The Tell-Tale Brain: A Neuroscientist's Quest for What Makes Us Human

We hooked Petra up to a machine that measured her RT to questions such as “Which is bigger, 36 or 38?” or (on a different trial) “36 or 23?” As often happens in science, the result wasn’t entirely clear one way or the other. Petra’s RT seemed to depend partially on the numerical distance and partially on spatial distance. This wasn’t the conclusive result we had hoped for, but it did suggest that her number-line representation wasn’t entirely left-to-right and linear as it is in normal brains. Some aspects of number representation in her brain were clearly messed up.

We published our finding in 2003 in a volume devoted to synesthesia, and it inspired much subsequent research. The results have been mixed, but at the very least we revived interest in an old problem that had been largely ignored by the pundits, and we suggested ways of testing it objectively.

Shai Azoulai and I followed up with a second experiment on two new number-space synesthetes that was designed to prove the same point. This time we used a memory test. We asked each synesthete to remember sets of nine numbers (for example, 13, 6, 8, 18, 22, 10, 15, 2, 24) displayed randomly on various spatial locations on the screen. The experiment contained two conditions. In condition A, nine random numbers were scattered randomly about the two-dimensional screen. In condition B, each number was placed where it “should” be on each synesthete’s personal convoluted line as if it had been projected, or “flattened,” onto the screen. (We had initially interviewed each subject to find out the geometry of his or her personal number line and determined which numbers the subject placed close to each other within that idiosyncratic coordinate system.) In each condition the subjects were asked to view the display for 30 seconds in order to memorize the numbers. After a few minutes they were simply asked to report all the numbers they could recall having seen. The result was striking: The most accurate recall was for the numbers they had seen in condition B. Again we had shown that these people’s personal number lines were real. If they weren’t, or if their shapes varied across time, why should it matter where the numbers had been placed? Putting the numbers where they “should” be in each synesthete’s personal number line apparently facilitated that person’s memory for the numbers—something you wouldn’t see in a normal person.

One more observation deserves special mention. Some of our number-space synesthetes told us spontaneously that the shape of their personal number lines strongly influenced their ability to do arithmetic. In particular, subtraction or division (but not multiplication, which, again, is memorized by rote) was much more difficult across sudden sharp kinks in their lines than it was along relatively straight portions of it. On the other hand, some creative mathematicians have told me that their twisted number lines enable them to see hidden relationships between numbers that elude us lesser mortals. This observation convinced me that both mathematical savants and creative mathematicians are not being merely metaphorical when they speak of wandering a spatial landscape of numbers. They are seeing relationships that are not obvious to us less-gifted mortals.

As for how these convoluted number lines come to exist in the first place, that is still hard to explain. A number represents many things—eleven apples, eleven minutes, the eleventh day of Christmas—but what they have in common are the semiseparate notions of order and quantity. These are very abstract qualities, and our apish brains surely were not under selective pressure to handle mathematics per se. Studies of hunter-gatherer societies suggest that our prehistoric ancestors probably had names for a few small numbers—perhaps up to ten, the number of our fingers—but more advanced and flexible counting systems are cultural inventions of historical times; there simply wouldn’t have been enough for the brain to evolve a “lookup table” or number module starting from scratch. On the other hand (no pun intended), the brain’s representation of space is almost as ancient as mental faculties come. Given the opportunistic nature of evolution, it is possible that the most convenient way to represent abstract numerical ideas, including sequentiality, is to map them onto a preexisting map of visual space. Given that the parietal lobe originally evolved to represent space, is it a surprise that numerical calculations are also computed there, especially in the angular gyrus? This is a prime example of what might have been a unique step in human evolution.