Discover
/
Article

A Continuous Model of Computation

MAY 01, 1999
Physicists should consider an alternative to the Turing‐machine model of computation.
Joseph F. Traub

A central dogma of computer science is that the Turing‐machine model is the appropriate abstraction of a digital computer. Physicists who’ve thought about the matter also seem to favor the Turing‐machine model. For example, Roger Penrose devoted some 60 pages of a book to a description of this abstract model of computation and its implications. I argue here that physicists should consider the real‐number model of computation as more appropriate and useful for scientific computation.

This article is only available in PDF format

References

  1. 1. R. Penrose, The Emperor’s New Mind, Oxford U. P., Oxford (1989).

  2. 2. A. M. Turing, Proc. London Math. Soc. 42, 230 (1937).https://doi.org/PLMTAL

  3. 3. J. F. Traub, G. W. Wasilkowski, H. Woźniakowski, Information‐Based Complexity, Academic Press, New York (1988).

  4. 4. J. F. Traub, A. G. Werschulz, Complexity and Information, Cambridge U. P., Cambridge, England (1998).

  5. 5. J. von Neumann, Collected Works, V. A. Taub, ed., Macmillan, New York (1963).

  6. 6. L. Blum, F. Cucker, M. Shub, S. Smale, Complexity and Real Computation, Springer‐Verlag, New York (1998).

  7. 7. A. G. Werschulz, The Computational Complexity of Differential and Integral Equations: An Information‐Based Approach, Oxford U. P., Oxford (1991).

  8. 8. A. S. Nemirovski, D. B. Yudin, Problem Complexity and Method Efficiency in Optimization, Wiley‐Interscience, New York (1983).

  9. 9. K. Sikorski, Optimal Solution of Nonlinear Equations, Oxford U. P., Oxford (1999).

  10. 10. E. Novak, Deterministic and Stochastic Error Bound in Numerical Analysis, Lecture Notes in Mathematics, No. 1349, Springer‐Verlag, New York (1988).

  11. 11. L. Plaskota, Noisy Information and Computational Complexity, Cambridge U. P., Cambridge, England (1996).

  12. 12. S. Paskov, J. F. Traub, J. Portfolio Management, 22, 113 (1995).

  13. 13. I. Sloan, H. Woźniakowski, J. Complexity 14, 1 (1998).https://doi.org/JOCOEH

  14. 14. A. Papageorgiou, J. F. Traub, Computers in Physics 11, 574 (1997).

  15. 15. B. Keister, Computers in Physics 10, 119 (1996).

  16. 16. G. W. Wasilkowski, H. Wozniakowski, J. Math. Phys. 37, 2071 (1996).https://doi.org/JMAPAQ

  17. 17. M. B. Pour‐El, J. I. Richards, Computability in Analysis and Physics, Springer‐Verlag, New York (1988).

  18. 18. A. G. Werschulz, Numer. Func. Anal. 9, 945 (1987).

More about the Authors

Joseph F. Traub. Columbia University, New York City.

Related content
/
Article
Figuring out how to communicate with the public can be overwhelming. Here’s some advice for getting started.
/
Article
Amid growing investment in planetary-scale climate intervention strategies that alter sunlight reflection, global communities deserve inclusive and accountable oversight of research.
/
Article
Although motivated by the fundamental exploration of the weirdness of the quantum world, the prizewinning experiments have led to a promising branch of quantum computing technology.
/
Article
As conventional lithium-ion battery technology approaches its theoretical limits, researchers are studying alternative architectures with solid electrolytes.
This Content Appeared In
pt-cover_1999_05.jpeg

Volume 52, Number 5

Get PT in your inbox

pt_newsletter_card_blue.png
PT The Week in Physics

A collection of PT's content from the previous week delivered every Monday.

pt_newsletter_card_darkblue.png
PT New Issue Alert

Be notified about the new issue with links to highlights and the full TOC.

pt_newsletter_card_pink.png
PT Webinars & White Papers

The latest webinars, white papers and other informational resources.

By signing up you agree to allow AIP to send you email newsletters. You further agree to our privacy policy and terms of service.