The Man Who Mistook His Wife for a Hat: Part 4, Chapter 23 Summary & Analysis

In 1966, Oliver Sacks met “the twins,” John and Michael, in a state hospital, at which time they were both twenty-six years old. At this time, the twins were already well known—they’d appeared on TV many times. They had been diagnosed as intellectually disabled, but also as autistic or psychotic, and they were at the same time known for their incredible mental gifts. However, in the twenty years since Sacks’s first meeting with the twins, there have been few, if any, studies conducted upon them. Sacks argues that the original neurological examinations of the twins were too reductive in their format. By focusing too exclusive on the superficial aspects of the twins’ existences, they reduced the twins’ “psychology, methods, and lives … almost to nothing.” To understand the twins more fully, Sacks says, one must study them as subjects, and observe them from day to day.

The twins, Sacks has found in the course of his 1966 tests, might seem grotesque at first—they’re unusually small, with high voices, disproportionately large heads, and poor vision. The twins have jaw-dropping intellectual abilities, however—they can determine the day of the week for any date in history, past or future, and can remember long numbers perfectly. The twins can also remember the weather on any day in their lives. Strangely, however, the twins can’t perform even the most basic arithmetic.

There have been many cases throughout history of people with phenomenal mathematical abilities. However, what makes the twins so interesting for Sacks is that they can perform complex mathematical calculations without understanding what they’re doing. Once, Sacks spilled matches on the ground, only to have the twins inform him that he’d spilled exactly 111 matches. The twins claimed that they hadn’t counted the matches at all—they’d simply “seen” the correct number. The twins then repeated “thirty-seven” three times—which, Sacks realized, suggested that they’d broken up the 111 matches into three groups of thirty-seven, without understanding the concepts of multiplication or factoring.

On another occasion, Sacks watched the twins exchanging long, six-figure numbers. After each number, the twins would smile as if savoring a fine wine. Sacks wondered if the numbers had any meaning. Only later did he realize that all the numbers the twins had named were primes (i.e., numbers that can only divided by themselves and one). The next day, Sacks joined in the twins’ game, naming seven-, eight-, and eventually ten-digit prime numbers. After each one, the twins would pause for a moment, and then smile, as if verifying that Sacks’s numbers were, indeed, prime. Even though there is no simple method for calculating prime numbers, the twins clearly had some method of calculating them.

Sacks draws an analogy between the twins’ mathematical talents and the talents of a great musician. Like a musician, the twins had an intuitive understanding of the “sense” of different numbers, even if they had little to no understanding of arithmetic. It was as if they could see the “harmony” in different numbers. The twins seemed to live in a world of numbers—and, as a result, they seemed to have developed an almost aesthetic sense for the beauty and proportion of different numbers, not unlike a musician’s sense for the beauty and proportion of different melodies. For the twins, numbers were both awesome, godlike entities and also intimate friends.

Ten years after Sacks met with the twins, it was decided that they should be separated to prevent their “unhealthy communication.” Now they both work in menial jobs for little money. Tragically, since being separated and working menial jobs, the twins seem to have lost their numerical powers, “the chief joy … of their lives.” But, Sacks comments, “This is considered a small price to pay, no doubt, for their having become quasi-independent and ‘socially acceptable.’”

In the Postscript, Sacks notes one hypothesis regarding the twins, proposed by the researcher Israel Rosenfield: although the twins couldn’t do basic arithmetical operations like multiplication, perhaps they were capable of modular arithmetic—for example, following the cyclical algorithm necessary to calculate days of the week. And perhaps the fact that the twins could calculate the number of matches—111—by dividing them up into three groups of thirty-seven suggests that the twins could do arithmetical operations, if only with primes. Sacks accepts that Rosenfield’s hypothesis may be true.

After publishing the original version of this chapter as an article, Sacks received many comments and letters from other doctors. Some parents wrote to him about their children’s abilities to visualize numbers. Sacks realized that prime numbers have played a special role in the lives of several mathematically gifted, autistic children. It’s still unclear how, precisely, gifted children calculate primes and prime factors—even the gifted patients themselves can’t explain how they do it. The great mathematician Kurt Gödel argued that, in the future, primes could serve as a way of marking different ideas, places, and people, paving the way for the total numeralization of the world. If Gödel’s hypothesis ever comes true, then people like the twins may truly be able to live in a world of numbers.