|Sunday, April 25, 2004|
Philosophy of Symmetry
THINK of what are considered to be some of the most beautiful things in the world: Undulating mountain ranges, the Taj, the Eiffel Tower, Dancing Shiva, Michelangelo’s David, or the face of someone you find irresistible. If you are musically inclined, then, perhaps, a haunting piece of music might come to your mind. And if you are a scientist or mathematician, you might find E=mc2 very beautiful.
Is there any common element in all these diverse beautiful things? Though it usually escapes our notice, it is the underlying symmetry, visual or abstract, that makes these things appealing to our senses. Unbeknown to us, we generally are uncomfortable with disorder, because it makes us uncertain, unsure and uncomfortable. But when we see a pattern in shapes and events, we find it attractive because it is very reassuring and helps us organise our world conceptually. German mathematician Hermann Weyl said through symmetry man always tried to perceive and create order, beauty and perfection. To put it simply, symmetry is the opposite of chaos.
Sundar Sarukkai, takes up this concept in his book Philosophy of Symmetry, and gives us an interesting overview of the role of symmetry in our world. Symmetry, the author says, offers a principle of individuation, allows us to perceive the unity and simplicity of objects. But symmetry loses its value when objects are too small or too diffused for composition there cannot be any unity in perception. Having an academic background of physics and philosophy of science, the author puts forward his thesis very clearly and precisely, although one must have at least post-gradate-level training in science or philosophy to appreciate the book.
The idea of symmetry is not culture specific, Sarukkai tells us, for we see it playing a significant role in the arts of both the Orient and the Occident. In Indian art, the Natyashastra is an excellent example which emphasises the use of symmetry in the representation of the body in sculpture and dance. The proportions of the human figure were also used in architecture, as seen in ancient temples.
But that is not all; the concept of symmetry extends to the sciences and mathematics albeit in a different way. If we take a circle and rotate it around its centre, we notice that it makes no difference to its shape. Hence, it is rotationally symmetrical. It can also be argued that the theory of relativity owes a lot to symmetry. Even Newtonian physics and quantum mechanics are based on fundamental principles of symmetry.
In one of the chapters we are told that external symmetries are important in studying composite systems like atoms and molecules. The movement of the electron around the nucleus of an atom possess rotational symmetry. This has important consequences in spectroscopy and in understanding molecular bonding.
"Beauty in science and art," sums up Sarukkai, "is a cause for a feeling of pleasure... beauty is indeed accepted as a scientific experience (and sometimes even as an ideal) but since it remains on the level of feeling, the difficulty of objectifying it in a manner suitable to scientists has led to a refusal to acknowledge aesthetic considerations as an element of scientific methodology."
The next time you go for a walk, take a keener look at the patterns surrounding you: the arrangement of leaves on a tree, the motifs of a well-designed building, or the reflections in water. A whole new world of beauty might open up for you.