A few queries interposed.

Regards,
Tim

> -----Original Message-----
-----snip-------
>
> > Another quote perhaps related to your comments:
> > "I claim that Godelian noncomputability results are a symptom, arising
> > within mathematics itself, indicating that we are trying to
> solve problems
> > in too limited a universe of discourse. The limits in question
> are imposed
> > in mathematics by an excess of "rigor", and in science by cognate
> > limitations of "objectivity" and "context independence". In
> both cases, our
> > universes are limited, not by the demands of the problems that
> need to be
> > solved but by extraneous standards of rigor [the "subjective
> limitations" -
> > TG]. The result, in both cases, is a mind-set of reductionism,
> of looking
> > only downward towards subsystems, and never upward or outward." [EL 2]
>
> FANTASTIC!.  I have been taking-on Godel since day-one of my writings,
> challenging erroneous premises and pre-set limits which invalidate
> any attempted generalization of his incompleteness theorems.
> There have been several "limits to knowledge" conferences, Sci-Am
> articles and books, and general extrapolations of Godel's
> theorems, which became the rage of the scientific community.
> All balderdash, IMO.   To know that Rosen also saw that
> emperor godel wears no clothes is gratifying.


[TG]
What do you mean when you say that "emperor godel wears no clothes"? That
sounds like it dismisses the Godelian results as unimportant.

Rosen takes Godelian noncomputability as a symptom that in science it is
erroneous to believe that all natural systems will have computable models,
or that Newtonian-style reductionism is a universal physical principle. In
his view, natural systems with noncomputable models are generic, and natural
systems with only computable models are non-generic.


>
>
> > And also:
> > "Despite the profound differences between those material
> systems that are
> > alive and those that are not, these differences have never been
> expressible
> > in the form of a list - an explicit set of conditions that formally
> > demarcate those material systems that are organisms from those that are
> > not......I take seriously the possibility that there is no list, no
> > algorithm, no decision procedure, that finds us the organisms in a
> > presumptively larger universe of inorganic systems. This possibility is
> > already a kind of noncomputability assertion, one that asserts that the
> > world of lists and algorithms is too small to deal with the problem, too
> > nongeneric." [EL 2-3]
>
> In this, I take another path than he did.  I -do- see a "decision
> procedure, that finds us the organisms in a presumptively larger
> universe of inorganic systems."
>
>
> > > >[shortened]
> > > >
> > >
> > > > > The two quotes of Rosen's you cited "defining"
> > > > > complexity, is one of them 'wrong'?  And how does
> > > > > an information set (a mathematical statement)
> > > > > 'not let itself be exhausted'?  Does the mathematics
> > > > > have intentional volition of some sort?  Do you
> > > > > think that's part of what Rosen was trying to convey?
> > >
> > > Any comments in reply to these questions, Tim?
> >
> > My comments in the first and second paragraph of my reply were somewhat
> > toward these questions. Mainly, to take only the second quote
> as a precise
> > definition, and the first one as his personal notes that were
> not originally
> > intended for publication in that form. They are both compatible
> with each
> > other, with the second being a more rigorous and concise version of the
> > first.
> >
> > "Exhausted", in his sense, refers to the dictionary sense of "To treat
> > completely, to cover thoroughly", as in "to exhaust a topic".
> So, there is
> > no vitalism or volition or other funky things being imputed to
> mathematical
> > systems or models. :)
>
> I never imputed any.  I'm asking about it in consideration
> of 'actions enactable' within a domain that is larger than,
> equal to, or smaller than, the whole performance domain,
> however large they may be individually or relationally.

[TG]
I know you didn't impute any. :) I thought you were asking if Rosen made any
such imputations. I do not know what "actions enactable" or "performance
domain" or "domain" mean in your terminology. If you could rephrase or
explain them, I might be able to respond.


>
>
> > He is saying that a complex system cannot be modeled
> > completely by any finite set of simple models or superposition of those
> > models. Instead, what is required is either the addition of
> noncomputable
> > models, or by regarding a complex system as the limit (in the
> mathematical
> > sense) of the set of simple models. [EL 338, LI 247, 280] I do
> not know of
> > any place where he elaborates on the latter option, which is
> too bad, since
> > it sounds intriguing.
>
> Again, I take a different tack.  I deduce that a small
> number of behavior rules -can- generate performances
> as we know them, and, can generate 'life' from primordial
> aspects that wouldn't qualify as 'life' in and of themselves
> alone.


[TG]
Are these behavioral rules all computable? Are they all mathematical
formulas? Does noncomputability enter in anywhere?

Just trying to get a grasp of the nature of these "rules".




> Thanks, Tim/all,
>
> Jamie
> 11/23/03