Today, nature and multiplication. The University of
Houston's College of Engineering presents this series
about the machines that make our civilization run, and
the people whose ingenuity created them.

Something struck me yesterday in
the large sub-basement that once housed much of our
University Law Library before the flood of 2001. I paced
the area, and did the multiplications. The flood, it
turns out, had filled it with almost *20,000,000*
pounds of water.

That number seemed almost unimaginably large. We look at
it and think there must be some mistake. Nature
constantly catches us by surprise in the way it generates
huge numbers. I first saw that basement as a mere
fifty-two paces across. The capacity of a
*three-dimensional* volume sneaks up on us here,
as in any situation.

Since volume is the product of three numbers it comes out
larger than we expect. Anyone who first enters the Space
Shuttle mid-deck is struck by how small it is. But it
works because astronauts live in all three dimensions of
that space, not just on its floor.

It is through such multiplications that nature generates
vast numbers in small spaces. The bookshelf in front of
me holds sixteen books. Are they in the best order? How
many ways might I rearrange them? The answer is
*sixteen factorial* -- sixteen times fifteen times
fourteen, and so on down to one.

It comes to over *twenty trillion* arrangements.
The shelf next to it, with thirty-two books, now offers
roughly ten to the power thirty-five possible
arrangements. And that's only a few books on one shelf.
In our universe, made up as it is of atomic arrangements,
the number of things that can *happen* is infinite
by any conception of that word.

And we aren't done yet. For, by now, we all know about
the *butterfly effect*. We know that tiny
influences utterly alter large outcomes. And a butterfly
is, in fact, a Sherman tank of an influence compared with
the flutterings that *truly* influence outcomes.
Random molecular movements create infinite
rearrangements, any one of which is enough to redirect
human history.

The complexity of it all reminds me of a story I once
heard about Albert Einstein. He supposedly used the same
soap for washing and for shaving because to use two soaps
would add needless complication to his life. Einstein was
on to something there.

Nature surrounds us with her multiplications. The
terrible tyranny of large numbers wells out of every
cranny of our lives -- our basements and our bookshelves.
Even now, as I try to think of ways to dodge that
tyranny, I write with the help of a computer that's doing
nearly a billion operations per second.

It really does depend on how we hold things up to the
light. The Space Shuttle, which first seems far too small
to accommodate six people, becomes large enough just
because of those multiplications. The fact is that
there's more space there than we would've dreamt, just as
there's more *opportunity* here on Earth than any
of us can ever imagine. And that's where hope is
ubiquitous. It can be found even in that devastated
basement library.

I'm John Lienhard, at the University of Houston, where
we're interested in the way inventive minds work.

(Theme music)