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In his essay "Objects as Tokens for Eigenbehaviours",
Heinz von Foerster created the concept of EigenForm,
a generalization of the notions of fixed point (of a transformation) and eigenvalue (as in quantum mechanics). EigenForm is an extraordinary and fruitful concept in cybernetics. This talk will be about EigenForm, Form and the relationship of these ideas to the use of mathematical forms in cybernetic discussion. Atthe simplest level an eigenform is a fixed point. Thus the golden ratio is a fixed point for the function F(x)=1+1/x. With the golden ration there is a long history extending rational numbers to so-called irrational numbers such as the golden ratio (geometric as it is!) that can make us complacent about this fixed point. On the other hand, if we look for a fixed point (in logic) for negation, then we must ascend to levels of imaginary values in the logical form. The classical logical values are simply True and False, each the negation of the other. By looking for EigenForm in Logic, we create domains of possibility. Just so, the EigenForms that correspond to the objects of our experience are our mutual creations in a dialogue that brings forth worlds. The "I" is such an eigenform. Heinz: "I am the observed link between myself and observing myself." This talk will discuss EigenForm as a key example of a Kernel, a formal idea whose unfolding affects our creativity, thought and action.

 

Louis H. Kauffman


  Louis H. Kauffman received his PhD. from Princeton University in 1972. He is professor of mathematics at the University of Illinois, Chicago. He is author of a large number of scholarly articles and editor of the Journal of Knot Theory and its Ramifications and of the Series on Knots and Everything. Louis H. Kauffman is president of the American Society for Cybernetics.

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