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The Devious Roads of Science

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Form and Strategy in Science

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Abstract

A mathematician of ancient Greece is credited with the saying “There are no Royal Roads in mathematics”. This is usually understood as meaning that it is impossible to understand the proof of a complicated theorem without having first understood the proofs of all preliminary theorems and lemmas that precede it. To put it differently, a person unfamiliar with geometry, cannot open a book on geometry in the middle and read with understanding, whatever is printed there. He has to read all the preliminaries.

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References

  1. Alfred J. Lotka, Elements of Physical Biology, Williams and Wilkins Co., Baltimore, 1925; reprinted under the title Elements of Mathematical Biology, Dover Publications, Inc., New York, 1956.

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  2. Vito Volterra, Leçons sur la Théorie mathématique de la Lutte pour la Vie, Gauthier-Villars, Paris, 1933.

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  3. J. H. Woodger, The Axiomatic Method in Biology, Cambridge University Press, Cambridge, London, 1937. See also his Biology and Language, Cambridge University Press, London, 1952.

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  4. H. Poincaré, Science et Méthode, E. Flammarion, Paris, 1909.

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  5. For a comprehensive summary of that work see N. Rashevsky’s Mathematical Biophysics Vol. I and II, third edition, Dover Publications, Inc., New York, 1960.

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  6. N. Rashevsky, ‘Topology and Life. In Search of General Mathematical Principles in Biology and Sociology’,The Bulletin of Mathematical Biophysics 16 (1954) 317–348; also a number of subsequent papers in the Bulletin. See also reference 5, Volume II.

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  7. R. Rosen, ‘The Representation of Biological Systems from the Standpoint of the Theory of Categories’, The Bulletin of Mathematical Biophysics 20 (1958) 317–341.

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Author information

Authors and Affiliations

  1. The University of Chicago, Chicago, Illinois, USA

    N. Rashevsky

Authors
  1. N. Rashevsky
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Editor information

Editors and Affiliations

  1. Duke University, Durham,N.C, USA

    John R. Gregg

  2. University of London, Middlesex Hospital Medical School, UK

    F. T. C. Harris

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© 1964 D. Reidel Publishing Company/Dordrecht-Holland

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Rashevsky, N. (1964). The Devious Roads of Science. In: Gregg, J.R., Harris, F.T.C. (eds) Form and Strategy in Science. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-3603-0_7

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  • DOI: https://doi.org/10.1007/978-94-010-3603-0_7

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-3605-4

  • Online ISBN: 978-94-010-3603-0

  • eBook Packages: Springer Book Archive

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