3.

Dershaw picked up a new X-ray and put it on the light box. It belonged to a forty-eight-year-old woman. Mammograms indicate density in the breast: the denser the tissue is, the more the X-rays are absorbed, creating the variations in black and white that make up the picture. Fat hardly absorbs the beam at all, so it shows up as black. Breast tissue, particularly the thick breast tissue of younger women, shows up on an X-ray as shades of light gray or white. This woman’s breasts consisted of fat at the back of the breast and more dense, glandular tissue toward the front, so the X-ray was entirely black, with what looked like a large, white, dense cloud behind the nipple. Clearly visible, in the black, fatty portion of the left breast, was a white spot. “Now, that looks like a cancer, that little smudgy, irregular, infiltrative thing,” Dershaw said. “It’s about five millimeters across.” He looked at the X-ray for a moment. This was mammography at its best: a clear picture of a problem that needed to be fixed. Then he took a pen and pointed to the thick cloud just to the right of the tumor. The cloud and the tumor were exactly the same color. “That cancer only shows up because it’s in the fatty part of the breast,” he said. “If you take that cancer and put it in the dense part of the breast, you’d never see it, because the whiteness of the mass is the same as the whiteness of normal tissue. If the tumor was over there, it could be four times as big and we still wouldn’t see it.”

What’s more, mammography is especially likely to miss the tumors that do the most harm. A team led by the research pathologist Peggy Porter analyzed 429 breast cancers that had been diagnosed over five years at the Group Health Cooperative of Puget Sound. Of those, 279 were picked up by mammography, and the bulk of them were detected very early, at what is called Stage One. (Cancer is classified into four stages, according to how far the tumor has spread from its original position.) Most of the tumors were small, less than two centimeters. Pathologists grade a tumor’s aggression according to such measures as the “mitotic count” – the rate at which the cells are dividing – and the screen-detected tumors were graded “low” in almost 70 percent of the cases. These were the kinds of cancers that could probably be treated successfully. “Most tumors develop very, very slowly, and those tend to lay down calcium deposits – and what mammograms are doing is picking up those calcifications,” Leslie Laufman, a hematologist-oncologist in Ohio, who served on a recent National Institutes of Health breast- cancer advisory panel, said. “Almost by definition, mammograms are picking up slow-growing tumors.”

A hundred and fifty cancers in Porter’s study, however, were missed by mammography. Some of these were tumors the mammogram couldn’t see – that were, for instance, hiding in the dense part of the breast. The majority, though, simply didn’t exist at the time of the mammogram. These cancers were found in women who had had regular mammograms, and who were legitimately told that they showed no sign of cancer on their last visit. In the interval between X-rays, however, either they or their doctor had manually discovered a lump in their breast, and these “interval” cancers were twice as likely to be in Stage Three and three times as likely to have high mitotic counts; 28 percent had spread to the lymph nodes, as opposed to 18 percent of the screen-detected cancers. These tumors were so aggressive that they had gone from undetectable to detectable in the interval between two mammograms.

The problem of interval tumors explains why the overwhelming majority of breast-cancer experts insist that women in the critical fifty-to-sixty-nine age group get regular mammograms. In Porter’s study, the women were X- rayed at intervals as great as every three years, and that created a window large enough for interval cancers to emerge. Interval cancers also explain why many breast-cancer experts believe that mammograms must be supplemented by regular and thorough clinical breast exams. (Thorough is defined as palpation of the area from the collarbone to the bottom of the rib cage, one dime-size area at a time, at three levels of pressure – just below the skin, the midbreast, and up against the chest wall – by a specially trained practitioner for a period not less than five minutes per breast.) In a major study of mammography’s effectiveness – one of a pair of Canadian trials conducted in the 1980s – women who were given regular, thorough breast exams but no mammograms were compared with those who had thorough breast exams and regular mammograms, and no 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

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