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Symmetry and Broken Symmetry in Science, in Perception and in Art

In: The Dynamics of Ambiguity

Author

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  • Giuseppe Caglioti

    (CESNEF, Dipartimento di Ingegneria Nucleare Politecnico di Milano)

Abstract

Many structures possess elements of symmetry (mirror planes, rotation axes, inversion center, etc.). They are transformed into themselves as a result of symmetry operations such as a reflection on a plane, a rotation around an axis, an inversion with respect to a point. By definition, such symmetry operations, once made, preserve the original structure. Thus, if we set a ball revolving around its center or one of its diameters, or a glass around its axis, we have no way of knowing that the rotation has been made. That is, it is impossible to measure an absolute, angular coordinate: measuring in fact implies a reference for the angles such as a notch, for example, which cannot be marked on the ball’s surface or cut into the rim of the glass without at the same time breaking the rotational symmetry.

Suggested Citation

  • Giuseppe Caglioti, 1992. "Symmetry and Broken Symmetry in Science, in Perception and in Art," Springer Books, in: The Dynamics of Ambiguity, chapter 0, pages 55-70, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-58080-2_4
    DOI: 10.1007/978-3-642-58080-2_4
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