Dear Conrad,
Thank you for your comments.
> Any mathematical structure, and in particular any useful equation in physics, can represent an infinite number of particular cases, only some of which are physically instantiated in any particular part of spacetime. Even if we assume the universe is infinite and contains all possible cases somewhere, a mathematical structure can be "isomorphic" to it only in a very partial and limited sense, that abstracts from every local viewpoint. [...] Yet isn't the existence of distinct instances at particular times and places a basic feature of the physical world? What do our equations refer to, if not to the dynamic relationships between these instances?
The statement "the universe is isomorphic to a mathematical structure" doesn't mean that it is to all solutions of an equation. Each initial condition gives a different solution, and maybe only one of them is a universe (ours), or maybe each of them is a different universe.
> In my current essay I've tried to show how quantum measurement can be treated as a form of natural selection ...
Maybe you will like quantum darwinism.
> My sense is that we conflate "having a particular point of view on the world" - which is something we can reasonably ascribe to atoms, or anything else that's localized in space and time - with the kind of reflective self-awareness we humans have.
Indeed, I think this conflation is common but unsupported yet.
Best regards,
Cristi