Shut-up and calculate!

Mr Multiverse, Max Tegmark, wrote an article in New Scientist a couple of weeks ago, advocating once more the notion that the physical universe is nothing more than a mathematical structure. The 'director's cut' version of this article can now be freely downloaded.

I have much sympathy with Tegmark's position, but I would personally say that the physical universe is an instantiation of a mathematical structure, not a mathematical structure itself. It's the difference between an individual thing and a type of thing.

I would also question Tegmark's insistence that a final theory of everything should be bereft of any interpretational 'baggage', by which he means not only observational and experimental terms and phrases, but also non-mathematical theoretical terms such as 'mass' and 'charge'. How does this work when a theory has multiple mathematical formulations, as is generally the case? For example, in quantum theory, the state of a system can be represented by a vector in a Hilbert space in one formulation, and by a positive normalized linear functional upon the self-adjoint part of a C*-algebra in another formulation. If we are to literally equate the state of a system with part of a mathematical structure, from which formulation are the structures to be taken?