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Significance of Models of Computation, from Turing Model to Natural Computation

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Abstract

The increased interactivity and connectivity of computational devices along with the spreading of computational tools and computational thinking across the fields, has changed our understanding of the nature of computing. In the course of this development computing models have been extended from the initial abstract symbol manipulating mechanisms of stand-alone, discrete sequential machines, to the models of natural computing in the physical world, generally concurrent asynchronous processes capable of modelling living systems, their informational structures and dynamics on both symbolic and sub-symbolic information processing levels. Present account of models of computation highlights several topics of importance for the development of new understanding of computing and its role: natural computation and the relationship between the model and physical implementation, interactivity as fundamental for computational modelling of concurrent information processing systems such as living organisms and their networks, and the new developments in logic needed to support this generalized framework. Computing understood as information processing is closely related to natural sciences; it helps us recognize connections between sciences, and provides a unified approach for modeling and simulating of both living and non-living systems.

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Notes

  1. “Cognitive sciences” here refer to “the interdisciplinary study of mind and intelligence, embracing philosophy, psychology, artificial intelligence, neuroscience, linguistics, and anthropology.”, according to Thagard, Paul, "Cognitive Science", The Stanford Encyclopedia of Philosophy (Summer 2010 Edition), Edward N. Zalta (ed.), URL = <http://plato.stanford.edu/archives/sum2010/entries/cognitive-science/>.

  2. Agent Based Models are the most important development in this direction, where a complex dynamical system is represented by interacting, in general adaptive, agents. Examples of such systems are in physics: turbulence, percolation, sand pile, weather; in biology: cells organs (including brain), organisms, populations, ecosystems; and in the social sphere: language, organizations, and markets.

  3. An extension of the basic Turing machine model introduced by (Turing 1939) which is the extension by oracles which enables new, external, and possibly noncomputable information to enter a computation. Such machines could compute an arbitrary non-recursive function from naturals to naturals. Turing showed that even in those more powerful systems, undecidability still appears. Oracle machines were only mathematical models, and were not thought of as physically realizable. The central ideas which (Cooper 2008) brings to this project are the concepts of definability and invariance in a context of the real-world computation. He is modeling causal relationships based on Turing's 1939 concept of interactive computation, which Cooper defines over reals.

  4. “Focusing on interaction without representation, concentrating on computation beyond the 'Turing barrier', without climbing the higher levels which become the subject in a mathematical analysis of the structures of interaction (see e.g. Cooper)”—I am thankful for the anonymous reviewer for this remark.

  5. http://www.idsia.ch/~juergen/digitalphysics.htm.

  6. (Hodges 2009) criticizes proposal by (Copeland and Proudfoot 1999) to use a physical device as an oracle, as Turing in (Turing 1939, p. 173) said: 'We shall not go any further into the nature of this oracle apart from saying that it cannot be a machine.'

  7. For more details about new computational paradigms, and how “classical computability has expanded beyond its original scope to address issues related to computability and complexity in algebra, analysis, and physics”, see (Cooper et al. 2008).

  8. Some authors identify the idea of computing universe with discrete computing, which is not necessarily the only possible interpretation. Lloyd for example argues that on the quantum mechanical level both continuum and discrete structures are necessary. Discrete models are abundant and very useful, but there are also models in physics which presuppose continuous descriptions.

References

  • Abramsky, S. (1997). Semantics of interaction: An introduction to game semantics. In P. Dybjer & A. Pitts (Eds.), Proceedings of the 1996 CLiCS Summer School, Isaac Newton Institute (pp. 1–31). Cambridge: Cambridge University Press.

    Google Scholar 

  • Abramsky, S. (2003). Sequentiality versus concurrency in games and logic. Mathematical Structures in Computer Science, 13, 531–565.

    Article  MathSciNet  MATH  Google Scholar 

  • Abramsky, S. (2007). A compositional game semantics for multi-agent logics of imperfect information in interactive logic. In J. van Benthem, D. Gabbay, & B. Lowe (Eds.), Texts in logic and games, Vol. 1 (pp. 11–48). Amsterdam: Amsterdam University Press.

