Hyatt, why do we find symmetry so beautiful?
We see it in the wings of a butterfly, in the
petals of a flower, and the intricate design
of a snowflake. We use symmetry in architecture,
in artwork, company logos, and the patterns woven
into clothing. Even the human face has a general
symmetry to it. One eye balances the other. One
side of the smile reflects the other. Something
about that balance captures our attention. But
in mathematics, symmetry means more than having
two sides that look alike. Symmetry is about
what remains unchanged when something is transformed.
Imagine a square. Rotate it one quarter of a
turn, and it still looks like the same square.
Rotate it again and again. Its appearance remains
unchanged. The square has moved, but something
about it has been preserved. A circle has even
more symmetry. You can rotate it by any amount,
and it still looks exactly the same. There is
no single direction that the circle prefers.
Mathematicians study symmetry by asking a surprisingly
simple question. What can we do to this object
without changing what it fundamentally is? We
might rotate it, reflect it, move it. Sometimes
we can even stretch it. The object undergoes
a transformation, but some important things remain
constant. And this is one of the reasons symmetry
is important. Scientists use it to study crystals,
molecules, and the fundamental laws of nature.
Engineers use it when designing buildings and
machines. Artists and musicians use patterns
of repetition and variation to create a sense
of order. Symmetry helps us recognize structure
within change. And I think that question extends
far beyond math. Our lives are filled with transformations.
We grow older. Our bodies change. Our relationships
change. We move into new homes or begin new careers
or take on new responsibilities. Experiences
reshape the way we see ourselves and the world.
Sometimes these changes are chosen and sometimes
they happen to us. But transformation does not
necessarily mean everything has been lost. Like
a square being rotated, our orientation may change
while something important remains. Perhaps our
deepest values remain. Perhaps it is our love
for particular people. Perhaps it is a faith
that continues to hold us even as our understanding
of that faith grows and changes. Do not confuse
Beauty with perfection. Beauty does not require
perfect symmetry. Sometimes beauty is found in
recognizing a deeper coherence, the thread that
continues through all the changes, joys, disappointments,
and unexpected turns. Mathematical symmetry teaches
us to look for what is preserved during a transformation.
So as you consider the changes that are taking
place in your life, a question to start with
is identifying what is changing. And then a follow
-up question is that beneath all those changes,
what do you hope will remain the same?