Physical limits of inference

We show that physical devices that perform observation, prediction, or recollection share an underlying mathematical structure. We call devices with that structure “inference devices”. We 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 nonquantum mechanical “uncertainty principle”. The mathematics of inference devices has close connections to the mathematics of Turing Machines (TM’s). In particular, the impossibility results for inference devices are similar to the Halting theorem for TM’s. Furthermore, one can define an analog of Universal TM’s (UTM’s) for inference devices. ...

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: David H. Wolpert
• Keywords: CORR 2007, Education, Impossibility, Inference Devices, Strong Inference Device