[tsimionescu]

> With a large enough machine, you could simulate any behavior you want

This is not exactly true, depending on what you mean by behavior. There are mathematical functions we know for a fact are not computable by a Turing machine, no matter how large. So a system that "behaves" like those functions couldn't be simulated by a TM. However, it's unclear whether such a system actually could exist in physical reality - which gets right back to the discussion of whether thinking is beyond Turing completeness or not.