Skip to main content
SpringerLink
Log in

Complex Systems and the Evolution of Artificial Intelligence

  • Chapter
Thinking in Complexity

  • 123 Accesses

Abstract

Can machines think? This famous question from Turing has new topicality in the framework of complex systems. The chapter starts with a short history of computer science since Leibniz and his program for mechanizing thinking (mathesis universalis) (Sect. 5.1). The modern theory of computability enables us to distinguish complexity classes of problems, meaning the order of corresponding functions describing the computational time of their algorithms or computational programs. Modern computer science is interested not only in the complexity of universal problem solving but also in the complexity of knowledge-based programs. Famous examples are expert systems simulating the problem solving behavior of human experts in their specialized fields. Further on, we ask if a higher efficiency of problem solving may be expected from quantum computers and quantum complexity theory (Sect. 5.2).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. For this chapter compare Mainzer, K.: Computer - Neue Flügel des Geistes?De Gruyter: Berlin/New York (1993);

    Google Scholar 

  2. Mainzer, K.: Die Evolution intelligenter Systeme. Zeitschrift für Semiotik 12 (1990) 81–104

    Google Scholar 

  3. Feigenbaum, E.A./McCorduck, P.: The Fifth Generation. Artificial Intelligence and Japan’s Computer Challenge to the World. Michael Joseph: London (1984)

    Google Scholar 

  4. Cf.Williams, M.R.: A History of Computing Technology. Prentice-Hall: Engle- wood Cliffs (1985)

    Google Scholar 

  5. Cohors-Fresenborg, E.: Mathematik mit Kalkülen und Maschinen. Vieweg: Braunschweig (1977) 7

    Book  MATH  Google Scholar 

  6. Herrn von Leibniz’ Rechnung mit Null und Eins. Siemens AG: Berlin (1966);

    Google Scholar 

  7. Mackensen, L. von: Leibniz als Ahnherr der Kybernetik–ein bisher unbekannter Leibnizscher Vorschlag einer “Machina arithmetica dyadicae”. In: Akten des II. Internationalen Leibniz-Kongresses 1972 Bd. 2. Steiner: Wiesbaden (1974) 255–268

    Google Scholar 

  8. Scholz, H.: Mathesis Universalis. Schwabe: Basel (1961)

    MATH  Google Scholar 

  9. Babbage, C.: Passages from the Life of a Philosopher. Longman and Co.: London (1864);

    Google Scholar 

  10. Bromley, A.G.: Charles Babbage’s Analytical Engine 1838. Annals of the History of Computing 4 (1982) 196–219

    Article  MathSciNet  MATH  Google Scholar 

  11. Cf. Minsky, M.: Recursive unsolvability of Post’s problem of “tag” and other topics in the theory of Turing machines. Annals of Math. 74 437–454;

    Google Scholar 

  12. Sheperdson, J.C./Sturgis, H.E.: Computability of recursive functions. J. Assoc. Comp. Mach. 10 (1963) 217–255. For the following description of register machines compare Rödding, D.: Klassen rekursiver Funktionen. In: Löb, M.H. (ed.): Proceedings of the Summer School in Logic. Springer: Berlin (1968) 159–222; CohorsFresenborg, E.: Mathematik mit Kalkülen und Maschinen (see Note 4 )

    Google Scholar 

  13. Turing, A.M.: On computable numbers, with an application to the “Entscheidungsproblem”. Proc. London Math. Soc., Ser. 2 42 (1936) 230–265;

