#turingcompleteness — Public Fediverse posts

We've computationally verified that Peano arithmetic emerges naturally from just two operators: Δ (distinction/branching) and Σ (connection/composition).

This isn't just coding — it's evidence for the Δ–Σ Turing Completeness Theorem: a system is Turing-complete iff it can be represented through Δ and Σ.

Code implements the proofs: https://github.com/muskin88/delta-sigma-peano/blob/main/Peano_from_deltasigma.py
Formal statement: https://zenodo.org/records/17895986
(Theorem 3)

The implications are ontological: these operators appear inevitable for any non-trivial reality. The framework unites computation, mathematics, and fundamental ontology.

#CategoryTheory #FoundationsOfMath #Computation #Ontology #FormalMethods #TypeTheory #PeanoArithmetic #TuringCompleteness #MathematicalPhilosophy

Accidentally Turing-Complete

https://beza1e1.tuxen.de/articles/accidentally_turing_complete.html

#HackerNews #Accidentally #Turing-Complete #TuringCompleteness #Programming #Languages #TechNews #HackerNews

A #TuringTest for #FreeWill by #SethLloyd

https://www.youtube.com/watch?v=5wyJlUUEpSE&ab_channel=FQXi

#Turing #AlanTuring #Philosophy #PhilosophyOfScience #Computing #Computability #HaltingProblem #TheHaltingProblem #Probability #QM #QuantumMechanics #Randomness #UniversalComputer #UniversalTuringMachine #TuringCompleteness #SelfReference #Recursion