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Philosophy of computation. (English) Zbl 1436.68105
Stepney, Susan (ed.) et al., Computational matter. Cham: Springer. Nat. Comput. Ser., 153-184 (2018).
Summary: Unconventional computation emerged as a response to a series of technological and societal challenges. The main source of these challenges is the expected collapse of Moore’s law. It is very likely that the existing trend of building faster digital information processing machines will come to an end. This chapter provides a broad philosophical discussion of what might be needed to construct a theoretical machinery that could be used to understand the obstacles and identify the alternative designs. The key issue that has been addressed is simple to formulate: given a physical system, what can it compute? There is an enormous conceptual depth to this question and some specific aspects are systematically discussed. The discussion covers digital philosophy of computation, two reasons why rocks cannot be used for computation are given, a new depth to the ontology of number, and the ensemble computation inspired by recent understanding of the computing ability of living cell aggregates.
For the entire collection see [Zbl 1443.68021].
MSC:
68Q01 General topics in the theory of computing
00A30 Philosophy of mathematics
Software:
GAP; SgpDec
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References:
[1] Adamatzky, A. (2010).Physarum Machines: Computers from Slime Mould. World Scientific.
[2] Ashby, William Ross (1956).An introduction to cybernetics. Champman & Hall. · Zbl 0071.12303
[3] Bar-Yam, Yaneer (2004). “Multiscale variety in complex systems”.Complexity9(4):37-45.
[4] Beer, Stafford (1984). “The viable system model: Its provenance, development, methodology and pathology”.Journal of the Operational Research Society35:7-25.
[5] Bennett, C. H. (1988). “Logical Depth and Physical Complexity”.The Universal Turing Machine: A Half-Century Survey. Ed. by R. Herken. Oxford University Press, pp. 227-257.
[6] Bremermann, H. J. (1962). “Optimization through evolution and recombination”.Self-Organizing Systems. Ed. by Marshall C. Yovitis and George T. Jacobi. Spartan, pp. 93-106.
[7] Brown, C. (2012). “Combinatorial-State Automata and Models of Computation”.Journal of Cognitive Science13:51-73.
[8] Chalmers, D. J. (1996). “Does a rock implement every finite-state automaton?”Synthese108:309-333. · Zbl 0931.03010
[9] Chrisley, R. L. (1994). “Why everything doesn’t realize every computation”. Minds and Machines4:403-420.
[10] Copeland, B. J. (1996). “What is computation?”Synthese108:335-359. · Zbl 0942.03004
[11] Dini, P., C. L. Nehaniv, A. Egri-Nagy, and M. J. Schilstra (2013). “Exploring the Concept of Interaction Computing through the Discrete Algebraic Analysis of the Belousov-Zhabotinsky Reaction”.BioSystems112(2):145- 162.
[12] Dodig-Crnkovic, Gordana and Mark Burgin (2011).Information and computation: Essays on scientific and philosophical understanding of foundations of information and computation. Vol. 2. World Scientific. · Zbl 1221.00068
[13] Egri-Nagy, A., C. L. Nehaniv, and J. D. Mitchell (2014).SgpDec- Hierarchical Decompositions and Coordinate Systems, Version 0.7.29.url: sgpdec.sf.net. · Zbl 1403.20002
[14] Foerster, Heinz von (2007).Understanding understanding: Essays on cybernetics and cognition. Springer.
[15] GAP Group (2014).GAP- Groups, Algorithms, and Programming, V 4.7.5. url:www.gap-system.org.
[16] Glanville, Ranulph (2004). “A (cybernetic) musing: Control, variety and addiction”.Cybernetics & Human Knowing11(4):85-92.
[17] Glanville, Ranulph, Hugh Dubberly, and Paul Pangaro (2007). “Cybernetics and service-craft: Language for behavior-focused design”.Kybernetes 36(9/10):1301-1317. · Zbl 1183.93010
[18] Godfrey-Smith, P. (2009). “Triviality arguments against functionalism”.Philosophical Studies145:273-295.
[19] Horsman, C., Susan Stepney, Rob C. Wagner, and Viv Kendon (2014). “When does a physical system compute?”Proceedings of the Royal Society A 470(2169):20140182. · Zbl 1353.68077
[20] Horsman, D. C. (2015). “Abstraction/Representation Theory for heterotic physical computing”.Phil. Trans. Roy. Soc. A373:20140224.
[21] Horsman, Dominic, Viv Kendon, and Susan Stepney (2018). “Abstraction/ Representation Theory and the Natural Science of Computation”.Physical Perspectives on Computation, Computational Perspectives on Physics. Ed. by Michael E. Cuffaro and Samuel C. Fletcher. Cambridge University Press, pp. 127-149.
[22] Horsman, Dominic, Susan Stepney, and Viv Kendon (2017a). “The Natural Science of Computation”.Communications of ACM60(8):31-34.
