Abstract
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).
Reprinted from Physics and Mathematics of the Nervous System, M. Conrad, W. Güttinger, Eds. Lecture Notes in Biomathematics 4. Berlin, Heidelberg, New York: Springer-Verlag, 1974, pp. 128–148.
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References
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.
Blair, E. (1932). On the intensity-time relations for stimulation by electric currents. Journal of General Physiology, 12, 709.
Brillouin, L. (1962). Science and information theory. New York: Academic.
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.
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.
Duda, R.O., & Hart, P.E. (1970). Experiment in scene analysis. In Proceedings of the First National Symposium on Industrial Robots, Chicago, April, 1970.
Eccles, J. C. (1973). The understanding of the brain. New York: McGraw-Hill.
Ghiselin, B. (Ed.). (1952). The creative process. Berkeley: University of California Press (Reprinted 1955 by Mentor Books, New York).
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.
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.
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, 291–304
Hadamard, J. (1945). The psychology of invention in the mathematical field. Princeton: Princeton University Press.
Handler, P. (Ed.). (1970). Biology and the future of man. New York: Oxford University Press. 360.
Harth, E. M., Csermely, T. J., Beek, B., & Lindsay, R. D. (1970). Brain function and neural dynamics. Journal of Theoretical Biology, 26, 93–120.
Hill, A. V. (1936). Excitation and accommodation in nerve. Proceedings of the Royal Society B of London, 19, 305.
Hubel, D. H., & Wiesel, T. N. (1968). Receptive fields and functional architecture of monkey striate cortex. Journal of Physiology, 195, 215–243.
Kauffman, S. A. (1969). Metabolic stability and epigenesis in randomly constructed nets. Journal of Theoretical Biology, 22, 437–467.
Keyes, R. W. (1970). Power dissipation in information processing. Science, 168, 796–801.
Landauer, R. (1961). Irreversibility and heat generation in the computing process. IBM Journal of Research and Development, 5, 183–191.
McCulloch, W. S., & Pitts, W. (1943). A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics, 5, 115–133.
Pattee, H. H. (1972). Physical problems of decision-making constraints. International Journal of Neuroscience, 3, 99–106.
Poincaré, H. (1913). Mathematical creation, from The Foundations of Science 1913, 1946. New York: Science Press
Polanyi, M. (1968). Life’s irreducible structure. Science, 160, 1308–1312.
Post, E. (1965). Selections from diary of E. Post. In M. Davis (Ed.), The undecidable (p. 420). Hewlett: Rowen Press.
Rashevsky, N. (1933). Outline of a physiomathematical theory of excitation and inhibition. Protoplasma, 20, 42–56.
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.
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.
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.
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.
von Neumann, J. (1958). The computer and the brain. New Haven: Yale University Press.
von Neumann, J. (1966). Theory of Self-Reproducing Automata. A.W. Burks (Ed.), Urbana: University of Illinois Press
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.
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.
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This work was supported in part by grant from National Aeronautics and Space Administration, No. NGR 33-015-002.
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Pattee, H.H. (2012). Discrete and Continuous Processes in Computers and Brains. In: LAWS, LANGUAGE and LIFE. Biosemiotics, vol 7. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5161-3_8
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