Re: Rosen and others

[Ayten Aydin <***>]

Dear Tim,
Thank you for your reflections on my queries. I am still wondering whether
it is feasible to enter from another door to the application process of
Rosennean Theory. That is why I suggested ART and thus meaning more of
geometry rather than algebra. I still think that Poincare`'s principles are
not fully exhausted, as shadowed by Einstein and others.

I browsed this morning Stephen Wolfram website, (the author of A New Kind Of
Science) as indicated by HP. I thought  the following excerpt may be
interesting to note in our pursuit in general:

""The difficulty of doing mathematics reflects computational irreducibility
Mathematical theorems such as Fermat's Last Theorem that are easy to state
often seem to require immensely long proofs. In A New Kind of Science this
fundamental observation about mathematics is explained on the basis of the
phenomenon of computational irreducibility, and is shown to be a reflection
of results like Gödel's Theorem being far more significant and widespread
than has been believed before.

Existing mathematics covers only a tiny fraction of all possibilities
Mathematics is often assumed to be very general, in effect covering any
possible abstract system. But the discoveries in A New Kind of Science show
that mathematics as it has traditionally been practiced has actually stayed
very close to its historical roots in antiquity, and has failed to cover a
vast range of possible abstract systems-many of which are much richer in
behavior than the systems actually studied in existing mathematics. Among
new results are unprecedentedly short representations of existing formal
systems such as logic, used to show just how arbitrarily systems like these
have in effect been picked by the history of mathematics. The framework
created in A New Kind of Science provides a major generalization of
mathematics, and shows how fundamentally limited the traditional
theorem-proof approach to mathematics must ultimately be.""

My best,
Ayten

----- Original Message -----
From: "Tim Gwinn" <***>
To: <***>
Sent: Tuesday, January 25, 2005 11:56 PM
Subject: Re: Rosen cf. Kauffman


> Ayten,
>
> AA:
> > How come could, these two scientists being contemporary and I
> > guess knowing
> > the work of each other, not think of  benefiting from each other and
> > collaborate, if not when Rosen was alive, but now Kauffman could think
of
> > finding the missing something in the Rosen's work?? With all the
knowledge
> > around why could disciples of Rosen make an attempt to merge the two not
> > close but perhaps complementary theories?
>
> TG: Kauffman specifically references Rosen and "Life Itself" in
> "Investigations" in at least two places; one where he agrees w/Rosen that
> category theory may be the way to "mathematize the concept of an
autonomous
> agent" [p. 106] and the other where he mentions Rosen while discussing the
> idea of "analogy between  formal proof and causal consequences" (i.e., a
> modelling relation) [p. 136] But I did not see a mention of Rosen
regarding
> organization. As to combining the ideas of the two, I'd agree with Judith
> that they probably can't be merged - they are not compatible.
>
> AA:
> > Therefore, can we not do the same
> > by to applying Rosen's theory into practice in variety of fields which
> > requires organization as their central concern by making the whole
system
> > (mostly complex) function synergistically? Are they naive
> > questions or even
> > so can they take put us on a right track?
>
> TG: I suppose I'd be concerned with the kind of incompatibility mentioned
> above generally being a problem and hindering such a goal. This is one
> reason why I am interested in Aloisius' phenomenological calculus. It
> provides an algebraic formalism using tensors and Hilbert spaces to
> represent qualities of system. He has confirmed to me that he can
represent
> impredicative entailment structures as well. So, I suspect this formalism
> may perhaps serve to act as a kind of bridge between relational and
> non-relational models. Of course, this possibility is probably only so
> because it is entirely algebraic and not analytic. It will be interesting
to
> see how much can be done algebraically, and then, what analytic models can
> be drawn from the results.
>
> Regards,
> Tim
>
>