Icons and Symmetries

In this work, three case studies illustrate the principle of symmetry and the history and properties of some of the major concepts used in science. The relation between physical objects, models and icons is discussed in an attempt to clear up some of the so-called symmetry paradoxes.

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This book grew out of a short series of lectures on symmetry, aimed at a general scientific audience, given by the author at the Catholic University of Leuven, Belgium, in October 1989. Using only elementary mathematics, he discusses the subtle relation between physical object, models and icons, and explains some of the so-called "symmetry paradoxes". Each of the three chapters uses a case-study to show the development, through both historical and physical ideas, of how some of the major concepts of symmetry became established. The concept and importance of an icon are illustrated in the first two chapters: in Chapter 1 the origins and applications of symmetry are illustrated with the famous Orsted paradox of the interaction between the magnetic needle and the electric current. Chapter 2 deals with rotations and the way in which Hamilton tried to describe them by means of quaternions - this gives an insight into the symmetry properties of vectors, and shows the way in which tensors and spinors gradually moved into the picture. Chapter 3 illustrates the use of symmetry in the classification of energy levels in atoms and solids and discusses broken symmetry.