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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,