Discrete and Continuous Processes in Computers and Brains

  • Howard Hunt Pattee
Part of the Biosemiotics book series (BSEM, volume 7)


Theories of computation and theories of the brain have close historical interrelations, the best-known examples being Turing’s introspective use of the brain’s operation as a model for his idealized computing machine (Turing 1936), McCulloch’s and Pitts’ use of ideal switching elements to model the brain (McCulloch and Pitts 1943), and von Neumann’s comparison of the logic and physics of both brains and computers (von Neumann 1958).


Switching Behavior Switching Function Discrete Mode Slow Manifold Continuous Dynamic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was supported in part by grant from National Aeronautics and Space Administration, No. NGR 33-015-002.


  1. Anninos, P. A., Beek, B., Csermely, T. J., Harth, E. M., & Pertile, G. (1970). Dynamics of neural structures. Journal of Theoretical Biology, 25, 121–148.CrossRefGoogle Scholar
  2. Blair, E. (1932). On the intensity-time relations for stimulation by electric currents. Journal of General Physiology, 12, 709.CrossRefGoogle Scholar
  3. Brillouin, L. (1962). Science and information theory. New York: Academic.Google Scholar
  4. Conrad, M. (1974). Molecular information processing in the central nervous system. Part I, selection circuits in the brain. In M. Conrad & W. Guttinger (Eds.), Physics and mathematics of the nervous system. Lecture notes in biomathematics 4 (pp. 82–107). Berlin/Heidelberg/New York: Springer.Google Scholar
  5. Cowan, J. D. (1973). Stochastic models of neuroelectric activity. In C. H. Waddington (Ed.), Towards a theoretical biology (Vol. 4, pp. 169–188). Edinburgh: University of Edinburgh Press.Google Scholar
  6. Duda, R.O., & Hart, P.E. (1970). Experiment in scene analysis. In Proceedings of the First National Symposium on Industrial Robots, Chicago, April, 1970.Google Scholar
  7. Eccles, J. C. (1973). The understanding of the brain. New York: McGraw-Hill.Google Scholar
  8. Ghiselin, B. (Ed.). (1952). The creative process. Berkeley: University of California Press (Reprinted 1955 by Mentor Books, New York).Google Scholar
  9. Gödel, K. (1964). On formally undecidable propositions of the Principia Mathematica and related systems. In M. Davis (Ed.), The Undecidable (pp. 4–38). Hewlett: Rowen Press.Google Scholar
  10. Griffith, J.S. (1963). A field theory of neural nets: I. Derivation of field equations, Bulletin of Mathematical Biophysics, 25, 111; II. Properties of field equations, Bulletin of Mathematical Biophysics, 27, 187.Google Scholar
  11. Guzman, A. (1968). Decomposition of a visual scene into three dimensional bodies. In Proceeding of the Fall Joint Computer Conference, Washington DC: IEEE Computer Society Press, 291–304Google Scholar
  12. Hadamard, J. (1945). The psychology of invention in the mathematical field. Princeton: Princeton University Press.Google Scholar
  13. Handler, P. (Ed.). (1970). Biology and the future of man. New York: Oxford University Press. 360.Google Scholar
  14. Harth, E. M., Csermely, T. J., Beek, B., & Lindsay, R. D. (1970). Brain function and neural dynamics. Journal of Theoretical Biology, 26, 93–120.PubMedCrossRefGoogle Scholar
  15. Hill, A. V. (1936). Excitation and accommodation in nerve. Proceedings of the Royal Society B of London, 19, 305.CrossRefGoogle Scholar
  16. Hubel, D. H., & Wiesel, T. N. (1968). Receptive fields and functional architecture of monkey striate cortex. Journal of Physiology, 195, 215–243.PubMedGoogle Scholar
  17. Kauffman, S. A. (1969). Metabolic stability and epigenesis in randomly constructed nets. Journal of Theoretical Biology, 22, 437–467.PubMedCrossRefGoogle Scholar
  18. Keyes, R. W. (1970). Power dissipation in information processing. Science, 168, 796–801.PubMedCrossRefGoogle Scholar
  19. Landauer, R. (1961). Irreversibility and heat generation in the computing process. IBM Journal of Research and Development, 5, 183–191.CrossRefGoogle Scholar
  20. McCulloch, W. S., & Pitts, W. (1943). A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics, 5, 115–133.CrossRefGoogle Scholar
  21. Pattee, H. H. (1972). Physical problems of decision-making constraints. International Journal of Neuroscience, 3, 99–106.PubMedCrossRefGoogle Scholar
  22. Poincaré, H. (1913). Mathematical creation, from The Foundations of Science 1913, 1946. New York: Science PressGoogle Scholar
  23. Polanyi, M. (1968). Life’s irreducible structure. Science, 160, 1308–1312.PubMedCrossRefGoogle Scholar
  24. Post, E. (1965). Selections from diary of E. Post. In M. Davis (Ed.), The undecidable (p. 420). Hewlett: Rowen Press.Google Scholar
  25. Rashevsky, N. (1933). Outline of a physiomathematical theory of excitation and inhibition. Protoplasma, 20, 42–56.CrossRefGoogle Scholar
  26. Rosen, R. (1969). Hierarchical organization in automata theoretical models of the nervous system. In K. N. Leibovic (Ed.), Information processing in the nervous system (pp. 21–35). New York: Springer.Google Scholar
  27. Sperry, R. W. (1970). Cerebral dominance in perception. In A. Y. Francis et al. (Eds.), Early experience in information processing in perceptual and reading disorders. Washington, DC: National Academy of Sciences.Google Scholar
  28. Thom, R. (1970). Topological models in biology. In C. H. Waddington (Ed.), Towards a theoretical biology (Vol. 3, pp. 89–116). Edinburgh: Edinburgh University Press.Google Scholar
  29. Turing, A.M. (1936). On computable numbers with an application to the Entscheidungs problem. In Proceedings of the London Mathematical Society, Series 2, 42, 230–265.Google Scholar
  30. von Neumann, J. (1958). The computer and the brain. New Haven: Yale University Press.Google Scholar
  31. von Neumann, J. (1966). Theory of Self-Reproducing Automata. A.W. Burks (Ed.), Urbana: University of Illinois PressGoogle Scholar
  32. Zeeman, E. C. (1972a). Differential equations for the heartbeat and nerve impulse. In C. H. Waddington (Ed.), Towards a theoretical biology (Vol. 4, pp. 8–67). Edinburgh: Edinburgh University Press.Google Scholar
  33. Zeeman, E. C. (1972b). Appendix: A catastrophe machine. In C. H. Waddington (Ed.), Towards a theoretical biology (Vol. 4, pp. 276–282). Edinburgh: Edinburgh University Press.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • Howard Hunt Pattee
    • 1
  1. 1.Binghamton UniversityVestalUSA

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