Advertisement

Cognitive Computation

, Volume 4, Issue 3, pp 236–245 | Cite as

A Computability Argument Against Superintelligence

  • Jiří WiedermannEmail author
Article
First Online:

Abstract

Using the contemporary view of computing exemplified by recent models and results from non-uniform complexity theory, we investigate the computational power of cognitive systems. We show that in accordance with the so-called extended Turing machine paradigm such systems can be modelled as non-uniform evolving interactive systems whose computational power surpasses that of the classical Turing machines. Our results show that there is an infinite hierarchy of cognitive systems. Within this hierarchy, there are systems achieving and surpassing the human intelligence level. Any intelligence level surpassing the human intelligence is called the superintelligence level. We will argue that, formally, from a computation viewpoint the human-level intelligence is upper-bounded by the \(\Upsigma_2\) class of the Arithmetical Hierarchy. In this class, there are problems whose complexity grows faster than any computable function and, therefore, not even exponential growth of computational power can help in solving such problems, or reach the level of superintelligence.

Keywords

Cognitive systems Intelligence Extended Turing machine thesis Singularity Superintelligence 
This is a preview of subscription content, log in to check access.

Notes

Acknowledgments

This research was carried out within the institutional research plan AV0Z10300504 and partially supported by a GA ČR grant No. P202/10/1333

