| I think you aren't following the defintion of 'computer' or 'computable', you seem to have a mixed physical notion of what a 'computer' is. A computer, from a formal pov, is just an abstract mathematical object (like a shape) which has abstract properties (eg., like being a circle) that are computable, ie., are functions from integers to integers. The physical devices we call 'computers', in many ways, arent. They exist in space and time and hence have non-computable properties, like their (continuous) extension in space and time. See Turing's own paper where he makes this point himself, ie., that physical machines arent computers in his sense because they're continuous in time. Insofar as you appeal to any causal aspects of a physical system you arent talking about a computer in turing's sense, and nothing like a turing equivalence would apply. We already know that all computable functions can be implemented by 'arbitary substrates' -- this is just the same as saying that you can 'make a circle out of any material'. In exactly the same sense as gears can be networked, sand dunes already are. You can just go around labelling particles of sand with 0s and 1s, and for a subset, there you have it: the computable aspects of the TCP/IP protocol. But this is irrelevant. TCP/IP isnt useful because of its computable aspects. It's useful as a design sheet for humans to rig systems of electrical devices with highly specific causal properties. The system we call 'the internet' is useful because it connects keyboards, screens, mice, microphones, webcams, SSDs, RAM, etc. together -- and because these devices are provide for human interaction. The sand dune is likewise already implementing arbitary computable functions, so is the sun, so is the air, and any arbitary part of the universe you care to choose. But the sand dune lacks all the properties the internet has: there's no webcam, no keybaord, no screen, etc. What we actually use are physical properties. Talk of algorithms is just a design tool for people to build stuff |