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The New God of Probability

As a society, we are becoming more sophisticated about the process we call reality. We accept (perhaps with some grumbling) that "there is a forty percent chance of rain this afternoon, dropping to twenty percent tonight." We put sunscreen on our bodies when we go to the beach, because we have been convinced (more or less) that it reduces our chances of contracting skin cancer. If we decide we cannot live without nicotine, we cross our fingers that we will not be among the X percent of smokers that develop lung cancer. And we breathe a little easier when we hear that our chances of being involved in an automobile accident have declined in recent years. In nearly every aspect of our lives, and mostly without realizing it, we have come to terms with the vast gray area of statistical probability.

Cause and effect are alive and well, but we are becoming increasingly aware of the complexity of what used to be known as the simple things in life. No longer do we take illness as punishment by God for some transgression that we must have perpetrated, but which we may not be able to identify precisely. Death may still be "God’s will," but we know that we can reduce our chances of dying prematurely by taking certain steps that have little apparent connection to our relationship with deity.

And those of us who attempt to learn the many, often interacting, "facts of life" come to some understanding of how the process works and what the basic rules are. When we read about a research study in which thirty percent of the people who took large daily doses of vitamin C had fewer colds over a winter than those who did not take the extra vitamin, we ask questions (at least in our own heads) about what other variables might have been operating—were the people in both groups otherwise comparable? Did they live in the same city? The same neighborhood? Did they eat the same foods? What were the differences in age between the groups? Was a placebo given to the control group? IF these questions cannot be answered satisfactorily, we might withhold our judgment, at least for the moment. Obviously, not everyone nurtures the same amount of skepticism in their day-to-day processing of information. And not always do even the most astute of us weigh information with such a fine scale. If we dislike someone who smokes, for example, we may be more apt to predict an early end for them than if we have an emotional stake in their survival.

The central point of all this is that black and white have become less and less important to us. We have become more aware of the vast continuum of shades of gray. Right and wrong are no longer so simple. The relatively few rules we have inherited from our ethnic and religious backgrounds have become obscured by the proliferation of influences on what we think and believe. Anyone who lives only by the Ten Commandments, and says that other than those, anything goes, is soon caught up in the sticky web of modern society. A posted speed limit may be 55 miles per hour, but if heavy traffic is moving at a fairly uniform 70 mph, one is exposing oneself and others to great danger by driving below the speed limit. We weigh the risk (i.e., the probability) of being caught by the highway patrol against the risk of causing an accident by making more impatient drivers find ways to get around us.

Just to live in a comfortable level of stress, we have to constantly re-evaluate circumstances at many levels. It never stops. In our busy lives, we estimate the chances that someone will be available for our phone call at this moment, and if our estimate seems low, we do something else and call later. Otherwise, our day would be filled with wasted time and frustration.

And we have little patience with those who insist that the world operates according to a few simple laws. If someone says "abortion is murder," and someone else says that "a woman has the right to make decisions about her own body," most of us accept the idea that both statements may be true, but neither by itself is a sufficient principle from which to make public policy decisions.

As a matter of fact, probability is the only means we have of coping with the complexity of modern life. The Ten Commandments may have been enough to guide the behavior of nomadic tribes three thousand years ago. Today, not even the millions of pages of legal code that regulate us to some degree can protect us from making mistakes.

Still we look for meaning in numbers, even when what is quantifiable is perhaps less important than another aspect that we have no numbers for. If we go out to buy a new digital camera, for example, it’s very tempting to pay more money for one that claims to have a sensor with six megapixels over one with but five megapixels. The quality of the optics, or the accuracy in reproducing colors, which neither manufacturer describes in numbers, may be far more important in the quality of the images than is the number of pixels.

Is it safer to plan a picnic when the chance of showers is twenty percent than when the chance is thirty percent? Does a thirty percent chance of rain mean that in every spot in the area, one’s chances of getting wet are thirty percent—or does it mean that there is a thirty percent chance of rain somewhere in the area during the same period?

Suppose I am taking a medication for high blood pressure, and I read that fifty-two thousand people have suffered heart attacks after taking that medication for five years. The number who has taken it without having a heart attack is a hundred times that. How do I translate that into a decision to stop taking it or to continue? There are just too many variables at work on us in our ordinary lives.

Statistics can be useful to the scientists who are concerned with large populations. A manufacturer that can reduce the number of rollover accidents in its vehicles by one percent if it changes this little part in the steering linkage might estimate that five hundred people will live through the next year, who otherwise might not. If I’m not one of the five hundred does it matter to me? Out of the million owners of that automobile model, am I one of the five hundred?

Ignoring such statistics and making our decisions on other things, such as the phase of the moon, leaves us just as open to the risks as one who carefully studies the numbers. Or, perhaps point oh five percent more. The new god of probability doesn’t care if we cross our fingers or not.

 

Donald Skiff, August 26, 1994, November 11, 2004

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