Today, large numbers do some strange things. 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.
In the field of statistical
physics we talk about the tyranny of large numbers.
For example: If I flip a coin three times, I
wouldn't be surprised to get three heads. In fact I
will get three heads one out of eight times I try
it. But if I flip a coin a million times, I'm
virtually certain to get 50 percent heads and 50
percent tails. The larger the population, the more
consistently average its behavior. Large numbers
hold us in an iron hand.
That tyranny of large numbers turns up again in our
concept of beauty. Psychologists have shown that
the face which at first glance we call beautiful is
the most average face. That's the reason we can
seldom remember who Miss America was last year.
Here in Texas we have a state lottery. That's a
sophisticated means for increasing the tax burden
on people who aren't very swift with numbers -- and
it's a strong reason for being math literate.
To play, you choose six different numbers between
one and 50. If those numbers are drawn, you win
several million dollars. But since the Lottery
takes in far more money than it gives out -- since
the average prize is far less than the cost of
playing -- it's a bad bet. If I were going to play
the lottery, I'd simply pick the numbers 1, 2, 3,
4, 5, and 6. They're easy to remember and they're
just as likely as any other numbers to win.
But it's on the molecular level that large numbers
really take hold of us. The number of
sodium-chloride molecules in a grain of salt is
like a one followed by 19 zeros. If it had a trace
element in it -- say one part in a trillion -- that
grain of salt would still hold ten million
molecules of the trace alone.
Here's a way to think about those numbers: Seven
years ago, my body was made up of entirely
different molecules. The process of cellular death
and regeneration has gradually replaced me. That
vast number of old molecules has reacted, turned
into water and CO2, been
reprocessed by plants, and stirred back into the
biosphere. By now I'm all around you. I'm growing
in your window planter. I'm in your soup. You
breathe me out and I breathe you in.
You and I were made of so many molecules seven
years ago that we're everywhere on earth today. We
occupy almost every ounce of water, every puff of
air. I can't help but think, when I see people
making ceremony of scattering ashes, that the
cremated loved one is spreading through the
biosphere while those few inorganic fragments
represent almost nothing of She-who-was.
The perceived world is statistical tyranny.
Solidity is an illusion born of large numbers. So
is time. But come back a moment to that matter of
beauty being a statistical illusion. Thoreau called
beauty a moral test. In that he offers a way out
from under tyranny, a ray of hope. He reminds us
that we're still responsible for how we perceive
reality -- and what we do with it.
I'm John Lienhard, at the University of Houston,
where we're interested in the way inventive minds
work.
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