    Google Scholar 

  • Abramsky, S. (2008). Petri nets, discrete physics, and distributed quantum computation. In P. Degano, R. De Nicola and J. Meseguer (Eds.), Concurrency, graphs and models, essays dedicated to Ugo Montanari on the occasion of his 65th birthday, Vol. 5065 of lecture notes in computer science. Springer, 527–543.

  • Abramsky, S., & Coecke, B. (2007). Physics from computer science, Int. Journal of Unconventional Computing, 3(3), 179–197.

    Google Scholar 

  • Allo, P. (2007). Formalising semantic information. Lessons from logical pluralism. In G. Dodig-Crnkovic & S. Stuart (Eds.), Computation, information, cognition: The Nexus and the Liminal (pp. 41–52). Cambridge: Cambridge Scholars Publishing.

    Google Scholar 

  • Ashby, W. R. (1964). An introduction to cybernetics. London: Methuen.

    Google Scholar 

  • Beall, J. C., & Restall, G. (2000). Logical pluralism. Australasian Journal of Philosophy, 78, 475–493.

    Article  Google Scholar 

  • Beall, J.C., Restall, G. (2005). Logical Consequence, The Stanford Encyclopedia of Philosophy (Winter 2005 Edition). In: Edward N. Zalta (ed.). URL = <http://plato.stanford.edu/archives/win2005/entries/logical-consequence/>.

  • Benthem van, J. (2001). Extensive games as process models. In M. Pauly & P. Dekker, (Eds.), Special issue of Journal of logic, language and information, 11, 289–313.

  • Benthem van, J. (2003). Logic and the dynamics of information. Minds and Machines, 13, 503–519.

    Article  Google Scholar 

  • Benthem van, J. (2008). Logical pluralism meets logical dynamics? The Australasian Journal of Logic, 6, 182–209.

    MathSciNet  MATH  Google Scholar 

  • Bohan Broderick, P. (2004). On communication and computation. Minds and Machines, 14, 1–19.

    Article  MATH  Google Scholar 

  • Bringsjord, S. (1994). Computation, among other things, is beneath us. Minds and Machines, 4, 469–488.

    Article  Google Scholar 

  • Bringsjord, S., & Zenzen, M. (2002). Toward a formal philosophy of hypercomputation. Minds and Machines, 12, 241–258.

    Article  MATH  Google Scholar 

  • Burgin, M. (1999). Super-recursive algorithms as a tool for high performance computing. In Proceedings of high performance computing symposium, San Diego, 224–228. http://www.math.ucla.edu/~mburgin/res/compsc/res2/highperfcomp.html

  • Burgin, M. (2005). Super-recursive algorithms. Springer Monographs in Computer Science.

  • Cantwell Smith, B. (1996). On the origin of objects. Cambridge, MA: MIT Press.

    Google Scholar 

  • Chaitin, G. J. (2006). Epistemology as information theory: From Leibniz to Ω. Collapse, 1, 27–51.

    Google Scholar 

  • Church, A. (1935). Abstract no. 204. Bulletin of the American Mathematical Society, 41, 332–333.

  • Church, A. (1936). An unsolvable problem of elementary number theory. American Journal of Mathematics, 58, 345–363.

    Article  MathSciNet  Google Scholar 

  • Colburn, T. R., & Shute, G. M. (2008). Metaphor in computer science. Journal of Applied Logic, 6, 526–533.

    Article  Google Scholar 

  • Cooper, S. B., Löwe, B., & Sorbi, A., Eds. (2008). New computational paradigms: Changing conceptions of what is computable. Springer.

  • Copeland, B. J. (1997). ‘The Church–Turing thesis’. In E. Zalta (Ed.), Stanford encyclopedia of philosophy, <http://plato.stanford.edu>.

  • Copeland, B. J. (1998). Super Turing-machines. Complexity, 4, 30–32.

    Article  MathSciNet  Google Scholar 

  • Copeland, B. J. (2000). Narrow versus wide mechanism. Journal of Philosophy, 96, 5–32.

