Fernando Rosas (unfortunately not on Mastodon) asked on bsky:
"Has anyone figured out what exactly is the relation between the ideas of feedback, recurrence, and self-reference?"
A really interesting question.
He pointed to this paper for ideas: https://arxiv.org/abs/1711.02456
"Self-referential basis of undecidable dynamics: from The Liar Paradox and The Halting Problem to The Edge of Chaos"
I did some desk research and found this cool paper:
https://arxiv.org/abs/1112.2141
"Resolving Gödel's Incompleteness Myth: Polynomial Equations and Dynamical Systems for Algebraic Logic"
that argues there is no essential incompleteness in formal reasoning systems if you look closely enough (using a more elaborate formalism based on polynomial equations to represent and evaluate logical proposition).
I wonder if analogous construction could be created for related theorems like the halting problem in computability theory.
#DynamicalSystems #IncompletenessTheorem #PolynomialEquations #HaltingProblem #Undecidability #SelfReference #Recurrence
