Today, we flip six heads in a row. The University
of Houston's College of Engineering presents this
series about the machines that make our
civilization run, and the people whose ingenuity
If you flip six coins in a
row, again and again, you can bet you'll get all
heads or all tails one time out of every thirty two
sets. A statistics instructor tells his class to
flip a coin a hundred times and to post the
sequence of results. Next day, he comes back and
identifies three students who cheated and just
wrote down the results they thought they'd
get. How does he know?
Real results show statistical clusters -
like a run of four tails. Students who're just
guessing don't dare write down four tails in a row.
It doesn't look random. Yet, in a hundred
flips you'd actually expect to get several runs of
Our lives are filled with cluster events like that.
I see three red Cadillacs at one intersection. One
day at work it seems that nothing I do can go
wrong. A basketball player sinks five
three-pointers in succession. I might go away
telling myself that everyone is buying red
Cadillacs, that I'm a superb worker, and that
center Olajuwon has become master of the
Of course none of those things is true. If we flip
coins, we do get four in a row, now and then. Atul
Gawande, writing for the New Yorker
magazine, asks us to think about cancer clusters.
We find six brain tumors in a single suburban
neighborhood and government investigators are
called in. Perhaps they find a high voltage power
line or a nearby waste dump. Maybe they find
nothing at all. The fact is that, with eighty or so
kinds of cancer, you can expect significant
outbreaks of at least one kind of cancer in, say,
2500 of the 5000 census tracts in California.
For the six people with tumors, and those who love
them, it's cold comfort to talk about statistical
clustering. But Gawande points to two kinds of
clustering. One is the close-contact of
occupational exposure. The other is the kind of
loose causal contact that may or may not be
involved with neighborhood clusters.
As early as 1775, a London physician found a huge
incidence of scrotal cancer among young chimney
sweeps. They'd been working naked because that made
it easier to get through a narrow chimney.
Carcinogenic coal dust worked into parts of the
body where it could linger. No statistical
clustering there! Nor can we shrug off the major
thyroid cancer epidemic downwind of the Chernobyl
But neighborhood clustering is something we expect
when there's no real threat at all. That's not to
say we can be casual about threats that do exist.
Those threats add up. But they contribute to cancer
in the peripatetic people who live for a while in
one place, then move on to be sick somewhere else.
Walking to a meeting the other day, I ran into four
friends I hadn't expected to see. Each buoyed me
with a smile and a good word. The meeting went
well. On the way back I saw only one friend coming,
and he turned off down another path as I drew near.
Good thing that didn't happen before the
meeting, now wasn't it!
I'm John Lienhard, at the University of Houston,
where we're interested in the way inventive minds