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.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
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 \(14+32\).
Aaronson, S. (2013). Why philosophers should care about computational complexity. In B. J. Copeland & O. S. C. Posy (Eds.), Computability: Turing, gdel, church, and beyond (pp. 261–328). London: MIT Press.
Adleman, L. (1994). Molecular computation of solutions to combinatorial problems. Science, 226, 1021–1024.
Alhazov, A., & Cavaliere, M. (2004). Computing by observing bio-systems: The case of sticker systems. In C. Ferretti, G. Mauri, & C. Zandron (Eds.), DNA (Vol. 3384, pp. 1–13)., Lecture Notes in Computer Science Berlin: Springer.
Bickle, J. (2013). Multiple realizability. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy (2013th ed.). Berlin: Springer.
Book, R., & Otto, F. (1993). String-rewriting systems. Berlin: Springer.
Cavaliere, M., Frisco, P., & Hoogeboom, H. J. (2006). Computing by only observing. In O. H. Ibarra & Z. Dang (Eds.), Developments in language theory (Vol. 4036, pp. 304–314)., Lecture Notes in Computer Science Berlin: Springer.
Cavaliere, M., & Leupold, P. (2003). Evolution and observation: A new way to look at membrane systems. In C. Martín-Vide, G. Mauri, G. Paun, G. Rozenberg, & A. Salomaa (Eds.), Workshop on membrane computing (Vol. 2933, pp. 70–87). Lecture Notes in Computer Science, Berlin: Springer.
Cavaliere, M., & Leupold, P. (2004). Evolution and observation—A non-standard way to generate formal languages. Theoretical Computer Science, 321, 233–248.
Cavaliere, M., & Leupold, P. (2006). Observation of string-rewriting systems. Fundamenta Informaticae, 74(4), 447–462.
Chalmers, D. J. (1996). Does a rock implement every finite-state automaton? Synthese, 108, 309–333.
Dassow, J., Mitrana, V., & Salomaa, A. (2002). Operations and language generating devices suggested by the genome evolution. Theoretical Computer Science, 270(1–2), 701–738.
Fodor, J. A. (1981). The mind–body problem. Scientific American, 241, 114–123.
Fresco, N. (2010). Explaining computation without semantics: Keeping it simple. Minds and Machines, 20, 165–181. https://doi.org/10.1007/s11023-010-9199-6.
Krassovitskiy, A., & Leupold, P. (2012). Computing by observing insertion. In A. H. Dediu & C. Martín-Vide (Eds.), LATA (Vol. 7183, pp. 377–388)., Lecture Notes in Computer Science Berlin: Springer.
Landweber, L. F., & Kari, L. (2002). Universal molecular computation in ciliates. In L. F. Landweber & E. Winfree (Eds.), Evolution as computation, natural computing series (pp. 257–274). Berlin: Springer.
Morse, M. (1938). A solution of the problem of infinite play in chess. Bulletin of the American Mathemetical Society, 44, 632.
Păun, G., Rozenberg, G., & Salomaa, A. (1998). DNA computing—New computing paradigms. Berlin: Springer.
Piccinini, G. (2008). Computation without representation. Philosophical Studies, 137(2), 205–241. https://doi.org/10.1007/s11098-005-5385-4.
Putnam, H. (1988). Representation and reality. London: MIT Press.
Searle, J. R. (1992). The rediscovery of the mind. London: MIT Press.
Turing, A. (1937). On computable numbers, with an application to the entscheidungsproblem. Proceedings of the London Mathematical Society, 2(42), 230–265.
von Braunmühl, B., & Verbeek, R. (1979). Finite-change automata. In K. Weihrauch (Ed.), Theoretical computer science 4th GI conference (Vol. 67, pp. 91–100)., Lecture Notes in Computer Science Berlin: Springer.
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.
About this article
Cite this article
Leupold, P. The Role of Observers in Computations. Minds & Machines 28, 427–444 (2018). https://doi.org/10.1007/s11023-018-9471-8