"Reflexivity in Mathematics and Cybernetics" is a 3-hours Workshop delivered by Professor Louis Kauffman at the The 14th World Multi-Conference on Systemics, Cybernetics and Informatics: WMSCI 2010, on June 29th, 2010.
Slides used in the Workshop
Related to the content of the Workshop
- File #1
- File #2
- File #3
- File #4
Abstract
Reflexive systems act on themselves and produce themselves from themselves and their environments. Linguistic and biological systems are transparently reflexive, and social systems as well. Models in the social and economic domain tend to use mathematical tools that ignore reflexivity except in the sense of direct recursion. But indeed, the very models that are used in such domains affect the actions in those domains and there is a fundamental circularity in the structure and evolution of systems so created and maintained. It is the purpose of this workshop to go to the mathematical and cybernetic roots of reflexivity, to explore relationship with recursive process, fixed points, eigenforms and the emergence of paradox in presence of circularity. By facing paradox directly we shall see how it is not a bugaboo for reflexive models but rather a goad to finding new contexts for holding antimony. The workshop will look at reflexivity and circularity in basic mathematical forms of process, including elementary topology and the beginnings of order and creative oppositions. The major difference between this workshop and a single talk on the same subject is that we will have time to explore these avenues and see how elementary forms (mathematical) affect our thought and action in the world.
Professor Kauffman was the President of the American Society for Cybernetics (1997-1998).
He is the 1993 recipient of the Warren McCulloch award of the American Society for
Cybernetics. He “is the founding editor and one of the managing editors of the Journal
of Knot Theory and its Ramifications, and editor of the World Scientific Book Series
On Knots and Everything. He writes a column entitled Virtual Logic for the journal
Cybernetics and Human Knowing.” his “interests are in cybernetics, topology (knot
theory and its ramifications) and foundations of mathematics and physics. His work
is primarily in knot theory and connections with statistical mechanics, quantum
theory, algebra, combinatorics and foundations. These fields include representation
and exploration of topology, fractals and recursions using computers, logical and
diagrammatic algebras, Hopf algebras, relations of topology with statistical mechanics
and quantum field theory, foundations of discrete physics, quantum computing. In
topology he introduced and developed the bracket polynomial and Kauffman polynomial.”
He has worked at many places as a visiting professor and researcher, including the
University of Zaragoza in Spain, the University of Iowa in Iowa City, the Institute
Hautes Etudes Scientifiques in Bures Sur Yevette, France, the Institute Henri Poincaré
in Paris, France, the Univesidad de Pernambuco in Recife, Brasil, and the Newton
Institute in Cambridge England.
Professor Kauffman has been a prominent leader in Knot Theory, one of the most active
research areas in mathematics today. His discoveries include a state sum model for
the Alexander-Conway Polynomial, the bracket state sum model for the Jones polynomial,
the Kauffman polyomial and Virtual Knot Theory.
He is author of several monographs on knot theory and mathematical physics. His
publication list numbers over 170. Among his books are the followings:
- 1987, On Knots, Princeton University Press 498 pp.
- 1993, Quantum Topology (Series
on Knots & Everything), with Randy A. Baadhio, World Scientific Pub Co Inc, 394
pp.
- 1994, Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds, with
Sostenes Lins, Princeton University Press, 312 pp.
- 1995, Knots and Applications
(Series on Knots and Everything, Vol 6)
- 1995, The Interface of Knots and Physics:
American Mathematical Society Short Course January 2-3, 1995 San Francisco, California
(Proceedings of Symposia in Applied Mathematics), with the American Mathematical
Society.
- 1998, Knots at Hellas 98: Proceedings of the International Conference
on Knot Theory and Its Ramifications, with Cameron Gordon, Vaughan F. R. Jones and
Sofia Lambropoulou,
- 1999, Ideal Knots, with Andrzej Stasiak and Vsevolod Katritch,
World Scientific Publishing Company, 414 pp.
- 2001, Knots and Physics (Series on
Knots and Everything, Vol. 1), World Scientific Publishing Company, 788 pp.
- 2002,
Hypercomplex Iterations: Distance Estimation and Higher Dimensional Fractals (Series
on Knots and Everything , Vol 17), with Yumei Dang and Daniel Sandin.
- 2006, Formal
Knot Theory, Dover Publications, 272 pp.
- 2007, Intelligence of Low Dimensional
Topology 2006, with J. Scott Carter and Seiichi Kamada.
(http://en.wikipedia.org/wiki/Louis_H._Kauffman)
