# The Role of Observers in Computations

## Abstract

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.

## Keywords

Computation Observer Observer-relativity## Notes

### Acknowledgements

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.

## References

- 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.Google Scholar - Adleman, L. (1994). Molecular computation of solutions to combinatorial problems.
*Science*,*226*, 1021–1024.CrossRefGoogle Scholar - 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.Google Scholar - Bickle, J. (2013). Multiple realizability. In E. N. Zalta (Ed.),
*The Stanford encyclopedia of philosophy*(2013th ed.). Berlin: Springer.Google Scholar - Book, R., & Otto, F. (1993).
*String-rewriting systems*. Berlin: Springer.CrossRefzbMATHGoogle Scholar - 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.CrossRefGoogle Scholar - 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.CrossRefGoogle Scholar - Cavaliere, M., & Leupold, P. (2004). Evolution and observation—A non-standard way to generate formal languages.
*Theoretical Computer Science*,*321*, 233–248.MathSciNetCrossRefzbMATHGoogle Scholar - Cavaliere, M., & Leupold, P. (2006). Observation of string-rewriting systems.
*Fundamenta Informaticae*,*74*(4), 447–462.MathSciNetzbMATHGoogle Scholar - Chalmers, D. J. (1996). Does a rock implement every finite-state automaton?
*Synthese*,*108*, 309–333.MathSciNetCrossRefzbMATHGoogle Scholar - 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.MathSciNetCrossRefzbMATHGoogle Scholar - Fodor, J. A. (1981). The mind–body problem.
*Scientific American*,*241*, 114–123.CrossRefGoogle Scholar - 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.CrossRefGoogle Scholar - 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.Google Scholar - 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.CrossRefGoogle Scholar - Morse, M. (1938). A solution of the problem of infinite play in chess.
*Bulletin of the American Mathemetical Society*,*44*, 632.Google Scholar - Păun, G., Rozenberg, G., & Salomaa, A. (1998).
*DNA computing—New computing paradigms*. Berlin: Springer.CrossRefzbMATHGoogle Scholar - Piccinini, G. (2008). Computation without representation.
*Philosophical Studies*,*137*(2), 205–241. https://doi.org/10.1007/s11098-005-5385-4.MathSciNetCrossRefGoogle Scholar - Putnam, H. (1988).
*Representation and reality*. London: MIT Press.Google Scholar - Searle, J. R. (1992).
*The rediscovery of the mind*. London: MIT Press.Google Scholar - Turing, A. (1937). On computable numbers, with an application to the entscheidungsproblem.
*Proceedings of the London Mathematical Society*,*2*(42), 230–265.MathSciNetCrossRefzbMATHGoogle Scholar - 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.CrossRefGoogle Scholar