Mathematics and Models for Autopoiesis

Abstract

Having considered the basic theory of autopoiesis, it is of interest to look at other forms of representation that have been developed for autopoiesis—mathematics and computer models. In mathematics, Varela (1975) has extended Spencer Brown’s Laws of Form (1972) into a calculus for self-reference and has then developed, with Goguen (Goguen and Varela, 1979), representations based on lattices, networks, and trees. The Laws of Form is itself a very unusual and contentious work, so Section 4.2 will try to provide some understanding of it before discussing Varela’s extension. His later work with Goguen will be discussed in Section 4.3. Jumarie (1987) and Fontana and Buss (1994) have also developed some mathematics relevant to autopoiesis. There are interesting similarities with the work of Peirce on entitative and existential graphs (Roberts, 1973). Spencer Brown references Peirce’s work in his book.