Anecdotes aren’t data: That’s a favorite expression of scientists. Anecdotes—stories—may be illuminating in the manner of Shakespeare. They may also alert us to something that needs scientific investigation. The proliferating stories of breast implants causing disease were certainly grounds for concern and aggressive research. But anecdotes don’t prove anything. Only data—properly collected and analyzed—can do that.
This has always been true, but the advance of science and technology has made it all the more important. We can now measure in microns and light-years and detect in parts per billion. Information and numbers are piling up. To really understand this proliferating information, we must do much more than tell stories.
Unfortunately, what isn’t increasing is Gut’s skill in handling numbers. Shaped in a world of campfires and flint spears, our intuition is as innately lousy with numbers as it is good with stories. Stanislas Dehaene, a neuroscientist at the Collège de France, notes that animals as varied as dolphins and rats have a very basic grasp of numbers. They can easily tell the difference between two and four and they “have elementary addition and subtraction abilities.” But as the numbers go up, their abilities go down rapidly. Even numbers as low as six and seven require more time and effort to grasp and use than one or two.
It turns out humans’ innate skill with numbers isn’t much better than that of rats and dolphins. “We are systematically slower to compute, say, 4 + 5 than 2 + 3,” writes Dehaene. And just as animals have to slow down and think to discriminate between close quantities such as 7 and 8, “it takes us longer to decide that 9 is larger than 8 than to make the same decision for 9 versus 2.” Of course humans also have the capacity to move beyond this stage, but the struggle every schoolchild has learning the multiplication tables is a reminder of the limits of our natural grasp of numbers. “Sadly enough, innumeracy may be our normal human condition,” writes Dehaene, “and it takes considerable effort to become numerate.”
How many of us make that effort isn’t clear. A Canadian polling company once asked people how many millions there are in a billion. Forty-five percent didn’t know. So how will they react when they’re told that the arsenic levels in their drinking water are three parts per billion? Even an informed layperson will have to gather more information and think hard to make sense of that information. But those who don’t know what a billion is can only look to Gut for an answer, and Gut doesn’t have a clue what a billion is. Gut does, however, know that arsenic is a Bad Thing: Press the panic button.
The influence of our ancestral environment is not limited to the strictly innumerate, however. Physicist Herbert York once explained that the reason he designed the nuclear warhead of the Atlas rocket to be one megaton was that one megaton is a particularly round number. “Thus the actual physical size of the first Atlas warhead and the number of people it would kill were determined by the fact that human beings have two hands with five fingers each and therefore count by tens.”
Numeracy also fails to give numbers the power to make us feel. Charities long ago learned that appeals to help one identifiable person are far more compelling than references to large numbers of people in need. “If I look at the mass, I will never act,” wrote Mother Teresa. “If I look at the one, I will.” The impotence of numbers is underscored by our reactions to death. If the death of one is a tragedy, the death of a thousand should be a thousand times worse, but our feelings simply do not work that way. In the early years of the 1980s, reporting on AIDS was sparse despite the steadily growing number of victims. That changed in July 1985, when the number of newspaper articles on AIDS published in the United States soared by 500 percent. The event that changed everything was Rock Hudson’s announcement that he had AIDS: His familiar face did what no statistic could. “The death of one man is a tragedy, the deaths of millions is a statistic,” said that expert on death, Joseph Stalin.
Numbers may even hinder the emotions brought out by the presence of one, suffering person. Paul Slovic, Deborah Small, and George Loewenstein set up an experiment in which people were asked to donate to African relief. One appeal featured a statistical overview of the crisis, another profiled a seven-year-old girl, and a third provided both the profile and the statistics. Not surprisingly, the profile generated much more giving than the statistics alone, but it also did better than the combined profile-and-statistics pitch— as if the numbers somehow interfered with the empathetic urge to help generated by the profile of the little girl.
Of course, big numbers can impress, which is why activists and politicians are so keen on using them. But big numbers impress by size alone, not by human connection. Imagine standing at midfield of a stadium filled with 30,000 people. Impressive? Certainly. That’s a lot of people. Now imagine the same scenario but with 90,000 people. Again, it’s impressive, but it’s not three times more impressive, because our feelings aren’t calibrated to that scale. The first number is big. The second number is big. That’s the best Gut can do.
A curious side effect of our inability to feel large numbers—confirmed in many experiments—is that proportions can influence our thoughts more than simple numbers. When Paul Slovic asked groups of students to indicate, on a scale from 0 to 20, to what degree they would support the purchase of airport safety equipment, he found they expressed much stronger support when told that the equipment could be expected to save 98 percent of 150 lives than when they were told it would save 150 lives. Even saving “85 percent of 150 lives” garnered more support than saving 150 lives. The explanation lies in the lack of feeling we have for the number 150. It’s vaguely good, because it represents people’s lives, but it’s abstract. We can’t picture 150 lives and so we don’t feel 150 lives. We can feel proportions, however. Ninety-eight percent is almost all. It’s a cup filled nearly to overflowing. And so we find saving 98 percent of 150 lives more compelling than saving 150 lives.
Daniel Kahneman and Amos Tversky underscored the impotence of statistics in a variation of the famous “Linda” experiment. First, people were asked to read a profile of a man that detailed his personality and habits. Then they were told that this man was drawn from a group that consisted of seventy engineers and thirty lawyers. Now, the researchers asked, based on everything you know, is it more likely this man is a lawyer or an engineer? Kahneman and Tversky ran many variations of this experiment and in every one, the statistics—seventy engineers, thirty lawyers—mattered less than the profile.
Statistical concepts may be even less influential than numbers. Kahneman once discovered that an Israeli flight instructor had concluded, based on personal experience, that criticism improves performance while praise reduces it. How had he come to this strange conclusion? When student pilots made particularly good landings, he praised them—and their subsequent landings were usually not as good. But when they made particularly bad landings, he criticized them—and the subsequent landings got better. Therefore, he concluded, criticism works but praise doesn’t. What this intelligent, educated man had failed to account for, Kahneman noted, was “regression to the mean”: If an unusual result happens, it is likely to be followed by a result closer to the statistical average. So a particularly good landing is likely to be followed by a landing that’s not as good, and a particularly bad landing is likely to be improved on next time. Criticism and praise have nothing to do with the change. It’s just numbers. But because we have no intuitive sense of regression to the mean, it takes real mental effort to catch this sort of mistake.