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. “The body has this whole mechanism to repair things, and maybe that’s what happened with these tumors.” Gilbert Welch, the medical-outcomes expert, thinks that we fail to understand the hit-or-miss nature of cancerous growth, and assume it to be a process that, in the absence of intervention, will eventually kill us. “A pathologist from the International Agency for Research on Cancer once told me that the biggest mistake we ever made was attaching the word ‘carcinoma’ to DCIS,” Welch says. “The minute carcinoma got linked to it, it all of a sudden drove doctors to recommend therapy, because what was implied was that this was a lesion that would inexorably progress to invasive cancer. But we know that that’s not always the case.”

In some percentage of cases, however, DCIS does progress to something more serious. Some studies suggest that this happens very infrequently. Others suggest that it happens frequently enough to be of major concern. There is no definitive answer, and it’s all but impossible to tell, simply by looking at a mammogram, whether a given DCIS tumor is among those lesions that will grow out from the duct, or part of the majority that will never amount to anything. That’s why some doctors feel that we have no choice but to treat every DCIS as life-threatening, and in 30 percent of cases that means a mastectomy, and in another 35 percent it means a lumpectomy and radiation. Would taking a better picture solve the problem? Not really, because the problem is that we don’t know for sure what we’re seeing, and as pictures have become better we have put ourselves in a position where we see more and more things that we don’t know how to interpret. When it comes to DCIS, the mammogram delivers information without true understanding. “Almost half a million women have been diagnosed and treated for DCIS since the early nineteen-eighties – a diagnosis virtually unknown before then,” Welch writes in his new book, Should I Be Tested for Cancer?, a brilliant account of the statistical and medical uncertainties surrounding cancer screening. “This increase is the direct result of looking harder – in this case with ‘better’ mammography equipment. But I think you can see why it is a diagnosis that some women might reasonably prefer not to know about.”

6.

The disturbing thing about DCIS, of course, is that our approach to this tumor seems like a textbook example of how the battle against cancer is supposed to work. Use a powerful camera. Take a detailed picture. Spot the tumor as early as possible. Treat it immediately and aggressively. The campaign to promote regular mammograms has used this early-detection argument with great success because it makes intuitive sense. The danger posed by a tumor is represented visually. Large is bad; small is better – less likely to have metastasized. But here, too, tumors defy our visual intuitions.

According to Donald Berry, who is the chairman of the Department of Biostatistics and Applied Mathematics at M. D. Anderson Cancer Center, in Houston, a woman’s risk of death increases only by about 10 percent for every additional centimeter in tumor length. “Suppose there is a tumor size above which the tumor is lethal, and below which it’s not,” Berry says. “The problem is that the threshold varies. When we find a tumor, we don’t know whether it has metastasized already. And we don’t know whether it’s tumor size that drives the metastatic process or whether all you need is a few million cells to start sloughing off to other parts of the body. We do observe that it’s worse to have a bigger tumor. But not amazingly worse. The relationship is not as great as you’d think.”

In a recent genetic analysis of breast-cancer tumors, scientists selected women with breast cancer who had been followed for many years, and divided them into two groups – those whose cancer had gone into remission, and those whose cancer had spread to the rest of their body. Then the scientists went back to the earliest moment that each cancer became apparent and analyzed thousands of genes in order to determine whether it was possible to predict, at that moment, who was going to do well and who wasn’t. Early detection presumes that it isn’t possible to make that prediction: a tumor is removed before it becomes truly dangerous. But scientists discovered that even with tumors in the one-centimeter range – the range in which cancer is first picked up by a mammogram – the fate of the cancer seems already to have been set. “What we found is that there is biology that you can glean from the tumor, at the time you take it out, that is strongly predictive of whether or not it will go on to metastasize,” Stephen Friend, a member of the gene-expression team at Merck, says. “We like to think of a small tumor as an innocent. The reality is that in that innocent lump are a lot of behaviors that spell a potential poor or good prognosis.”

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