difference was found in the death rates from breast cancer between the two groups. The Canadian studies are controversial, and some breast-cancer experts are convinced that they may have understated the benefits of mammography. But there is no denying the basic lessons of the Canadian trials: that a skilled pair of fingertips can find out an extraordinary amount about the health of a breast, and that we should not automatically value what we see in a picture over what we learn from our other senses.

“The finger has hundreds of sensors per square centimeter,” says Mark Goldstein, a sensory psychophysicist who cofounded MammaCare, a company devoted to training nurses and physicians in the art of the clinical exam. “There is nothing in science or technology that has even come close to the sensitivity of the human finger with respect to the range of stimuli it can pick up. It’s a brilliant instrument. But we simply don’t trust our tactile sense as much as our visual sense.”

4.

On the night of August 17, 1943, two hundred B-17 bombers from the United States Eighth Air Force set out from England for the German city of Schweinfurt. Two months later, 228 B-17s set out to strike Schweinfurt a second time. The raids were two of the heaviest nights of bombing in the war, and the Allied experience at Schweinfurt is an example of a more subtle—but in some cases more serious—problem with the picture paradigm.

The Schweinfurt raids grew out of the United States military’s commitment to bombing accuracy. As Stephen Budiansky writes in his wonderful recent book Air Power, the chief lesson of aerial bombardment in the First World War was that hitting a target from eight or ten thousand feet was a prohibitively difficult task. In the thick of battle, the bombardier had to adjust for the speed of the plane, the speed and direction of the prevailing winds, and the pitching and rolling of the plane, all while keeping the bombsight level with the ground. It was an impossible task, requiring complex trigonometric calculations. For a variety of reasons, including the technical challenges, the British simply abandoned the quest for precision: in both the First World War and the Second, the British military pursued a strategy of morale or area bombing, in which bombs were simply dropped, indiscriminately, on urban areas, with the intention of killing, dispossessing, and dispiriting the German civilian population.

But the American military believed that the problem of bombing accuracy was solvable, and a big part of the solution was something called the Norden bombsight. This breakthrough was the work of a solitary, cantankerous genius named Carl Norden, who operated out of a factory in New York City. Norden built a fifty-pound mechanical computer called the Mark XV, which used gears and wheels and gyroscopes to calculate airspeed, altitude, and crosswinds in order to determine the correct bomb-release point. The Mark XV, Norden’s business partner boasted, could put a bomb in a pickle barrel from twenty thousand feet. The United States spent $1.5 billion developing it, which, as Budiansky points out, was more than half the amount that was spent building the atomic bomb. “At air bases, the Nordens were kept under lock and key in secure vaults, escorted to their planes by armed guards, and shrouded in a canvas cover until after takeoff,” Budiansky recounts. The American military, convinced that its bombers could now hit whatever they could see, developed a strategic approach to bombing, identifying, and selectively destroying targets that were critical to the Nazi war effort. In early 1943, General Henry (Hap) Arnold— the head of the Army Air Forces—assembled a group of prominent civilians to analyze the German economy and recommend critical targets. The Advisory Committee on Bombardment, as it was called, determined that the United States should target Germany’s ball-bearing factories, since ball bearings were critical to the manufacture of airplanes. And the center of the German ball-bearing industry was Schweinfurt. Allied losses from the two raids were staggering. Thirty-six B-17s were shot down in the August attack, 62 bombers were shot down in the October raid, and between the two operations, a further 138 planes were badly damaged. Yet, with the war in the balance, this was considered worth the price. When the damage reports came in, Arnold exulted, “Now we have got Schweinfurt!” He was wrong.

The problem was not, as in the case of the Scud hunt, that the target could not be found, or that what was thought to be the target was actually something else. The B-17s, aided by their Norden Mark XVs, hit the ball- bearing factories hard. The problem was that the picture Air Force officers had of their target didn’t tell them what they really needed to know. The Germans, it emerged, had ample stockpiles of ball bearings. They also had no difficulty increasing their imports from Sweden and Switzerland, and, through a few simple design changes, they were able to greatly reduce their need for ball bearings in aircraft production. What’s more, although the factory buildings were badly damaged by the bombing, the machinery inside wasn’t. Ball-bearing equipment turned out to be surprisingly hardy. “As it was, not a tank, plane, or other piece of weaponry failed to be produced because of lack of ball bearings,” Albert Speer, the Nazi production chief, wrote after the war. Seeing a problem and understanding it, then, are two different things.

In recent years, with the rise of highly accurate long-distance weaponry, the Schweinfurt problem has become even more acute. If you can aim at and hit the kitchen at the back of a house, after all, you don’t have to bomb the whole building. So your bomb can be two hundred pounds rather than a thousand. That means, in turn, that you can fit five times as many bombs on a single plane and hit five times as many targets in a single sortie, which sounds good—except that now you need to get intelligence on five times as many targets. And that intelligence has to be five times more specific, because if the target is in the bedroom and not the kitchen, you’ve missed him.

This is the issue that the US command faced in the most recent Iraq war. Early in the campaign, the military mounted a series of air strikes against specific targets, where Saddam Hussein or other senior Baathist officials were thought to be hiding. There were fifty of these so-called decapitation attempts, each taking advantage of the fact that modern-day GPS-guided bombs can be delivered from a fighter to within thirteen meters of their intended target. The strikes were dazzling in their precision. In one case, a restaurant was leveled. In another, a bomb burrowed down into a basement. But, in the end, every single strike failed. “The issue isn’t accuracy,” Watts, who has written extensively on the limitations of high-tech weaponry, says. “The issue is the quality of targeting information. The amount of information we need has gone up an order of magnitude or two in the last decade.”

5.

Mammography has a Schweinfurt problem as well. Nowhere is that more evident than in the case of the breast lesion known as ductal carcinoma in situ, or DCIS, which shows up as a cluster of calcifications inside the ducts that carry milk to the nipple. It’s a tumor that hasn’t spread beyond those ducts, and it is so tiny that without mammography few women with DCIS would ever know they have it. In the past couple of decades, as more and more people have received regular breast X-rays and the resolution of mammography has increased, diagnoses of DCIS have soared. About fifty thousand new cases are now found every year in the United States, and virtually every DCIS lesion detected by mammography is promptly removed. But what has the targeting and destruction of DCIS meant for the battle against breast cancer? You’d expect that if we’ve been catching fifty thousand early-stage cancers every year, we should be seeing a corresponding decrease in the number of late- stage invasive cancers. It’s not clear whether we have. During the past twenty years, the incidence of invasive breast cancer has continued to rise by the same small, steady increment every year.

In 1987, pathologists in Denmark performed a series of autopsies on women in their forties who had not been known to have breast cancer when they died of other causes. The pathologists looked at an average of 275 samples of breast tissue in each case, and found some evidence of cancer—usually DCIS—in nearly 40 percent of the women. Since breast cancer accounts for less than 4 percent of female deaths, clearly the overwhelming majority of these women, had they lived longer, would never have died of breast cancer. “To me, that indicates that these kinds of genetic changes happen really frequently, and that they can happen without having an impact on women’s health,” Karla Kerlikowske, a breast-cancer expert at the University of California at San Francisco, says.

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