References

  1. 1.
    Balcázar JL, Diáz J, Gábarró J. Structural complexity, Vol. I, 2nd ed. Berlin: Springer; 1995.CrossRefGoogle Scholar
  2. 2.
    Bernstain E, Vazirani U. Quantum complexity theory. In: Proceeding of the 25th annual symposium on the theory of computing. New York: ACM; 1993. p. 11–20.Google Scholar
  3. 3.
    Blum M. Can (theoretical computer) science come to grips with consciousness? Invited talk at FOCS 2009, 2009.Google Scholar
  4. 4.
    Chalmers DJ. A computational foundation for the study of cognition. Minds Mach. 1994;4(4).Google Scholar
  5. 5.
    Chalmers DJ. The singularity: a philosophical analysis, 2009, cf. http://consc.net/papers/singularity.pdf.
  6. 6.
    Cooper SB. Computability theory. London: Chapman & Hall/CRC; 2004.Google Scholar
  7. 7.
    Cooper SB. From descartes to Turing: the computational content of supervenience. In: Burgin M, Dodig-Crnkovic G, editors. Information and computation. Singapore: World Scientific Publishing Co; 2011. p. 107–48.Google Scholar
  8. 8.
    Deutsch D. Quantum theory, the Church-Turing principle and the universal quantum computer. Proc R Soc Lond A 1985;400:97–117.CrossRefGoogle Scholar
  9. 9.
    Étesi G, Nésmeti I. Non-Turing computations via Malament–Hogarth space-times. Int. J. Theor. Phys. 2002;41:341–70.CrossRefGoogle Scholar
  10. 10.
    Goertzel B. Artificial general intelligence: now is the time. Published on KurzweilAI.net, April 9, 2007.Google Scholar
  11. 11.
    Goldin DQ, Smolka SA, Attie PC, Sonderegger E. Turing machines, transition systems, and interaction. Inf Comput 2004;194(2):101–28.CrossRefGoogle Scholar
  12. 12.
    Green MW. A lower bound on Rado’s sigma function for binary Turing machines. In: Proceedings of the IEEE 5th annual symposium on switching circuits theory and logical design; 1964. p. 91–4Google Scholar
  13. 13.
    Hopcroft J, Motwani R, Ullman JD. Introduction to automata theory, languages and computation, 2nd ed. Reading: Addison-Wesley; 2000.Google Scholar
  14. 14.
    Karp RM, Lipton RJ. Some connections between non-uniform and uniform complexity classes. In: Proceeding 12th annual ACM symposium on the theory of computing (STOC’80); 1980. p. 302–9.Google Scholar
  15. 15.
    Karp RM, Lipton R. Turing machines that take advice, L’Enseignement Mathématique, IIe Série, Tome XXVIII; 1982. p. 191–209.Google Scholar
  16. 16.
  17. 17.
    Kurzweil, R.: The singularity is near. New York: Viking Books; 2005. p. 652.Google Scholar
  18. 18.
    Levin LA. Universal sequential search problems. Probl Inf Transm 1973;9(3):265–66.Google Scholar
  19. 19.
    Lloyd S. Ultimate physical limits to computation. Nature 2000;406(6799):1047–54.PubMedCrossRefGoogle Scholar
  20. 20.
    Lloyd S. How fast, how small, and how powerful: Moor’s law and the ultimate laptop. In: Rebooting civilization, http://www.edge.org/3rd_culture/rebooting/rebooting.html, 2001.
  21. 21.
    Michel P. Historical survey of busy beavers, http://www.logique.jussieu.fr/michel/ha.html#tm62.
  22. 22.
    Penrose R. Shadows of the mind (a search for the missing science of consciousness). Oxford: Oxford University Press; 1994. p. 457Google Scholar
  23. 23.
    Shettleworth S. Cognition, evolution, and behavior. Oxford: Oxford University Press; 1998.Google Scholar
  24. 24.
    Turing AM. On computable numbers, with an application to the Entscheidungsproblem. Proc London Math Soc. 1936;42-2:230–65. A correction, ibid. 1937;43:544–46.Google Scholar
  25. 25.
    Turing AM. Systems of logic based on ordinals. Proc Lond Math Soc Ser 2, 1939;45:161–228.CrossRefGoogle Scholar
  26. 26.
    van Leeuwen J, Wiedermann J. The Turing machine paradigm in contemporary computing. In: Enquist B, Schmidt W, editors, Mathematics unlimited—2001 and beyond. Berlin: Springer; 2001. p. 1139–55.CrossRefGoogle Scholar
  27. 27.
    van Leeuwen J, Wiedermann J. Beyond the Turing limit: evolving interactive systems. In: Proceeding SOFSEM’01, LNCS Vol. 2234. Berlin: Springer; 2001. p. 90–109.Google Scholar
  28. 28.
    van Leeuwen J, Wiedermann J. A theory of interactive computation. In: Goldin D, Smolka SA, Wegner P, editors. Interactive computation: the new paradigm. Berlin: Springer; 2006. p. 119–42.CrossRefGoogle Scholar
  29. 29.
    van Leeuwen J, Wiedermann J. Computation as unbounded process. Theoretical computer science; 2012. doi: 10.1016/j.tcs2011.12.049.
  30. 30.
    Verbaan PRA, van Leeuwen J, Wiedermann J. Complexity of evolving interactive systems. In: Karhumäki J et al editors, Theory is forever, essays dedicated to arto Salomaa on the occasion of his 70th birthday. LNCS Vol. 3113. Berlin: Springer; 2004, p. 268–81.Google Scholar
  31. 31.
    Verbaan PRA. The computational complexity of evolving systems, Ph.D. Thesis, Dept. of Information and Computing Sciences, Utrecht University; 2006.Google Scholar
  32. 32.
    Wiedermann J, van Leeuwen J. The emergent computational potential of evolving artificial living systems. Ai Commun 2002;15(4):205–16.Google Scholar
  33. 33.
    Wiedermann J, van Leeuwen J. Relativistic computers and non-uniform complexity theory. In: Unconvential models of computation (UMC’2002), LNCS Vol. 2509. Berlin: Springer; 2002, p. 287–99.Google Scholar
  34. 34.
    Wiedermann J, van Leeuwen J. How we think of computing today. (invited talk). In: Proceeding CiE 2008, LNCS 5028. Berlin: Springer; 2008. p. 579–93.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Institute of Computer ScienceAcademy of Sciences of the Czech RepublicPragueCzech Republic

Personalised recommendations

Cite article

Buy options