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The Ouroboros Equation

by Negative Origin

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The Ouroboros Equation:

The ultimate selfreferential equation: f(f) = f
Notice that f (supposedly a function) applies to itself, as
an argument, the result being again f. So f plays simultaneously the roles of argument, function and value.

A most remarkable fact is the similarity of methods of constructing solutions to Ouroboros, developed in fields apparently as unrelated as logic (Scott, 1972, 1973) Hyperset Theory (Aczel, 1988), Cognitive Sciences (Kampis,1995; Kauffman, 1987), Computer Science and Informatics (Scott, 1972; Kampis, 1995; Milner, 2006), Systems Theory and Theoretical Biology (Rosen, 1991; Soto-Andrade and Varela, 1984; Maturana and Varela, 1980; Letelier et al., 2006, 2005), and metabolic systems theory (Letelier et al., 2006, 2005), motivated by the construction of actual mathematical models for untyped lambda calculus and virtual infinite regress in metabolic systems.

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released November 20, 2023

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