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Mathematical Symmetry Principles in the Scientific World View

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Philosophy of Mathematics Today

Part of the book series: Episteme ((EPIS,volume 22))

Abstract

The term symmetry is used in a very broad sense, not only as a mathematical notion, but as something bridging disciplines, cultures, sciences and arts. It is used as a general term similar to the categories in philosophy, a general umbrella, used in most sciences and arts, in any culture. The contributions to the present volume were discussed at a meeting hosted by Symmetrion — The Institute for Advanced Symmetry Studies, an institution which is striving to lend a certain generality to the activities it supports, in some sense similar to the role played by philosophy towards the sciences. Let the reader forgive the author for being inspired by the genius loci, and placing subjectively more emphasis on the role of symmetry among all other mathematical tools that generate philosophical problems.

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References

  • Chua, L. O. [1989] Symmetry principles in nonlinear circuits, Vol. I, p. 75, In: Darvas, G., Nagy, D., eds., Symmetry of Structure, Extended Abstracts, Budapest: ISIS-Symmetry, Vols. I–II, 656 pp.

    Google Scholar 

  • Darvas, G. [1987] Level theories in philosophy and physics — Exploring and interpreting the structure of matter, Vol. 5,Part 3, pp. 76–79, In: 8th International Congress of Logic, Methodology, and Philosophy of Science, Abstracts, Moscow: Nauka.

    Google Scholar 

  • Darvas, G. [1995] ISIS-Symmetry: Looking for truth and beauty, Symmetry: Culture and Science, 6,1, 9–17.

    MathSciNet  Google Scholar 

  • Darvas, G. [1996] Dichotomies and trichotomies in the Eastern and Western cultures, pp. 91–99, In: Ogawa, T., Miura, K., Masunari, T. and Nagy, D., eds., Katachi U Symmetry, Tokyo: Springer Verlag, xxiv + 417 pp.

    Google Scholar 

  • Darvas, G., Nagy, D. [1994] Wasan versus Western mathematics: Asymmetry of the brain and education, pp. 321–324, In: Ogawa, T., ed., Katachi U Symmetry, Extended Abstracts, Tsukuba: University of Tsukuba, xiv + 360 pp.

    Google Scholar 

  • Fidelman, U. [1990] Creative cerebral asymmetry, Symmetry: Culture and Science, 1,2,195–204.

    MathSciNet  Google Scholar 

  • Gortari, E. [1970] Symmetry as a scientific method, pp. 30–34, In: La symetrie. Comme principe heuristique dans les differentes sciences, Bruxelles: Office international de librairie, 135 pp.

    Google Scholar 

  • Hambidge, J. [1926] The Elements of Dynamic Symmetry, (reprinted by New York: Dover, 1967].

    Google Scholar 

  • Heisenberg, W. [1971] Physics and Beyond Encounters and Conversations, New York: Harper and Row Publ. Inc.

    Google Scholar 

  • Husimi, K. [1996] Symmetry in mon and mon-yô: Artisans preceded mathematicians, pp. 75–80, In: Ogawa, T., Miura, K., Masunari, T. and Nagy, D., eds., Katachi U Symmetry, Tokyo: Springer Verlag, xxiv + 417 pp.

    Google Scholar 

  • Mainzer, K. [1990] Symmetiy in philosophy and history of science, Symmetry: Culture and Science, 1,3, 319–328.

    MathSciNet  MATH  Google Scholar 

  • Maróth, M. [1989] Two ways of thinking in Greek and Arabic philosophy, Vol. II, pp. 357–358, In: Darvas, G., Nagy, D., eds., Symmetry of Structure, Extended Abstracts, Budapest: ISIS-Symmetry, Vols. I–II, 656 pp.

    Google Scholar 

  • Nagy, D. [1990] Manifesto on (dis)symmetry, with some preliminary symmetries, Symmetry: Culture and Science, 1,1, 3–26.

    MathSciNet  MATH  Google Scholar 

  • Nagy, D. [1994] Wasan and discrete geometry: From ethnomathematics and aesthetics to education and research, pp. 328–332, In: Ogawa, T., ed., Katachi U Symmetry, Extended Abstracts, Tsukuba: University of Tsukuba, xiv + 360 pp.

    Google Scholar 

  • Nagy, D. [1995] The 2,500-year old term symmetry in science and art and its ‘missing link’ between the antiquity and the modern age, Symmetry: Culture and Science, 6,1, 18–28.

    MathSciNet  MATH  Google Scholar 

  • Noether, E. A. [1918] Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen: Mathematisch-physikalische Klasse, 235.

    Google Scholar 

  • Rosen, J. [1995] Symmetry in Science, New York: Springer-Verlag, 213 pp.

    MATH  Google Scholar 

  • Roska, T. [1989] A dual way of computing — learning from cerebral asymmetry, Vol II, pp. 495–498, In: Darvas, G., Nagy, D., eds., Symmetry of Structure, Extended Abstracts, Budapest: ISIS-Symmetry, Vols. I–II, 656 pp.

    Google Scholar 

  • Thorn, R. [1983] Paraboles et catastrophes: Entretiens sur les mathématiques, la science et la philosophie, [Paraboles and Catastrophes: Discussions about Mathematics, Science and Philosophy, in French], Argenton-sur-Creuse: Flammarion.

    Google Scholar 

  • Trivedi, K. [1990] Symmetry in Hindu philosophy, Symmetry: Culture and Science, 1,4, 369–386.

    MathSciNet  Google Scholar 

  • Vicsek, M. and Vicsek, T. [1993] Fractals (guest editorial of Special issue), Symmetry: Culture and Science, 4,3, 227–228.

    Google Scholar 

  • Vitruvius, Ten Books on Architecture, [De architectura libri decern, in Latin], 1st c. B.C.

    Google Scholar 

  • Weyl, H. [1929] Zeitschrift für Physik, 56, 330.

    Google Scholar 

  • Wigner E. P. [1931] Gruppentheorie und ihre Anwendung auf die Quantenmechanik der Atomspektren, Braunschweig: Friedrich Vieweg, [Engl, transi.: Group Theory and Its Application in the Quantum Mechanics of Atomic Spectra, New York: Academic Press, 1959].

    MATH  Google Scholar 

  • Wigner, E. P. [1949] Invariance in physical theory, Proceedings of the American Philosophical Society, 93,7, 521–526.

    Google Scholar 

  • Wigner, E. P. [1954] Process in Theoretical Physics, 11, 437.

    Google Scholar 

  • Wigner, E. P. [1960] The unreasonable effectiveness of mathematics in the natural sciences, Communications in Pure and Applied Mathematics, 13,1 (Reprinted In: Symmetries and Reflections, Bloomington: Indiana University Press, 1967).

    Google Scholar 

  • Wigner, E. P. [1964] Symmetry and conservation laws, Proceedings of the National Academy of Sciences, 51,5, 956–965.

    Google Scholar 

  • Yang, C. N. [1962] Elementary Particles, Princeton: University Press, p. 59.

    Google Scholar 

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Darvas, G. (1997). Mathematical Symmetry Principles in the Scientific World View. In: Agazzi, E., Darvas, G. (eds) Philosophy of Mathematics Today. Episteme, vol 22. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5690-5_19

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  • DOI: https://doi.org/10.1007/978-94-011-5690-5_19

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