I never thought of the analogy between needing to choose a gauge and needing to choose a particular Turing machine. I have, however (in conversation with T. Clark), mused a lot about the possible generalizations of gauge theory beyond physics. You have economic gauge theory (Eric Weinstein), you have arithmetic gauge theory (Minhyong Kim), you have gauge theory in deep learning (equivariant networks). Maybe there is an abstract homotopic approach to the costs of translating from one Turing machine to another.
Regarding gauge theory itself, I’ve never read this book, but Richard Healey’s “Gauging What’s Real” is said to be a good study of the ontological questions.
I never thought of the analogy between needing to choose a gauge and needing to choose a particular Turing machine. I have, however (in conversation with T. Clark), mused a lot about the possible generalizations of gauge theory beyond physics. You have economic gauge theory (Eric Weinstein), you have arithmetic gauge theory (Minhyong Kim), you have gauge theory in deep learning (equivariant networks). Maybe there is an abstract homotopic approach to the costs of translating from one Turing machine to another.
Regarding gauge theory itself, I’ve never read this book, but Richard Healey’s “Gauging What’s Real” is said to be a good study of the ontological questions.