I don't know that my mind is capable of imagining a universe which could not be simulated on a Turing Machine.

I never said it could not be, just that the Turing Machine would not be a concept that is likely to evolve there.

Imagine a universe where there are no discrete entities, so numbers/addition is not a useful model. Whatever inhabits such a universe, if anything, would not develop the abstraction of counting. This universe could still be Turing-simulated (Turing Machine is an abstraction from our universe),

This is the essential point I am trying to make. Mathematics is determined by the structure of the universe and is not an independent abstract entity. I feel like I failed, though.