I don't see what this paper is contributing other than the assertion that a physical system needs to functorially agree with the mathematical model that represents it. And that if that model is Turing complete, or represents some useful subset of computational functionality, then the physical system "computes." The fact that a sitting rock does nothing but sit is a perfectly fine, albeit severely limited, computational system (it even satisfies their definition of a computing physical system!). All of this just seems...obvious.<p>It looks like their definitions are so general that they don't answer their own questions, which by their main motivations (section XI) are fundamentally problems of construction and scale. It's not enough that there exists a theory that proves your physical system computes, you have to know the representation explicitly and be able to scale the system arbitrarily. [Edit:] The problem being that this doesn't show up in their actual definitions.<p>Maybe I'm reading it too shallowly, though. Can someone who's more well-versed in the background of this paper explain it better? It also doesn't help my confidence that they seem to completely ignore the rest of computer science (mentioning Turing machines only as an aside, and as part of a false assertion about (quantum) Turing machines being the only universal logical systems).