Undecidability, Lawvere's Theorem, and Universality

Certain spin models are universal, meaning that they contain all other models when seen in the appropriate light. What is the relation between universal spin models, universal Turing machines and notions of universality in neural networks? And what is their relation to forms of unreachability such as uncomputability or undecidability? I will explore these questions in the light of our recent framework for universality (arxiv:2307.06851). I will also share some philosophical perspectives on these structures.