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

[Chris Landauer]

hi, glen, i see i'm at it again - i'll try not to run off

Perhaps I was remembering the conference discussions and not the book -
clearly, i will have to read it again

formal systems and models:

the description of a formal system is fine, and using such a thing as a model
is, too; what i remember is a heated discussion between the folx who didn't
maintain the proper distinction between models and the phenomena modeled, and
those who did - the transition between a real-world phenomenon and a formal
system that is a model of that phenomenon is especially tricky when the model
is very good, as newtonian mechanics and many other physics models are (this
seems to be what confuses some folx, like prigogine, into thinking that the
models are, or even could be, complete descriptions of reality)

go:del's theorem:

go:del's theorems do not exactly show that you require external influences in
a formal system; they show that, because the formal system allows no external
influences, you need to be _outside_ the system to prove some true statements
(so if you have a goal of proving any true statements, then you are interested
in something which is outside the formal system) - so here i think we are not
disagreeing exactly; we just have different interests in the systems

for some years now, we have been trying to stimulate the mathematical
community to come up with some new kinds of mathematics, precisely in this
area (among others): mathematics is the most concrete form of reasoning we
have, because you have to define everything you use up front - go:del's
theorem shows that that approach has limitations, and we are looking for some
new ideas - for example, linguistic arguments allow new information to be
brought in after the reasoning process starts, and sometimes completely change
the nature of the entities under discussion - one of the things we are trying
to get is a combination of the reliability of mathematical reasoning and the
expressive power of natural language (yes i know this is real hard 8-))

models of Alife:

i am very intrigued by these questions; i just wish the math were done better
in the treatments (one way to do it better is to keep to the story, define the
important qualities, and not try to choose a formal systems and write down
formulas; many authors mess up at that point because there aren't enough of
the right ideas yet to make the models formal in a useful way)

there are several other models that look quite appropriate for various aspects
of Alife - the actor model in computing (in which all interaction is via
messages, but of course physics has been moving that way for a long time with
its particles that carry the various forces), a kind of strange alternative
model due to ben goertzel (which is really the same as the actor model, i
think, just described differently **oh, and beware the math; it isn't very
well done**), but the important thing is to define the qualities any
appropriate model must have, and only then try to define formal systems that
have enough of those properties to be interesting - i think this is a
completely doable project that is well suited to this mailing list

*whew* there, see? not just flames, but an actual concrete proposal for action
8-)

more later,
cal

Dr. Christopher Landauer
Aerospace Integration Science Center
The Aerospace Corporation
P.O.Box 92957
Los Angeles, California 90009-2957
e-mail: address@hidden
Phone: (310) 336-1361

PS - some references on these topics
(these are in LaTeX: **\em means emphasis, usually italics**)

\bibitem {Landauer-Bellman94}
        Christopher Landauer, Kirstie L. Bellman, ``New Mathematical
Foundations for Computer Science'', Initiative announcement available via
anonymous ftp from aerospace.aero.org, in directory ``/pub/newmath'', in file
``workbook.html'' (original July 1994), revision 1.4 (February 1995)
(availability last checked 1 October 1997)

\bibitem {Landauer-Bellman96b}
        Christopher Landauer, Kirstie L. Bellman, ``Integration Systems and
Interaction Spaces'', pp. 161-178 in {\em Proceedings of FroCoS'96: The First
International Workshop on Frontiers of Combining Systems}, 26-29 March 1996,
Munich (March 1996)

\bibitem {Landauer-Bellman96j}
        Christopher Landauer, Kirstie L. Bellman, ``Mathematics and
Linguistics'', pp. 153-158 in Alex Meystel, Jim Albus, R. Quintero (eds.),
{\em Intelligent Systems: A Semiotic Perspective}, {\em Proceedings of the
1996 International Multidisciplinary Conference}, {\em Volume I: Theoretical
Semiotics}, {\em Workshop on New Mathematical Foundations for Computer
Science}, 20-23 October 1996, Gaithersburg, Maryland (1996)

\bibitem {Bellman-Landauer97d}
        Kirstie L. Bellman, Christopher Landauer, ``Computational Embodiment:
Biological Considerations'', pp. 422-427 in A. M. Meystel (ed.), {\em
Proceedings of ISAS'97: The 1997 International Conference on Intelligent
Systems and Semiotics: A Learning Perspective}, 22-25 September 1997, NIST,
Gaithersburg, Maryland (1997)

\bibitem {Landauer97a}
        Christopher Landauer, ``Conceptual Categories as Knowledge
Structures'', pp. 44-49 in A. M. Meystel (ed.), {\em Proceedings of ISAS'97:
The 1997 International Conference on Intelligent Systems and Semiotics: A
Learning Perspective}, 22-25 September 1997, NIST, Gaithersburg, Maryland
(1997);


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