    Google Scholar 

  14. Post, E.L.: Finite combinatory processes–Formulation I. Symbolic Logic I (1936) 103–105;

    Google Scholar 

  15. Davis, M.: Computability and Unsolvability. McGraw-Hill: New York (1958) 3

    MATH  Google Scholar 

  16. Arbib, M.A.: Brains, Machines, and Mathematics. Springer: New York (1987) 131

    Book  MATH  Google Scholar 

  17. Mainzer, K.: Der Konstruktionsbegriff in der Mathematik. Philosophia Naturalis 12 (1970) 367–412

    MathSciNet  Google Scholar 

  18. Cf. Knuth, D.M.: The Art of Computer Programming. Vol. 2. Addison-Wesley: Reading, MA (1981);

    Google Scholar 

  19. Börger, E.: Berechenbarkeit, Komplexität, Logik. Vieweg: Braunschweig (1985)

    MATH  Google Scholar 

  20. Grötschel, M./Lovâsc, L./Schryver, A.: Geometric Algorithms and Combinatorial Optimization. Springer: Berlin (1988)

    Google Scholar 

  21. Gardner, A.: Penrose Tiles to Trapdoor Ciphers. W.H. Freeman: New York (1989)

    Google Scholar 

  22. Cf. Arbib, M.A.: Speed-up theorems and incompleteness theorem. In: Caianiello, E.R. (ed.): Automata Theory. Academic Press (1966) 6–24;

    Google Scholar 

  23. Mostowski, A.: Sentences Undecidable in Formalized Arithmetic. North-Holland: Amsterdam (1957);

    Google Scholar 

  24. Beth, E.W.: The Foundations of Mathematics, North-Holland: Amsterdam (1959);

    MATH  Google Scholar 

  25. Kleene, S.C.: Introduction to Metamathematics. North-Holland: Amsterdam (1967)

    Google Scholar 

  26. Mainzer, K.: Rationale Heuristik und Problem Solving. In: Burrichter, C./Inhetveen, R./Kötter, R. (eds.): Technische Rationalität und rationale Heuristik. Schöningh: Paderborn (1986) 83–97

    Google Scholar 

  27. Mainzer, K.: Knowledge-based systems. Remarks on the philosophy of technology and Artificial Intelligence. Journal for General Philosophy of Science 21 (1990) 47–74

    Google Scholar 

  28. Bibel, W./Siekmann, J.: Künstliche Intelligenz. Springer: Berlin (1982);

    Google Scholar 

  29. Nilson, N.J.: Principles of Artificial Intelligence. Springer: Berlin (1982);

    Google Scholar 

  30. Kredel, L.: Künstliche Intelligenz und Expertensysteme. Droemer Knaur: München (1988)

    Google Scholar 

  31. Puppe, F.: Expertensysteme. Informatik-Spektrum 9 (1986) 1–13

    MathSciNet  Google Scholar 

  32. For instance, one of the constructors of DENDRAL and MYCIN received a Ph.D. in philosophy for his dissertation “Scientific Discoveries”, supervised by Gerald Massey (today Center for Philosophy of Science, Pittsburgh). Also refer to Glymour, C.: AI is philosophy. In: Fetzer, J.H. (ed.): Aspects in Artificial Intelligence. Kluwer Academic Publisher: Boston (1988) 195–207

    Google Scholar 

  33. Buchanan, B.G./Sutherland, G.L./Feigenbaum, E.A.: Heuristic DENDRAL: A program for generating processes in organic chemistry. In: Meltzer, B./Michie, D. (eds.): Machine Intelligence 4. Edinburgh (1969);

    Google Scholar 

  34. Buchanan, B.G./Feigenbaum, E.A.: DENDRAL and META-DENDRAL: Their applications dimension. In: Artificial Intelligence 11 (1978) 5–24

    Google Scholar 

  35. McCarthy, J.: LISP Programmer’s Manual (Rep. MIT Press ). Cambridge, MA (1962);

    Google Scholar 

  36. Stoyan, H./Goerz, G.: LISP — Eine Einführung in die Programmierung. Springer: Berlin (1984)

    Google Scholar 

  37. Randall, D./Buchanan, B.G./Shortliffe, E.H.: Production rules as a representation for a knowledge-based consultation program. Artificial Intelligence 8 (1977);

    Google Scholar 

  38. Shortliffe, E.H.: MYCIN: A rule-based computer program for advising physicians regarding antimicrobial therapy selection. AI Laboratory, Memo 251, STANCS-74–465, Stanford University; Winston, P.H.: Artificial Intelligence. Addison-Wesley: Reading, MA (1977) Chap. 9

