Symmetry and Physics

The concept of symmetry is as ancient as human civilization. How it was born will probably remain for ever a mystery. But early men must have been deeply impressed with the amazingly symmetrical structures in both the biological world (Fig. 1) and the physical world (Fig. 2). And of course, the bilateral symmetry of the human body could not have failed to inspire the creative instincts of early men. Out of such beginnings, it is easy to imagine, the concept of symmetry was abstracted, first perhaps subconsciously, later in more explicit forms. As civilization developed, symmetry gradually permeated into all areas of human activities: painting, sculpture, music, architecture, literature, etc. Figure 3 exhibits a poem written by the great poet of the Sung Dynasty, Su Dongpo (1036-1101), which consists of eight vertical lines of seven characters each, a standard Chinese poetic form. The poem is read vertically downwards, starting from the first column on the right, followed by the second column, and so forth. But it can also be read backwards, starting upwards from the bottom of the last (eighth) column, followed by the seventh column, etc. Both ways the poem reads beautifully, with correct meter and correct rhyme. The "Crab Canon" of J. S. Bach (1685-1750) is a violin duet