Professor Kauffman was the President of the American Society for Cybernetics (2005-2008). He is the 1993 recipient of the Warren McCulloch award of the American Society for Cybernetics and the 1996 recipient of the award of the Alternative Natural Philosophy Association for his work on discrete physics. He is the founding editor and editor in chief 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. This work is founded in understanding the nature of the distinctions that generate these structures.
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 is a prominent worker 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 polynomial and the theory of virtual knots and links.
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.
· 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.
· (First published by Princeton University Press in 1983) 2007, Intelligence of Low Dimensional Topology 2006, with J. Scott Carter and Seiichi Kamada.
· 2012, Knots and Physics (Series on Knots and Everything, Vol. 1- Fourth Edition 2012, First Published in 1991), World Scientific Publishing Company, 788 pp.
· 2013, The Mereon Matrix - Unity, Perspective and Paradox, ed by Lynnclairce Dennis, Jytte Bender McNair and Louis H. Kauffman, Elsevier Pub. Co.
(http://homepages.math.uic.edu/~kauffman/)
(http://en.wikipedia.org/wiki/Louis_H._Kauffman)
(http://www.youtube.com/playlist?list=PLiK4NNHYj1YGOK5IqS_Dlp52ICsvR8BWV)
Cybernetics has, from its very beginnings been concerned with circularity - the circularity of feedback in biological, social, scientific and mathematical systems, the fundamental circularities behind our forms of explanation and the ever-present circularity of thought and understanding acting on itself. At a certain key point, Margaret Mead spoke of the cybernetics of cybernetics and this was taken up as a call for a second-order cybernetics by Heinz von Foerster and eventually many others. The understanding behind so-called second-order cybernetics is inherent in cybernetics itself. Along with considering a self-conscious cybernetics that includes the observer, we make the shift to a fully embodied scientific view. In this view one cannot avoid seeing the participation of the scientist as part of the science itself. This is nowhere more clear than in the biology of cognition, where a theory of cognition must wrap around and explain itself, or in economic practice where the theories of action are embodied in the participants in the economy and these participants form that economy. But this is also the case in all scientific endeavor once one is quite precise about the role of thought and concept in the practice of that science. There are no objects of study that are not combinations of percept and concept. Each place where we contact experience meaningfully is an amalagam of appropriate concept and the accuracy of perception.
All objects come along with a perception, a conception and an awareness. We make generalizations and theories but each act of understanding is founded in the circularity of percept and concept and thought acting upon itself. Second-order science includes its practitioners and must be fully accurate in that accounting.
The consequences of this point of view go across the board, taking the axis of second-order cybernetics fully to a coordination of all forms of knowledge. This talk will discuss these issues of second order science in the context of topological models. Such models are an invaluable aid in sharpening the understanding of these issues of circularity and knowledge.
