Posted by
Steve Smith on
Apr 10, 2010; 2:34pm
URL: http://friam.383.s1.nabble.com/invitation-introduction-tp4862386p4882114.html
John
Owen
Thanks for asking the question. In my answer, below, I describe the technical terminology impressionistically. If you want more precision, the Wikipedia articles are usually pretty good at giving precise definitions, along with some sense of the underlying ideas.
Very good summary of Category Theory (CT)... very accessible and
intuitive (for anyone who already knows what groups, rings, etc. are ;)
Category theory has been mentioned several times, especially in the early days of friam. Could you help us out and discuss how it could be applied here? CT certainly looks fascinating but thus far I've failed to grasp it. I'd love a concrete example (like how to address Rosen's world) of it's use, and possibly a good introduction (book, article).
I'm left wondering how you might think it applies to Complex Adaptive
Systems (CAS)?
My colleagues, Dr. Tom Caudell (UNM) and Dr. Michael Healy (UW
emeritus) are working on a theory of Neural Architectures based on
Category Theory
http://portal.acm.org/citation.cfm?id=1568850
http://portal.acm.org/citation.cfm?id=1704175.1704367
http://www.ece.unm.edu/~mjhealy/Healy-LOR-rev.pdf
that begins to encroach on the application of CT to CAS .
This fits with Leigh's announcement of Melanie's talk, or at least
Melanie's seminal work in "Analogy Making as Perception". My
interest as a Visualization Scientist (Trained in Physics/Math,
practiced in CS/CE and focused mostly on the range of topics revolving
around synthesized perceptual spaces for exploration, discovery and
analysis of (possibly complex) phenomena) is in the formalization of
Metaphor (Thus
Analogy Making as Perception and
Category
Theory models of Cognition.) I'm also convinced that it has
application to Agency (what really good, deep, Agents should have?)
I've read through Jocelyn Paine's compilation of her own exposition in
this area:
http://www.j-paine.org/why_be_interested_in_categories.html
and find it motivating but beyond my limited capabilities.
However, Jocelyn's expose on how Excel Spreadsheets have motivated her
to investigate Category Theory and getting to that was worth the effort
of reading it through to the end!
I look forward to more unfolding on the application of Category Theory
to CAS here... if it has legs anyway.
- Steve
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