conceptual distance between numbers or would reflect the idiosyncratic geometry of her own personal number line. In 2001 we managed to recruit an Austrian student named Petra who was a number-space synesthete. Her highly convoluted number line doubled back on itself so that, for example, 21 was spatially closer to 36 than it was to 18. Ed and I were very excited. As of that time there had not been any study on the number-space phenomenon since the time when Galton discovered it in 1867. No attempt had been made to establish its authenticity or to suggest what causes it. So any new information, we realized, would be valuable. At least we could set the ball rolling.
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.
In the spirit of taking a speculative leap, I would like to argue that further specialization might have occurred in our space-mapping parietal lobes. The left angular gyrus might be involved in representing ordinality. The right angular gyrus might be specialized for quantity. The simplest way to spatially map out a numerical sequence in the brain would be a straight line from left to right. This in turn might be mapped onto notions of quantity represented in the right hemisphere. But now let’s assume that the gene that allows such remapping of sequence on visual space is mutated. The result might be a convoluted number line of the kind you see in number-space synesthetes. If I were to guess, I’d say other types of sequence—such as months or weeks—are also housed in the left angular gyrus. If this is correct, we should expect that a patient with a stroke in this area might have difficulty in quickly telling you whether, for example, Wednesday comes after or before Tuesday. Someday I hope to meet such a patient.
ABOUT THREE MONTHS after I had embarked on synesthesia research, I encountered a strange twist. I received an email from one of my undergraduate students, Spike Jahan. I opened it expecting to find the usual “please reconsider my grade” request, but it turned out that he’s a number-color synesthete who had read about our work and wanted to be tested. Nothing strange so far, but then he dropped a bombshell: He’s color-blind. A color-blind synesthete! My mind began to reel. If he experiences colors, are they anything like the colors you or I experience? Could synesthesia shed light on that ultimate human mystery, conscious awareness?
Color vision is a remarkable thing. Even though most of us can experience millions of subtly different hues, it turns out our eyes use only three kinds of color photoreceptors, called cones, to represent all of them. As we saw in Chapter 2, each cone contains a pigment that responds optimally to just one color: red, green, or blue. Although each type of cone responds optimally only to one specific wavelength, it will also respond to a lesser extent to other wavelengths that are close to the optimum. For example, red cones respond vigorously to red light, fairly well to orange, weakly to yellow, and hardly at all to green or blue. Green cones respond best to green, less well to yellowish green, and even less to yellow. Thus every specific wavelength of (visible) light stimulates your red, green, and blue cones by a specific amount. There are literally millions of possible three-way combinations, and your brain knows to interpret each one as a separate color.
Color blindness is a congenital condition in which one or more of these pigments is deficient or absent. A color-blind person’s vision works perfectly normally in nearly every respect, but she can see only a limited range of hues. Depending on which cone pigment is lost and on the extent of loss, she may be red-green color-blind or blue- yellow color-blind. In rare cases two pigments are deficient, and the person sees purely in black and white.
Spike had the red-green variety. He experienced far fewer colors in the world than most of us do. What was truly bizarre, though, was that he often saw numbers tinged with colors that he had never seen in the real world. He referred to them, quite charmingly and appropriately, as “Martian colors” that were “weird” and seemed quite “unreal.” He could only see these when looking at numbers.
Ordinarily one would be tempted to ignore such remarks as being crazy, but in this case the explanation was staring me in the face. I realized that my theory about cross-activation of brain maps provides a neat explanation for this bizarre phenomenon. Remember, Spike’s cone receptors are deficient, but the problem is entirely in his eyes. His retinas are unable to send the full normal range of color signals up to the brain, but in all likelihood his cortical color-processing areas, such as V4 in the fusiform, are perfectly normal. At the same time, he is a number-
