Black-Swan Event

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by Richard Crews
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Swans are white. ALL swans are white. If one ever were to see a black swan, it would be a very, very strange observation indeed. It would represent some really weird configuration of genetic or environmental factors.

An event which is so unusual that one really never expects to see it is termed a "black-swan event": a storm or earthquake or flood so severe that it is likely to occur only once in a several hundred years; a constellation of economic risk factors so unlikely that, realistically, it is never going to happen (such as the constellation that led to the spectacular collapse of Long-Term Capital Management in 1998); a genetic mutation that has less than a one-in-a-million chance of occurring; etc.

But the point is the "etc." That is the key. There are so many, many black-swan events that, in fact, one actually comes along now and then. A baby falls from a fifth-floor window and survives; a mother gives birth to octuplets and all eight survive and thrive; a man jubilantly fires his rifle into the air and the bullet kills his father two miles away. Really weird, really rare, really unlikely things do, in fact, sometimes happen. Black-swan events, unlikely (or "impossible") as they are, do sometimes happen.

It is very difficult, even for scientists, to be entirely sure how anything will turn out. Yogi Berra is credited with saying, "It is very tough to make predictions, especially about the future." Harry Truman said he wished he could find an economics adviser who only had one hand--he was so frustrated by their always saying, "On the other hand...."

Let's look at an example of this black-swan (or statistical outlier) phenomenon from medical practice. You are feeling well, but you go to your doctor for a routine health check. He or she, being a conscientious person (and also worried about the cost of malpractice insurance) doesn't want to miss anything and orders a battery of tests--say 100 different routine, screening blood tests (which is not unusual). Each of those tests has been standardized on thousands of normal people; for each test, there is a bell-shaped distribution curve: that means that most people have values for that blood test within a limited range. To understand how this standardization process works, let's look at measuring the heights of a lot of people. If you measure the heights of 1,000 people who are passing by on a busy city street, almost all of them are between 5-foot-3-inches and 6-foot-5-inches tall--not all, but most. The few who are outside this range are not necessarily sick or disabled in any way, but they are--by definition--"abnormal," that is, their heights do not fall into the "normal" range.

In medical tests, the usual definition of "normal" is "within two standard deviations of the mean." That means simply that 95% of people fall within the "normal" range.

When the results of the 100 blood tests your doctor orders come back, five of them (statistically) are "abnormal." So naturally (and "defensively" considering the cost of malpractice insurance) the thought goes, "We'd better check these out" with a battery of further tests that are specific to each of the physiological areas concerned. Again, the phantom hand of statistics strikes--several of these tests come back outside the "normal" range. In fact, we now have several tests suggestive of thyroid malfunction--or an imbalance of calcium metabolism, or heart incompetance, or something else.

Get the idea? You came in to the doctor's office feeling fine; you are, in fact, healthy. But a few hundred dollars worth of laboratory tests later, the doctor is hot on the trail of some hidden disease complex.

The result? The doctor starts you on some medication--something mild--just to be on the safe side. And has you come back for a follow-up visit in a month. At which time you have some minor side-effects from the medication: you are constipated--but there is a pill for that; you are having some difficulty falling asleep at night--but there is another pill for that. A few weeks later, a few more side-effects: some forgetfulness and mood swings; sometimes you feel tired out a lot, and even get quite depressed. Nothing serious, but perhaps you'd better have an evaluation with a psychiatrist--just to be on the safe side.

This essay started out to be about "black-swan events" and other statistical anomalies, and wound up being about "progressive" modern medical practice. I guess the moral is--it takes courage to "suffer the slings and arrows of outrageous fortune" but it is subtly foolhearty not to. Or perhaps the moral is merely--be careful what you try to write about.