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Title Ouroboros Avatars: A Mathematical Exploration of Self-reference and Metabolic Closure
Authors Jorge Soto Andrade, Sebastian Jaramillo, Claudio Gutierrez, Juan Carlos Letelier
Publication date 2011
Abstract One of the most important characteristics observed in
metabolic
networks is that they produce themselves. This intuition, already advanced
by the theories of Autopoiesis and (M,R)-systems, can be mathematically
framed in a weird looking equation, full of implications and potentialities:
f(f) = f . This equation (here referred as Ouroboros equation), arises in
apparently dissimilar contexts, like Robert Rosens synthetic view of
metabolism, hyperset theory and, importantly, untyped lambda calculus. In
this paper we survey how Ouroboros equation appeared in those contexts, with
emphasis on Rosens (M,R)-systems and Dana Scotts work on reflexive
domains, and explore different approaches to construct solutions to it. We
envision that the ideas behind this equation, a unique kind of mathematical
concept, initially found in biology, would play an important role towards
the development of a true systemic theoretical biology.
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Conference name European Conference on Artificial Life
Publisher MIT Press (Boston, MA, USA)
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