    Article  MathSciNet  Google Scholar 

  • Copeland, B. J. (2002). Hypercomputation. Minds and Machines, 12, 461–502.

    Article  MATH  Google Scholar 

  • Copeland, B. J., & Proudfoot, D. (1999). Alan Turing’s forgotten ideas in computer science. Scientific American, 280, 76–81.

    Article  Google Scholar 

  • Copeland, B. J., & Shagrir, O. (2007). Physical computation: How general are Gandy’s principles for mechanisms? Minds and Machines, 17, 217–223.

    Article  Google Scholar 

  • Copeland, B. J., & Sylvan, R. (1999). Beyond the universal Turing machine. Australian Journal of Philosopy, 77, 46–67.

    Article  MATH  Google Scholar 

  • Denning, P. (2007). Computing is a natural science, communications of the ACM, 50(7), 13–18. http://cs.gmu.edu/cne/pjd/PUBS/CACMcols/cacmJul07.pdf.

  • Dodig-Crnkovic, G. (2003). ‘Shifting the paradigm of the philosophy of science: The philosophy of information and a new renaissance’. Minds and Machines, 13(4), 521–536. http://www.springerlink.com/content/g14t483510156726/fulltext.pdf.

  • Dodig-Crnkovic, G. (2006). Investigations into information semantics and ethics of computing. Mälardalen University Press http://www.idt.mdh.se/personal/gdc/work/publications.html.

  • Dodig-Crnkovic, G. (2010). The cybersemiotics and info-computationalist research programmes as platforms for knowledge production in organisms and machines, entropy 12, 878–901. http://www.mdpi.com/1099-4300/12/4/878/pdf

  • Dodig-Crnkovic, G., & Müller, V. (2010). A dialogue concerning two world systems: Info-computational versus mechanistic. In Information and computation. World Scientific, Singapore. Preprint available at: http://arxiv.org/abs/0910.5001

  • Dodig-Crnkovic, G., & Stuart, S. (Eds.). (2007). Computation, information, cognition–The Nexus and the Liminal. Cambridge: Cambridge Scholar Press.

    Google Scholar 

  • Floridi, L. (2004). Open problems in the philosophy of information. Metaphilosophy, 35.4, 554–582.

    Google Scholar 

  • Goldin, D., Smolka, S., & Wegner P. (Eds.). (2006). Interactive computation: The new paradigm. Springer-Verlag.

  • Goldin, D., & Wegner, P. (2002). Paraconsistency of interactive computation, PCL 2002 (Workshop on paraconsistent computational logic). Denmark.

  • Hintikka, J. (1973). Logic, language-games and information: Kantian themes in the philosophy of logic. Oxford: Clarendon Press.

    MATH  Google Scholar 

  • Hintikka, J. (1982). Game-theoretical semantics: Insights and prospects. Notre Dame Journal of Formal Logic, 23(2), 219–241.

    Article  MathSciNet  MATH  Google Scholar 

  • Hodges, W. (2004). Logic and Games, The Stanford encyclopedia of philosophy (Winter 2004 Edition). Edward N. Zalta (Ed.). URL = <http://plato.stanford.edu/archives/win2004/entries/logic-games/>.

  • Hodges, A. (2009). Alan Turing, The Stanford encyclopedia of philosophy (Winter 2009 Edition). In Edward N. Zalta (Ed.). URL = <http://plato.stanford.edu/archives/win2009/entries/turing/>.

  • Japaridze, G. (2006). In the beginning was game semantics. In O. Majer, A.-V. Pietarinen, & T. Tulenheimo (Eds.), Logic and games: Foundational perspectives. Berlin: Springer Verlag.

    Google Scholar 

  • Kampis, G. (1991). Self-modifying systems in biology and cognitive science: A new framework for dynamics, information and complexity. Pergamon: Pergamon Press.

    Google Scholar 

  • Kelly, K. T. (2004). Uncomputability: The problem of induction internalized. Theoretical Computer Science, 317, 227–249.

    Article  MathSciNet  MATH  Google Scholar 

  • Kuipers, T. A. F. (2006). Theories looking for domains. Fact or fiction? Structuralist truth approximation by revision of the domain of intended applications, to appear. In L. Magnani (ed.), Model-based reasoning in science and engineering.

