This week, math is on trial, and today's charge
is that mathematics fits the physical universe
far better than we might expect. Ideas that begin
in the human mind somehow, someway, describe
things far beyond it. Why should that be true?
Math often begins with someone exploring an idea
simply because it's interesting. or not doing
math to solve a practical problem. Yet again
and again, these ideas turn out to describe the
physical world with remarkable precision. We
can use equations to describe how planets move,
how light travels, how atoms behave, and how
the universe expands. It reaches inside things
too small for us to see, and across distances
too large for us to imagine. Isn't that amazing?
And the surprising part isn't simply that mathematics
is useful. We expect a tool designed for a particular
job to be useful. The surprising part is that
mathematical ideas developed without a physical
purpose often fit the universe anyway. In 1960,
a famous physicist, Eugene Wigner called this
the unreasonable effectiveness of mathematics
in the natural sciences. He was not surprised
that mathematics worked. What surprised him was
just how well it worked. I mean, why should the
universe have patterns that we can express mathematically?
And why should the human mind be able to discover
them? Math cannot answer these questions by itself,
but the fit between mathematics and the universe
is difficult to ignore. Well, when I think about
my life, I can move through my day focused on
the next problem that needs to be solved. And
when I do that, it's easy to treat the universe
as little more than just the background of my
life. But when I stop and consider that the same
mathematics that we explore in our minds can
describe galaxies and atoms and light and space,
it fills me with wonder. I do not know why we
can understand the universe this way, but the
fact that it can gives me a reason to pay attention.
Mathematics reminds me that the world is not
only something to study or to use. but it is
also something to notice, appreciate, and enjoy.
I find it deeply satisfying when math goes from
explanation to wonder. So on the charge of fitting
the universe with unreasonable effectiveness,
mathematics is guilty. Well, maybe today is the
day to pause from explaining something and simply
notice something that fills you with wonder and
joy.