Hi, have you ever encountered an idea so beautiful
that you wanted it to be true? The ancient Greeks
were fascinated by a special group of three -dimensional
shapes that we now call the platonic solids.
These shapes are remarkable because every face
is the same regular shape, every edge has the
same length, and every corner is arranged. in
exactly the same way. A cube is one example.
Each of its six faces is an identical square.
Another is the tetrahedron. It's formed from
four identical triangles. There are also shapes
that are made from eight triangles, 20 triangles,
and 12 pentagons. And that is the complete list.
There are exactly five platonic solids. Not six,
not a hundred, only five. The ancient Greeks
found this deeply significant. And personally,
I find it pretty cool. These shapes seem to possess
a kind of mathematical perfection. Plato even
connected them to the structure of the physical
world. He associated four of the solids with
what were believed at that time as the basic
elements, earth, water, air, and fire. The fifth
was connected to the cosmos itself. That theory
was beautiful. Each fundamental part of nature
had its own perfect shape. Mathematics appeared
to reveal the hidden architecture of the universe.
Nearly 2 ,000 years later, the astronomer Johannes
Kepler was captivated by these same five shapes.
At the time, only six planets were known, and
Kepler noticed that five platonic solids could
be placed between six spheres, and he wondered
whether these shapes explained the distances
between the planets. He imagined one sphere representing
the orbit of a planet. Inside it, he placed a
platonic solid. Then he placed another sphere
inside that solid, followed by another solid,
and so on. It was an extraordinarily beautiful
model. But it was wrong. As measurements of the
planets became more accurate, the distances did
not fit Kepler's model. Now, I find Kepler's
story encouraging. because his mistake did not
make him a poor scientist. His desire to understand
the heavens eventually contributed to a much
greater discovery that the planets travel in
ellipses rather than perfect circles. Kepler
was willing to release a beautiful theory when
reality would not support it. But that can be
difficult. We are drawn to explanations that
feel, balanced, complete, and elegant. When all
the pieces fit neatly together, we experience
the satisfaction of seeing a pattern. But our
ability to find a pattern does not guarantee
that the pattern is true. Sometimes we discover
the hidden structure of reality. Other times,
we impose a structure because we want reality
to be simpler and more orderly than it is. Now,
this does not mean beauty should make us suspicious.
Beauty is often a valuable guide in mathematics
and science and art and faith. It awakens curiosity
and invites us to look more closely. But beauty
is an invitation to investigate, not permission
to stop asking questions. The platonic solids
really are beautiful. Kepler's model really was
imaginative. But reality was larger than the
beautiful shape he had created for it. Perhaps
humility means allowing reality to correct even
our favorite ideas. So, here is a challenging
question for you and for me. Are there ideas
that we are so passionate about that our passion
sometimes leads us astray? And to be honest,
that is a difficult lesson that I have had to
learn. Passion can inspire us to see possibilities
that others miss. But if we're not careful, it
can persuade us to see patterns that are not
really there. Humility allows us to remain passionate
while still giving reality the final word.