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 created them.
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 four alike.
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 three-point shot.
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 reactor.
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 work.
Gawande, A., The Cancer-Cluster Myth. The New Yorker, Feb. 8, 1999, pp. 34-37.
I am grateful to Art Pollett for pointing out the Gawande article and providing me with a copy of it.