The purpose of this essay is to sketch a picture of the connections between the concept self-reference and important aspects of mathematical and cybernetic thinking. In order to accomplish this task, we begin with a very simple discussion of the meaning of self-reference and then let this unfold into many ideas. Not surprisingly, we encounter wholes and parts, distinctions, pointers and indications. local-global, circulation, feedback. recursion, invariance. self-similarity, re-entry of forms, paradox, and strange loops. But we also find topology, knots and weaves. fractal and recursive forms, infinity, curvature and imaginary numbers! A panoply of fundamental mathematical and physical ideas relating directly to the central turn of self-reference.

Excerpt: The author of this article adequately criticizes the use of the notion of information by biologists in general, and by sociobiologists in particular. He, however, does not go far enough; and this, presumably, because, judging by two questions that he asks, he thinks that there is some fundamental significance in the notion of information that is still hidden. His questions are … how the discernible events described by the strict sense of information (restriction imposed upon a set of possibilities) interact with those described by the meaning (metaphorical) sense of information?’; and … there remains more fundamental problems, one of which is to understand how the two senses of information interact and, in fact, become one another?’.

The question ‘What is intelligence?” can be approached with at least two attitudes: (a) to assume ‘intelligence’ denotes a distinct property or attribute of some organisms; (b) to assume there is a class of behaviour of organisms in general, that an observer calls ‘intelligent behaviour’, making connotative reference to the relations that take place between the participating systems. We take the second approach and pose the biological question ‘What is intelligent behaviour as a phenomenon proper to living systems and how is it generated?’. The notions of problem-solving or goal-oriented behaviour, being observerdependent descriptions, are shown to be irrelevant in this view, since intelligent behaviour results from a kind of interactions between organisms within a particular context. Living systems are autopoietic entities with a plastic structure which allows them to interact with each other in a recursive manner, generating a form of ontogenic structural coupling called consensual domain, or to interact with its environment, generating another form of ontogenic structural coupling called ontogenic adaptation. The processes that generate intelligent behaviour are those that participate in the establishment of any domain of ontogenic structural coupling and those that participate in the operation of the involved organisms within such a domain. Although one can refer to intelligence as a phenomenon, because it is a configuration of relations between processes occurring during structural coupling, it is not directly observable and thus it cannot be measured. All that can be observed are instances of consensuality or of ontogenic adaptation in the form of intelligent behaviour. The IQ Test can, at most, estimate a subdomain of the domain of consensuality between the observer and the subject. No biological basis can be found for racial, social or educational discrimination, based on intelligence since the word ‘intelligence’ does not refer to a discrete individual attribute or property.

Complementarity is an epistemological principle derived from the subject – object or observer – system dichotomy, where each side requires a separate mode of description that is formally incompatible with and irreducible to the other, and where one mode of description alone does not provide comprehensive explanatory power. The classical physics paradigm, on which biological, social and psychological sciences are modelled, completely suppresses the observer or subject side of this dichotomy in order to claim unity and consistency in theory and objectivity in experimental observations. Quantum mechanical measurements have shown this paradigm to be untenable. Explanation of events requires both an objective, causal representation and a subjective, prescriptive representation that are complementary. The concepts of description and function in biological systems, and goals and policies in social systems, are found to have the same epistemological basis as the concept of measurement in physics. The concepts of rate-dependent and rate-independent processes are proposed as a necessary distinction for applying the principle of complementarity to explanations of physical, biological and social systems.

Cells and the extracellular matrix (ECM) immediately surrounding them engage in reciprocal determinations. But the ECM is also a global structure because it is continuous throughout the body. We argue that this local-global articulation is a central element in the determination of an animal’s form, and we show how it participates in all the other dimensions of animal life. Specific experimental implications and further consequences of this view are discussed.