A configuration can store a single complex value - "complex" as in the complex numbers (a + bi).

Any complex number? I.e. you're invoking an uncountable infinity for explaining the lowest known layer of physics? How does that fit in with being an infinite-set atheist - assuming you still hold that position?
I'm speaking as a nonphysicist reader, so I may well be missing something awfully obvious here. Any clarification would be appreciated.