World Scientific
  • Search
Skip main navigation

Cookies Notification

We use cookies on this site to enhance your user experience. By continuing to browse the site, you consent to the use of our cookies. Learn More
×
Our website is made possible by displaying certain online content using javascript.
In order to view the full content, please disable your ad blocker or whitelist our website www.worldscientific.com.

System Upgrade on Tue, Oct 25th, 2022 at 2am (EDT)

Existing users will be able to log into the site and access content. However, E-commerce and registration of new users may not be available for up to 12 hours.
For online purchase, please visit us again. Contact us at [email protected] for any enquiries.
Special Issue: Hypercomputation, Physics and ComputationNo Access

THE MYTH OF 'THE MYTH OF HYPERCOMPUTATION'

    A myth has unfortunately arisen in connection with Martin Davis's rather aggressively titled paper "The Myth of Hypercomputation." The myth is that Davis is profoundly and decisively right therein, and that hypercomputation is indeed therefore a myth. We show herein that Davis is wrong: i.e., that it's a myth that hypercomputation is a myth. We begin by pointing out and putting to use an obvious fact about the adjective 'mythic.' (E.g., if it's a myth that ϕ (= if ϕ is mythic), where ϕ is some declarative statement, then ϕ is false.) These facts allow us to quickly prove that some of the propositions Davis can be charitably read as advancing are provably false, that some are vacuously true, and that the remainder are indeterminate. Since all that he advances falls into one of these categories, his project is an utter failure.

    References

    • M. Alan, Proceedings of the London Mathematical Society 45, 161 (1939). ISIGoogle Scholar
    • S. Bringsjord, Minds and Machines 11, 95 (2001). Crossref, ISIGoogle Scholar
    • S. Bringsjord and K. Arkoudas, Theoretical Computer Science 317, 167 (2004). Crossref, ISIGoogle Scholar
    • Bringsjord, S. & Arkoudas, K. (2006), On the provability, veracity, and AI-relevance of the church-turing thesis, in A. Olszewski, J. Wolenski & R. Janusz, eds, 'Church's Thesis After 70 Years', Ontos Verlag, Frankfurt, Germany, pp. 66–118. This book is in the series Mathematical Logic, edited by W. Pohlers, T. Scanlon, E. Schimmerling, R. Schindler, and H. Schwichtenberg. URL: , http://kryten.mm.rpi.edu/ct_bringsjord_arkoudas_final.pdf . Google Scholar
    • S. Bringsjord and N. S. Govindarajulu, International Journal of Unconventional Computing 6, 353 (2011), http://kryten.mm.rpi.edu/SB_NSG_CTTnotprovable_091510.pdf. ISIGoogle Scholar
    • S. Bringsjordet al., Applied Mathematics and Computation 176, 516 (2006). Crossref, ISIGoogle Scholar
    • S. Bringsjord and M. Zenzen, Minds and Machines 12, 241 (2002). Crossref, ISIGoogle Scholar
    • S.   Bringsjord and M.   Zenzen , Superminds: People Harness Hypercomputation, and More ( Kluwer Academic Publishers , Dordrecht, The Netherlands , 2003 ) . CrossrefGoogle Scholar
    • M. Burgin, Notes of the Russian Academy of Sciences 325(4), 654 (1986). Google Scholar
    • M.   Burgin and M.   Burgin , Super-recursive algorithms ( Springer , 2005 ) . Google Scholar
    • B. Copeland, Minds and Machines 12(2), 281 (2002). Crossref, ISIGoogle Scholar
    • M. Davis, Alan Turing: Life and Legacy of a Great Thinker, ed. C. Teuscher (Springer, Berlin, 2004) pp. 195–211. CrossrefGoogle Scholar
    • M. Davis, Applied Mathematics and Computation 178(1), 4 (2006). Crossref, ISIGoogle Scholar
    • M.   Davis , R.   Sigal and E.   Weyuker , Computability, Complexity, and Languages: Fundamentals of Theoretical Computer Science ( Academic Press , New York, NY , 1994 ) . Google Scholar
    • E. Eberbach, Theoretical Computer Science 383(2-3), 200 (2007). Crossref, ISIGoogle Scholar
    • E. Eberbach, International Journal of Approximate Reasoning 49(2), 316 (2008). Crossref, ISIGoogle Scholar
    • E. Eberbach and M. Burgin, Evolutionary Automata as Foundation of Evolutionary Computation: Larry Fogel Was Right, Proc. 2009 Congress on Evolutionary Computation CEC 2009 (2009) pp. 2149–2156. Google Scholar
    • M.   Garzon , Models of massive parallelism: analysis of cellular automata and neural networks ( Springer-Verlag , 1995 ) . CrossrefGoogle Scholar
    • M. Gold, Journal of Symbolic Logic 30(1), 28 (1965). CrossrefGoogle Scholar
    • M. Gold, Information and Control 10, 447 (1967). CrossrefGoogle Scholar
    • J. D. Hamkins and A. Lewis, Journal of Symbolic Logic 65(2), 567 (2000). Crossref, ISIGoogle Scholar
    • S.   Jain et al. , Systems that learn ( MIT press , 1999 ) . CrossrefGoogle Scholar
    • R.   Milner , Communicating and Mobile Systems: The π-Calculus ( Cambridge Univ Pr. , 1999 ) . Google Scholar
    • R. Milner, ACM Turing award lectures (ACM, 2007) p. 1991. CrossrefGoogle Scholar
    • T. Ord, Applied mathematics and computation 178(1), 143 (2006). Crossref, ISIGoogle Scholar
    • H. Putnam, Journal of Symbolic Logic 30(1), 49 (1965). CrossrefGoogle Scholar
    • Y.   Rao , An introduction to thermodynamics ( Universities Press , 2004 ) . Google Scholar
    • M. Schaller and K. Svozil, The European Physical Journal B-Condensed Matter and Complex Systems 69(2), 297 (2009). Crossref, ISIGoogle Scholar
    • H. Siegelmann, Science 268, 545 (1995). Crossref, ISIGoogle Scholar
    • H. Siegelmann and E. Sontag, Theoretical Computer Science 131, 331 (1994). Crossref, ISIGoogle Scholar
    • H. T.   Siegelmann , Neural Networks and Analog Computation: Beyond the Turing Limit ( Birkhäuser , Boston, MA , 1999 ) . CrossrefGoogle Scholar
    • P.   Smith , An Introduction to Gödel's Theorems ( Cambridge University Press , Cambridge, UK , 2007 ) . CrossrefGoogle Scholar
    • M.   Stannett , Industrial Hypercomputation , The Grand Challenge in Non-Classical Computation International Workshop , ed. S.   Stepney ( 2005 ) . Google Scholar
    • M. Stannett, Applied mathematics and computation 178(1), 8 (2006). Crossref, ISIGoogle Scholar
    • A.   Syropoulos , Hypercomputation: Computing Beyond the Church-Turing Barrier ( Springer-Verlag New York Inc. , 2008 ) . CrossrefGoogle Scholar
    • P. Wegner, Communications of the ACM 40(5), 91 (1997). ISIGoogle Scholar
    • Z. Xia, Annals of mathematics 135(3), 411 (1992). Crossref, ISIGoogle Scholar