Eigenforms - Objects as Tokens for Eigenbehaviors

This essay is a contemplation of the notion of eigenform as explicated by Heinz von Foerster in his paper [4]. In that paper Heinz performs the magic trick of convincing us that the familiar objects of our existence can be seen to be nothing more than tokens for the behaviors of the organism that create stable forms. This is not to deny an underlying reality that is the source of these objects, but rather to emphasize the role of process and the role of the organism in the production of a living map that is so sensitive that map and territory are conjoined. Von Foerster's papers [4,5,6] in the book [3] were instrumental in pioneering the field of second order cybernetics. The notion of an eigenform is inextricably linked with second order cybernetics. One starts on the road to such a concept as soon as one begins to consider a pattern of patterns, the form of form or the cybernetics of cybernetics. Such concepts appear to close around upon themselves, and at the same time they lead outward. They suggest the possibility of transcending the boundaries of a system from a locus that might have been within the system until the circular concept is called into being, and then the boundaries have turned inside out. As Ranulph Glanville has pointed out “The inside is the outside is the inside is the...” Forms are created from the concatenation of operations upon themselves and objects are not objects at all, but rather indications of processes. Upon encountering an object, after that essay of Heinz, you are compelled to ask: How is that object created? How is it designed? What do I do to produce it? What is the network of productions? Where is the home of that object? In what context does it exist? How am I involved in its creation? Taking Heinz's suggestion to heart we find that an object in itself is a symbolic entity, participating in a network of interactions, taking on its apparent solidity and stability from these interactions. We ourselves are such objects, we as human beings are “signs for ourselves,” a concept originally due to the American philosopher C. S. Peirce [9]. In many ways Heinz's eigenforms are mathematical companions to Peirce's work. We will not follow this comparison in the present essay, but the reader familiar with Peirce is encouraged to do so.