[23] Horsman, Dominic, Susan Stepney, Viv Kendon, and J. P. W. Young (2017b). “Abstraction and representation in living organisms: when does a biological system compute?”Representation and Reality in Humans, Other Living Organisms and Intelligent Machines. Ed. by Gordana Dodig-Crnkovic and Raffaela Giovagnoli. Springer, pp. 91-116.
[24] Joslin, D. (2006). “Real realization: Dennett’s real patterns versus Putnam’s ubiquitous automata”.Minds and Machines16:29-41.
[25] Kauffman, S. (1993).The Origins of Order: Self-Organisation and Selection in Evolution. Oxford University Press.
[26] Kendon, Viv, Angelika Sebald, and Susan Stepney (2015). “Heterotic computing: past, present, and future”.Phil. Trans. Roy. Soc. A373:20140225. · Zbl 1330.68076
[27] Kirby, K. (2009). “Putnamizing the Liquid State (extended abstract)”. NACAP 2009.
[28] Konkoli, Zoran (2015). “A Perspective on Putnam’s Realizability Theorem in the Context of Unconventional Computation”.International Journal of Unconventional Computing11:83-102.
[29] Krohn, K. and J. Rhodes (1965). “Algebraic Theory of Machines. I. Prime Decomposition Theorem for Finite Semigroups and Machines”.Transactions of the American Mathematical Society116:450-464. · Zbl 0148.01002
[30] Ladyman, J. (2009). “What does it mean to say that a physical system implements a computation?”Theoretical Computer Science410:376-383. · Zbl 1160.68011
[31] Maler, O. (2010). “On the Krohn-Rhodes Cascaded Decomposition Theorem”.Time for Verification: Essays in Memory of Amir Pnueli. Ed. by Z. Manna and D. Peled. Vol. 6200. LNCS. Springer.
[32] Maruyama, Magoroh (1963). “The second cybernetics: Deviation-amplifying mutual causal processes”.American Scientist51:164-179.
[33] Nehaniv, Chrystopher L. (2005). “Self-replication, Evolvability and Asynchronicity in Stochastic Worlds”.Stochastic Algorithms: Foundations and Applications. Vol. 3777. LNCS. Springer, pp. 126-169. · Zbl 1159.68648
[34] Nehaniv, Chrystopher L, Frank F¨orster, Joe Saunders, Frank Broz, Elena Antonova, Hatice Kose, Caroline Lyon, Hagen Lehmann, Yo Sato, and Kerstin Dautenhahn (2013). “Interaction and experience in enactive intelligence and humanoid robotics”.IEEE Symposium on Artificial Life (IEEE ALIFE 2013). IEEE, pp. 148-155.
[35] Nehaniv, Chrystopher L., John Rhodes, Attila Egri-Nagy, Paolo Dini, Eric Rothstein Morris, G´abor Horv´ath, Fariba Karimi, Daniel Schreckling, and Maria J. Schilstra (2015). “Symmetry structure in discrete models of biochemical systems: natural subsystems and the weak control hierarchy in a new model of computation driven by interactions”.Philosophical Transactions of the Royal Society A373:2040223. · Zbl 1353.92043
[36] Pepper, John W. (2003). “The evolution of evolvability in genetic linkage patterns”.BioSystems69(2):115-126.
[37] Putnam, H. (1988).Representation and Reality. MIT Press.
[38] Rhodes, J. (2010).Applications of Automata Theory and Algebra via the Mathematical Theory of Complexity to Biology, Physics, Psychology, Philosophy, and Games. World Scientific Press. · Zbl 1195.20066
[39] Robinson, Michael (1979). “Classroom control: Some cybernetic comments on the possible and the impossible”.Instructional Science8(4):369-392.
[40] Scheutz, M. (1999). “When Physical Systems Realize Functions”.Minds and Machines9:161-196.
[41] Searle, J. R. (1992).The Rediscovery of the Mind. MIT Press.
[42] Shagrir, O. (2012). “Computation, Implementation, Cognition”.Minds and Machines22:137-148.
[43] Shannon, C. E. (1948). “A mathematical theory of communication”.Bell System Technical Journal27(3):379-423. · Zbl 1154.94303
[44] Turing, A. (1936). “On Computable Numbers, with an Application to the Entscheidungsproblem”.Proceedings of the London Mathematical Society (2)42:A correction, ibid, 43, 1937, pp. 544-546, 230-265. · Zbl 0016.09701
[45] Varela, Francisco J. (1979).Principles of Biological Autonomy. North Holland.
[46] Varela, Francisco J., Evan Thompson, and Eleanor Rosch (1991).The Embodied Mind. MIT Press.
[47] Von Eckardt, B. (1995).What is cognitive science?MIT Press.
[48] Wegner, P. (1997). “Why Interaction Is More Powerful than Algorithms”. Communications of the ACM40(5):80-91.
[49] West-Eberhard, Mary Jane (1989). “Phenotypic plasticity and the origins of diversity”.Annual Review of Ecology and Systematics:249-278.
[50] Wiener, Norbert (1961).Cybernetics or Control and Communication in the Animal and the Machine. MIT Press. · Zbl 0098.11705
[51] Zeiger, H.
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