John Searle raised the question whether all computation is observer-relative. Indeed, all of the common views of computation, be they semantical, functional or causal rely on mapping something onto the states of a physical or abstract process. In order to effectively execute such a mapping, this process would have to be observed in some way. Thus a probably syntactical analysis by an observer seems to be essential for judging whether a given process implements some computation or not. In order to be able to explore the nature of these observers in a more formal way, we look at the Computing by Observing paradigm, a theoretical model of computation that includes an observer. We argue that the observers used there, monadic transducers, are good candidates for formalizing the way in which the syntax of a process must be analysed in order to judge whether it is computational.
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In a setting like the one of the example of Sect. 2 we could imagine that for an addition \(14+32\) the process has to do the additions \(1+3\) and \(4+2\) separately; the observation does not contain these but only the compact result \(14+32\).
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The two anonymous referees have invested a great amount of time in the long refereeing process and in sharing their knowledge in a very constructive way with the author. Thus they have effectuated several important changes in the manuscript and have had an essential part in letting it evolve to its current state. The author feels greatly indebted to both of the referees for their memorable patience and their openness of mind.
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Leupold, P. The Role of Observers in Computations. Minds & Machines 28, 427–444 (2018). https://doi.org/10.1007/s11023-018-9471-8