Physical Limits of Inference

          @misc{ pirsa_PIRSA:08110000,
            doi = {10.48660/08110000},
            url = {https://pirsa.org/08110000},
            author = {Wolpert, David},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Physical Limits of Inference},
            publisher = {Perimeter Institute},
            year = {2008},
            month = {nov},
            note = {PIRSA:08110000 see, \url{https://pirsa.org}}
          }
          

Abstract

I show that physical devices that perform observation, prediction, or recollection share an underlying mathematical structure. I call devices with that structure ``inference devices\'\'. I present a set of existence and impossibility results concerning inference devices. These results hold independent of the precise physical laws governing our universe. In a limited sense, the impossibility results establish that Laplace was wrong to claim that even in a classical, non-chaotic universe the future can be unerringly predicted, given sufficient knowledge of the present. Alternatively, these impossibility results can be viewed as a non-quantum mechanical ``uncertainty principle\'\'. Next I explore the close connections between the mathematics of inference devices and of Turing Machines. I end by informally discussing the philosophical implications of these results, e.g., for whether the universe ``is\'\' a computer.