Oracles and Advice as Measurements
Abstract
In this paper we will try to understand how oracles and advice functions, which are mathematical abstractions in the theory of computability and complexity, can be seen as physical measurements in Classical Physics. First, we consider how physical measurements are a natural external source of information to an algorithmic computation, using a simple and engaging case study, namely: Hoyle’s algorithm for calculating eclipses at Stonehenge. Next, we argue that oracles and advice functions can help us understand how the structure of space and time has information content that can be processed by Turing machines. Using an advanced case study from Newtonian kinematics, we show that non-uniform complexity is an adequate framework for classifying feasible computations by Turing machines interacting with an oracle in Nature, and that by classifying the information content of such a natural oracle, using Kolmogorov complexity, we obtain a hierarchical structure based on measurements, advice classes and information.
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