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Animals as Mathematicians

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References

  1. Plutarch, Symposium, ref. Stevenson's Book of Quotations, fifth ed. (Cassell, 1946).

    Google Scholar 

  2. Bernstein, J., New Yorker, Oct. 19, 56; Oct. 26, 54 (1963).

  3. Freudenthal, H., Lincos. Design of a Language for Cosmic Intercourse, Part 1 (North Holland Publishing Co., Amsterdam, 1960).

  4. Hempelmann, W., Verh. deutsch. Zool. Ges., 228 (1913).

  5. Lichtenberg, G. C., (The Elder), Aphorismen (edit. by Leitzman), Deutsch. Literaturdenkmale 18 + 19 Jh (1902–08).

    Google Scholar 

  6. Köhler, O., Verh. deutsch Zool. Ges., 219 (1949).

  7. Hurrell, H. G., Atlanta, My Seal (William Kimber, London, 1962).

    Google Scholar 

  8. Hurwitz, H. M. B., Animal Behaviour, 11, 4, 449 (1963).

    Article  Google Scholar 

  9. Leppik, E. E., Amer. Nat., 87, 229 (1953).

    Article  Google Scholar 

  10. Kalmus, H., Denes, P., and Fry, D. B., Nature, 175, 1078 (1955).

    Article  ADS  CAS  Google Scholar 

  11. Russell, B., The Principles of Mathematics, 1 (Camb. Univ. Press, 1903).

    MATH  Google Scholar 

  12. Courant, R., and Robbins, H., What is Mathematics ? (Oxf. Univ. Press, 1943).

    MATH  Google Scholar 

  13. James, G., and James, R., Mathematical Dictionary (van Nostrand, N. Y., 1949).

    Google Scholar 

  14. Galton, F., Inquiries into Human Faculty and its Development (Dent, London, 1907).

    Google Scholar 

  15. Poincaré, H., “Mathematical Creation” (transl. by G. Bruce Halsted) in Foundations of Science (N.Y.: Science Press, 1913).

    MATH  Google Scholar 

  16. Hadamard, J., The Psychology of Invention in the Mathematical Field (Princeton Univ. Press, 1945).

    MATH  Google Scholar 

  17. Piaget, J., Inhelder, B., and Sceminska, A., The Child's Conception of Geometry (Routledge and Kegan Paul, 1960).

    Google Scholar 

  18. Piaget, J., and Inhelder, B., The Child's Conception of Space (Routledge and Kegan Paul, London, 1956).

    Google Scholar 

  19. Müller, F. M., Lectures on the Science of Language (Boyal Inst. Lectures) (Longmans Green, London, 1966).

    Google Scholar 

  20. Darcy Thompson, W., On Growth and Form, second ed. (Camb. Univ. Press, 1952).

    Google Scholar 

  21. Ratcliffe, F. N., Gray, F. J., and Greaves, T., Australian Termites (Melbourne, 1952).

    Google Scholar 

  22. Elias, H., Sci. Monthly, 70, 229 (1950).

    Google Scholar 

  23. Kalmus, H., and Mayer, A. E., Proc. Roy. Entomol. Soc. Lond., A, 16, 15 (1941).

    Google Scholar 

  24. Leppik, E. E., Acta Biotheoretica, 14, Fasc. 1/2, 1 (1961).

    Article  Google Scholar 

  25. Li, C. C., Population Genetics (Univ. Chicago Press, 1955).

    Google Scholar 

  26. Polya, G., Patterns of Plausible Inference. (Vol. II of Mathematics and Plausible Reasoning.) (Oxf. Univ. Press, 1954).

  27. Laplace, P. S., Essai philosophique sur les probabilités (1843). (Engl. transl. Dover Publ., N.Y., 1951.)

    MATH  Google Scholar 

  28. Kalmus, H., Biol. Generalis (Vienna), 11, 93 (1935).

    Google Scholar 

  29. Keynes, J. M., A Treatise on Probability (Macmillan, London, 1921).

    MATH  Google Scholar 

  30. Fisher, R. A., Sanktya, Calcutta, 18, 201 (Calcutta, 1957).

    Google Scholar 

  31. Jaynes, E. T., Microwave Lab. and Dept. Physics, M.L. No. 421. Stanford University, Calif. (1957).

  32. Kalmus, H., Physiologia Comp. et Oecol., 1, 127 (1948).

    Google Scholar 

  33. v. Holst, E., and Mittelstaedt, H., Naturwiss., 37, 464 (1950).

    Article  ADS  Google Scholar 

  34. Sherrington, C. S., The Integrative Action of the Nervous System (Constable, London, 1906).

    Google Scholar 

  35. Hassenstein, B., Naturwiss., 48, 207 (1961).

    Article  ADS  Google Scholar 

  36. Kalmus, H., Nature, 173, 657 (1954).

    Article  ADS  Google Scholar 

  37. Kalmus, H., Ann. Rev. Physiol., 26, 109 (1964).

    Article  CAS  Google Scholar 

  38. Blest, A. D., Behaviour, 16, 188 (1960).

    Article  Google Scholar 

  39. Jander, R., Ann. Rev. Entomol., 8, 95 (1963).

    Article  Google Scholar 

  40. Kalmus, H., Zeit. Tierpsychol., 2, 72 (1938).

    Article  Google Scholar 

  41. Vowles, D. M., J. Exp. Biol., 31, 341 (1954).

    Google Scholar 

  42. v. Frisch, K., and Lindauer, M., Naturwiss., 48, 581 (1961).

    Article  ADS  Google Scholar 

  43. Birukow, G., Cold Spring Harbor Symp., 25, 403 (1960).

    Article  Google Scholar 

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KALMUS, H. Animals as Mathematicians. Nature 202, 1156–1160 (1964). https://doi.org/10.1038/2021156a0

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