Nobody knew precisely what had happened to Monsieur N.; perhaps he had just tripped, or maybe it was a stroke that had triggered the fall and the consequent blow to his head. He showed up at a hospital in Orléans one day in 1986 with a giant hematoma in his brain’s left hemisphere. The surgeons kept him from bleeding to death, but they couldn’t keep the lesion from growing even larger as they worked. By the time they were done, large parts of his left temporal, parietal, and occipital lobes--the rear half of the hemisphere, essentially--were useless. By the time Stanislas Dehaene came to see him, three years later, it was clear that N. was going to be severely impaired for life. It was a sad business: the man was in his early 40s, had been a successful salesman, was married with two young daughters-- only now his wife and kids had left him and he had been forced to move back in with his aging parents. Dehaene, a young neuropsychologist with a family of his own, felt the burden of sympathy as much as anyone would. But he also felt something else, and seven years later his face still brightens at the recollection. The first question he asked N. was What’s 2 plus 2? When N. answered 3, Dehaene knew he had landed a spectacular case.
That encounter took place at the Hôpital de la Salpêtrière in Paris, where Dehaene’s friend and research partner, Laurent Cohen, works as a neurologist. N.’s provincial doctor had sent him to the well-known medical center to seek help from the specialists. There was in fact little to be done for him, and treating N. was not Dehaene’s or Cohen’s job anyway. Their interest was in finding out what the trauma had left of his ability to process numbers. And as they questioned him closely, what was left turned out to be far more substantial than his performance on 2 plus 2 would have indicated. Even his dramatic failure on tests like that one was suggestive. N. might say that 2 plus 2 was 3, or that it was 5, but never that it was 9 or 47. He was never absurd.
N. had lost the ability to calculate--but not, it seemed, to approximate. Numbers existed for him only as approximations, which became increasingly fuzzy the larger they got. It was not just his arithmetic that was affected; his memory for number facts was similarly blurred. A year had about 350 days, a month 15 or 20. N. had no precise knowledge of the meaning of 9, but he knew that 9 children was too much for one mother and too few for a whole school. Dehaene asked him how many eggs in a douzaine, and he did not answer douze, the French word for 12; he said 6 or 10. Six or 10, though, isn’t 60 or a hundred. It is close to the mark. Somewhere deep within the posterior folds of his brain, N. still had an intuitive, almost primordial sense of numbers.
This was of course little consolation to him. When N. realized that he could not tell whether a number was odd or even, and was just guessing, he became so upset that Dehaene had to stop the experiment.
In the January 15, 1880, issue of the journal Nature, the British anthropologist Francis Galton published a curious little research note of the kind you could still publish a century ago. As part of a general study of mental imagery, Galton had passed around a questionnaire to a bunch of friends and acquaintances, asking them to report on whether they could see numbers and if so in what way. Some of them could, it seemed, mostly the women. (I have been astonished to find how superior women usually are to men in the vividness of their mental imagery and their powers of introspection. . . . Galton wrote. The former usually show an unexpected amount of intelligence, while many of the latter are as unexpectedly obtuse.) Usually the numbers were arranged along a line, or a series of lines, that got progressively less distinct and sometimes vanished into the mental distance as the numbers got larger. Sometimes the numbers had color or texture (There are sorts of woolly lumps at the tens, one subject reported). And on occasion they had a great deal of personality: 9 is a wonderful being of whom I felt almost afraid, 8 I took for his wife . . . 6, of no particular sex but gentle and straightforward. . . . That report came from an unusually visual male philosopher.
