Eigenform

Louis Hirsch Kauffman

Abstract


EigenForm is the speaker's term for the generalized eigenvalues that Heinz von Foerster introduced into cybernetic discourse in theinception of second-order cybernetics. An eigenformis a fixed point of an operator, seen as the emergence of an "object" or distinction in the course of a recursion. This is in accord with von-Foerster's paper title "Objects as tokens for eigen-behaviours". It is enlightening and frustrating that at the abstract level every recursion has a fixed point (by infinite iteration or by the Church - Curry method of lambda calculus). At this level, the existence of fixed points sheds light on paradox, time, Godelian incompleteness and the nature of systems that can observe themselves. At this level the existence of the fixed point indicates a leap to a new level and a shift to a larger language of discourse. Within a given system, the fact that the fixed point may well be beyond that system leads to the exquisite frustration of finding a wider context for already-agreed-upon modes of working. We will discuss the context of Eigenforms in relation to systems and models.

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