    Google Scholar 

  39. Doyle, J.: A truth maintenance system. Artificial Intelligence 12 (1979) 231–272

    Article  MathSciNet  Google Scholar 

  40. Lenat, D.B./Harris, G.: Designing a rule system that searches for scientific discoveries. In: Waterman, D.A./Hayes-Roth, F. (eds.): Pattern Directed Inference Systems. New York (1978) 26;

    Google Scholar 

  41. Lenat, D.B.: AM: Discovery in mathematics as heuristic search. In: Davis, R./Lenat, D.B. (eds.): Knowledge-Based Systems in Artificial Intelligence. New York (1982) 1–225

    Google Scholar 

  42. Langley, P: Data-driven discovery on physical laws. Cognitive Science 5 (1981) 31–54

    Article  Google Scholar 

  43. Langley, P./Simon, H.A./Bradshaw, G.L./Zytkow, J.M.: Scientific Discovery:Computational Explorations of the Creative Processes. Cambridge, MA (1987)

    Google Scholar 

  44. Kulkarni, D./Simon, H.A.: The process of scientific discovery: The strategy of experimentation. Cognitive Science 12 (1988) 139–175

    Article  Google Scholar 

  45. Cf. Winston, P.H.: Artificial Intelligence (see Note 23)

    Google Scholar 

  46. Audretsch, J./Mainzer, K. (eds.): Wieviele Leben hat Schrödingers Katze? B.I. Wissenschaftsverlag: Mannheim (1990) 273 (Fig. 5.14a), 274 (Fig. 5.14.b), 276 (Fig. 5. 14c )

    Google Scholar 

  47. Penrose, R.: Newton, quantum theory and reality. In: Hawking, S.W./Israel, W: 300 Years of Gravity. Cambridge University Press: Cambridge (1987)

    Google Scholar 

  48. Deutsch, D.: Quantum theory, the Church-Turing principle and the universal quantum computer. Proc. Roy. Soc. A400 (1985) 97–117

    Article  MathSciNet  ADS  MATH  Google Scholar 

  49. For this chapter compare Mainzer, K.: Computer — Neue Flügel des Geistes? De Gruyter: Berlin (1993);

    Google Scholar 

  50. Mainzer, K.: Philosophical concepts of computational neuroscience. In: Eckmiller, R./Hartmann, G./Hauske, G. (eds.): Parallel Processing in Neural Systems and Computers. North-Holland: Amsterdam (1990) 9–12

    Google Scholar 

  51. McCullock, W.S./Pitts, W: A logical calculus of the ideas immanent in nervous activity. In: Bulletin of Mathematical Biophysics 5 (1943) 115–133; Arbib, M.A.: Brains, Machines and Mathematics (see Note 10 ) 18

    Google Scholar 

  52. Neumann, J. von: The Computer and the Brain. Yale University Press: New Haven (1958)

    MATH  Google Scholar 

  53. Cf. Burks, A.W. (ed.): Essays on Cellular Automata. University of Illinois Press (1970); Myhill, J.: The abstract theory of self-reproduction. In: Mesarovic, M.D. (ed.): Views on General Systems Theory. John Wiley (1964) 106–118

    Google Scholar 

  54. Wolfram, S.: Universality and complexity in cellular automata. In: Farmer, D./Toffoli, T./Wolfram, S. (eds.): Cellular Automata. Proceedings of an Interdisciplinary Workshop. North-Holland: Amsterdam (1984) 1–35;

    Google Scholar 

  55. Wolfram, S.: Theory and Applications of Cellular Automata. World Scientific: Singapore (1986);

    MATH  Google Scholar 

  56. Demongeot, J./Golés, E./Tchuente, M. (eds.): Dynamical Systems and Cellular Automata. Academic Press: London (1985);

    Google Scholar 

  57. Poundstone, W: The Recursive Universe. Cosmic Complexity and the Limits of Scientific Knowledge. Oxford University Press: Oxford (1985)

    Google Scholar 

  58. Rosenblatt, F.: The perceptron: A probabilistic model for information storage and organization in the brain. Psychological Review 65 (1958) 386–408

