Why does nature make such persistent use of symmetry? Symmetry is
a very effective way to exploit successes, because it repeats the
same structures over and over again. Because of symmetry, a
structure that 'works' in its own right can be produced in bulk and
used as a reliable building block.
Symmetry is also a way to trace the development of organic forms
from an inorganic world. Early in evolution, the only structures
available were those that could arise spontaneously through purely
physical (or chemical) processes. Because the laws of physics
and chemistry are symmetric -- they are the same at all positions
in space and at all instants of time -- so are many of the
structures that arise from those laws.
Evolution then is built upon these structures to produce ever more
complex life forms. Any symmetries that led to useful organs or
functions were preserved, such as the multiple legs of a centipede
or the multiple vertebrae of the human backbone.
Virtually all living creatures have visible symmetries of form and
function. Every structure that is repeated -- such as our two
arms, but also our five toes on each foot and the many thousands of
hairs on our heads -- is an example of symmetry, or of a symmetry
that has been built on and slowly changed by evolution.
Pigs, polecats, and people are bilaterally symmetric -- their left
and right sides are (almost) mirror-images of each other. Starfish
have fivefold symmetry -- or tenfold, or nineteenfold, depending on
the species. Snail shells have spiral symmetry, and delphiniums
have five equally spaced petals.
Life is a production line, molded by genetics but driven by
dynamics. It is the result of a partnership between genetics and
dynamics -- biology and mathematics. Mathematics Awareness Week,
the last week of April, is a time to remember that we are not just
a collection of genes. All multi-celled creatures have a hidden
symmetry at the very core of their being.
Back to Math Awareness Week 1995