  • Lloyd, S. (2006). Programming the universe: A quantum computer scientist takes on the cosmos. In Alfred A. Knopf.

  • MacLennan, B. (2004). Natural computation and non-Turing models of computation. Theoretical Computer Science, 317, 115–145.

    Article  MathSciNet  MATH  Google Scholar 

  • Milner, R. (1989). Communication and concurrency. Prentice-Hall: International Series in Computing Science.

    MATH  Google Scholar 

  • Piccinini, G. (2007). Computational modeling versus computational explanation: Is everything a Turing machine, and does it matter to the philosophy of mind? Australasian Journal of Philosophy, 85(1), 93–115.

    Article  MathSciNet  Google Scholar 

  • Priest, G., & Tanaka, K. (2004). Paraconsistent Logic, The Stanford encyclopedia of philosophy (Winter 2004 Edition). In Edward N. Zalta (Ed.). URL = <http://plato.stanford.edu/archives/win2004/entries/logic-paraconsistent/>.

  • Rozenberg, G., & Kari, L. (2008). The many facets of natural computing. Communications of the ACM, 51, 72–83.

    Google Scholar 

  • Schachter, V. (1999). How does concurrency extend the paradigm of computation? Monist, 82(1), 37–58.

    Google Scholar 

  • Sieg, W. (2007). Church without dogma–Axioms for computability. In B. Löwe, A. Sorbi, & S. B. Cooper (Eds.), New computational paradigms: Changing conceptions of what is computable (pp. 18–44). Heidelberg: Springer.

    Google Scholar 

  • Siegelman, H. T. (1999). Neural networks and analog computation. Berlin: Birkhauser.

    Google Scholar 

  • Sloman, A. (1996). Beyond Turing equivalence. In P.J.R. Millican & A. Clark (Eds.), Machines and thought: The legacy of Alan Turing, vol I, OUP(The Clarendon Press) pp 179–219, Revised version of paper presented to Turing Colloquium, University of Sussex, 1990. http://www.cs.bham.ac.uk/research/projects/cogaff/96-99.html#1

  • Turing A. M. (1936). On computable numbers, with an application to the Entscheidungsproblem. In Proceedings of the London mathematical society, Vol. 42, pp. 230–265; reprinted in A. M. Turing, Collected works: mathematical logic, 18–53.

  • Turing A. M. (1939). Systems of logic based on ordinals.In Proceedings of the London mathematical society, ser. 2, Vol. 45, 162–228.

  • Turing, A. M. (1948). ‘Intelligent machinery’. National Physical Laboratory Report. In B. Meltzer, D. Michie (Eds.), 1969. Machine intelligence 5. Edinburgh: Edinburgh University Press. http://www.AlanTuring.net/intelligent_machinery.

  • Turing, A. M. (1950). Computing machinery and intelligence, Mind LIX, 433–60. http://cogprints.org/499/0/turing.html

  • Wegner, P. (1998). Interactive foundations of computing. Theoretical Computer Science, 192, 315–351.

    Article  MathSciNet  MATH  Google Scholar 

  • Wolfram, S. (2002) A new kind of science. Wolfram Science.

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Acknowledgments

The author would like to thank Björn Lisper, Lars-Göran Johansson and Kaj Börje Hansen for reviewing the manuscript and offering valuable suggestions. Further credit is extended to Richard Bonner and George Masterton for their interesting comments and discussions. I am most indebted to Vincent Müller with whom I newly wrote a dialogue article based on several years of discussions on topics of foundation of information and computation. Last but not list I would like to acknowledge the constructive criticisms and helpful suggestions of two anonymous reviewers on an earlier version of this paper.

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  1. Computer Science Laboratory, School of Innovation, Design and Engineering, Mälardalen University, Västerås, Sweden

    Gordana Dodig-Crnkovic

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Dodig-Crnkovic, G. Significance of Models of Computation, from Turing Model to Natural Computation. Minds & Machines 21, 301–322 (2011). https://doi.org/10.1007/s11023-011-9235-1

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