Editing Ouroboros (section)

=== Cybernetics ===
[[W. Ross Ashby]] applied ideas from biology to his own work as a psychiatrist in "Design for a Brain" (1952): that living things maintain essential variables of the body within critical limits with the brain as a regulator of the necessary feedback loops. Parmar contextualises his practices as an artist in applying the cybernetic Ouroboros principle to musical improvisation.<ref>Parmar, Robin. "No Input Software: Cybernetics, Improvisation, and the Machinic Phylum." ISSTA 2011 (2014). He further discusses the cybernetics in elementary actions (like picking up a drum stick), the evolution of cybernetic science from [[Norbert Wiener]] to [[Gordon Pask]], [[Heinz von Foerster]], and Autopoiesis, and in related fields such as [[Autocatalysis]], the philosophical system of [[Gilles Deleuze]] and [[Félix Guattari]], and [[Manuel DeLanda]].</ref>

Hence the snake eating its tail is an accepted image or metaphor in the autopoietic calculus for self-reference,<ref>Varela, Francisco J. "A Calculus for Self-reference." International Journal of General Systems 2 (1975): 5–24.</ref> or self-indication, the logical processual notation for analysing and explaining self-producing autonomous systems and "the riddle of the living", developed by [[Francisco Varela]]. Reichel describes this as:

{{blockquote|an abstract concept of a system whose structure is maintained through the self-production of and through that structure. In the words of
Kauffman, is "the ancient mythological symbol of the worm ouroboros embedded in a mathematical, non-numerical calculus".<ref>Kauffman sub-reference: Kauffman L. H. 2002. Laws of form and form dynamics. Cybernetics & Human Knowing 9(2): 49–63, pp. 57–58.</ref><ref name="Snakes all the Way Down">{{Cite journal |last=Reichel |first=André |year=2011 |title=Snakes all the Way Down: Varela's Calculus for Self-Reference and the Praxis of Paradis |journal=Systems Research and Behavioral Science |volume=28 |issue=6 |pages=646–662 |doi=10.1002/sres.1105 |s2cid=16051196| url=http://www.andrereichel.de/resources/REI_2011_Snakes.pdf}}</ref>}}

The calculus derives from the confluence of the cybernetic logic of feedback, the sub-disciplines of [[autopoiesis]] developed by Varela and [[Humberto Maturana]], and calculus of indications of [[George Spencer Brown]]. In another related biological application:

{{blockquote| It is remarkable, that Rosen's insight, that metabolism is just a mapping ..., which may be too cursory for a biologist, turns out to show us the way to construct [[Recursion|recursively]], by a limiting process, solutions of the self-referential Ouroborus equation f(f) {{=}} f, for an unknown function f, a way that mathematicians had not imagined before Rosen.<ref>Gutiérrez, Claudio, Sebastián Jaramillo, and Jorge Soto-Andrade. "Some Thoughts on A. H. Louie's ''More Than Life Itself: A Reflection on Formal Systems and Biology''." Axiomathes 21, no. 3 (2011): 439–454, p. 448.</ref><ref>Soto-Andrade, Jorge, Sebastia Jaramillo, Claudio Gutierrez, and Juan-Carlos Letelier. "[https://web.archive.org/web/20150722004806/https://mitpress.mit.edu/sites/default/files/titles/alife/0262297140chap115.pdf Ouroboros Avatars: A Mathematical Exploration of Self-reference and Metabolic Closure]". "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 to as Ouroboros equation), arises in apparently dissimilar contexts, like Robert Rosen's synthetic view of metabolism, hyper set theory and, importantly, untyped lambda calculus. ... We envision that the ideas behind this equation, a unique kind of mathematical concept, initially found in biology, would play an important role in the development of a true systemic theoretical biology." MIT Press online.</ref>}}

[[Second-order cybernetics]], or the cybernetics of cybernetics, applies the principle of self-referentiality, or the participation of the observer in the observed, to explore observer involvement.<ref>Müller, K. H. [https://books.google.com/books?id=c5zXjwEACAAJ Second-order Science: The Revolution of Scientific Structures. Complexity, design, society.] Edition Echoraum, 2016.</ref> including D. J. Stewart's domain of "observer valued imparities".<ref>Scott, Bernard. "The Cybernetics of Systems of Belief". Kybernetes: The International Journal of Systems & Cybernetics 29, nos. 7–8 (2000): 995–998.</ref>