    Article  MathSciNet  Google Scholar 

  59. Minsky, M./Papert, S.A.: Perceptrons. MIT Press: Cambridge MA (1969) (expanded edition 1988 )

    Google Scholar 

  60. Gorman, R.P./Sejnowski, T.J.: Analysis of hidden units in a layered network trained to classify sonar targets. Neural Networks 1 (1988) 75–89;

    Google Scholar 

  61. Churchland, PM.: A Neurocomputational Perspective. The Nature of Mind and the Structure of Science. MIT Press: Cambridge MA (1989)

    Google Scholar 

  62. Sejnowski, T.J./Rosenberg, C.R.: NETtalk: A parallel network that learns to read aloud. The Johns Hopkins University Electrical Engineering and Computer Science Technical Report IHU/EECS-86/01 (1986) 32; Cf.

    Google Scholar 

  63. Kinzel, W/Deker, U.: Der ganz andere Computer: Denken nach Menschenart. Bild der Wissenschaft 1 (1988) 43

    Google Scholar 

  64. Schöneburg, E./Hansen, N./Gawelczyk: Neuronale Netzwerke. Markt and Technik: München (1990) 176, 177

    Google Scholar 

  65. Rumelhart, D.E./Smolensky, P./McClelland, J.L./Hinton, G.E.: Schemata and sequential thought processes. In: McClelland, J.L./Rumelhart, D.E. (eds.): Parallel Distributed Processing: Explorations in the Microstructure of Cognition vol. 2: Applications. MIT Press: Cambridge MA (1986); Churchland, P.S.: Neurophilosophy. Toward a Unified Science of the Mind-Brain. MIT Press: Cambridge MA (1988) 465

    Google Scholar 

  66. Haken, H. (ed.): Neural and Synergetic Computers. Springer: Berlin (1988) 5–7

    MATH  Google Scholar 

  67. Haken, H.: Synergetics as a tool for the conceptualization and mathematization of cognition and behaviour — How far can we go? In: Haken, H./Stadler, M. (eds.): Synergetics of Cognition. Springer: Berlin (1990) 23–24

    Chapter  Google Scholar 

  68. For chapter 5.4 compare Mainzer, K.: Philosophical foundations of neurobionics. In: Bothe, H.W./Samii, M./Eckmiller, R. (eds.): Neurobionics. An Interdisciplinary Approach to Substitute Impaired Functions of the Human Nervous System. North-Holland: Amsterdam (1993) 31–47

    Google Scholar 

  69. Cf. Samii, M. (ed.): Peripheral Nerve Lesions. Springer: Berlin (1990)

    Google Scholar 

  70. Eckmiller, R. (ed.): Neurotechnologie-Report. Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie: Bonn (1995);

    Google Scholar 

  71. Stein, R.B./Peckham, P.H. (eds.): Neuroprostheses: Replacing Motor Function After Disease or Disability. Oxford University Press: New York (1991)

    Google Scholar 

  72. Cosman, E.R.: Computer-assisted technologies for neurosurgical procedures. In: Bothe, H.W./Samii, M./Eckmiller, R. (eds.): Neurobionics (see Note 46 ) 365

    Google Scholar 

  73. Foley, J.D./Dam, A. van: Fundamentals of Interactive Computer Graphics. Addison-Wesley: Amsterdam (1982); Foley, J.D.: Neuartige Schnittstellen zwischen Mensch und Computer. Spektrum des Wissenschaft 12 (1987)

    Google Scholar 

  74. Gibson, W: Neuromancer. Grafton: London (1986) 67

    Google Scholar 

  75. Putnam, H.: Reason, Truth and History. Cambridge University Press: Cambridge (1981) 6

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lehrstuhl für Philosophie und Wissenschaftstheorie, Universität Augsburg, Universitätsstrasse 10, D-86135, Augsburg, Deutschland

    Professor Dr. Klaus Mainzer

Authors
  1. Professor Dr. Klaus Mainzer
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Mainzer, K. (1996). Complex Systems and the Evolution of Artificial Intelligence. In: Thinking in Complexity. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03305-0_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-03305-0_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-03307-4

  • Online ISBN: 978-3-662-03305-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation