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

FIGURE 3.7 Which of these shapes is “bouba” and which is “kiki”? Such stimuli were originally used by Heinz Werner to explore interactions between hearing and vision.

I HAVE ARGUED so far that synesthesia, and in particular the existence of “higher” forms of synesthesia (involving abstract concepts rather than concrete sensory qualities) can provide clues to understanding some of the high-level thought processes that humans alone are capable of.⁸ Can we apply these ideas to what is arguably the loftiest of our mental traits, mathematics? Mathematicians often speak of seeing numbers laid out in space, roaming this abstract realm to discover hidden relationships that others might have missed, such as Fermat’s Last Theorem or Goldbach’s conjecture. Numbers and space? Are they being metaphorical?

One day in 1997, after I had consumed a glass of sherry, I had a flash of insight—or at least thought I had. (Most of the “insights” I have when inebriated turn out to be false alarms.) In his original Nature paper, Galton described a second type of synesthesia that is even more intriguing than the number-color condition. He called it “number forms.” Other researchers use the phrase “number line.” If I asked you to visualize the numbers 1 to 10 in your mind’s eye, you will probably report a vague tendency to see them mapped in space sequentially, left to right, as you were taught in grade school. But number-line synesthetes are different. They able to visualize numbers vividly and do not see the numbers arranged sequentially from left to right, but on a snaking, twisting line that can even double back on itself, so that 36 might be closer to 23, say, than it is to 38 (Figure 3.8). One could think of this as “number-space” synesthesia, in which every number is always in a particular location in space. The number line for any individual remains constant even if tested on intervals separated by months.

FIGURE 3.8 Galton’s number line. Notice that 12 is a tiny bit closer to 1 than it is to 6.

As with all experiments in psychology, we needed a method to prove Galton’s observation experimentally. I called upon my students Ed Hubbard and Shai Azoulai to help set up the procedures. We first decided to look at the well-known “number distance” effect seen in normal people. (Cognitive psychologists have examined every conceivable variation of the effect on hapless student volunteers, but its relevance to number-space synesthesia was missed until we came along.) Ask anyone which of two numbers is larger, 5 or 7? 12 or 50? Anyone who has been through grade school will get it right every time. The interesting part comes when you clock how long it takes people to spit out each of their answers. This latency between showing them a number pair and their verbal response is their reaction time (RT). It turns out that the greater the distance between two numbers the shorter the RT, and contrariwise, the closer two numbers are, the longer it takes to form an answer. This suggests that your brain represents numbers in some sort of an actual mental number line which you consult “visually” to determine which is greater. Numbers that are far apart can be easily eyeballed, while numbers that are close together need closer inspection, which takes a few extra milliseconds.

We realized we could exploit this paradigm to see if the convoluted number-line phenomenon really existed or not. We could ask a number-space synesthete to compare number pairs and see if her RTs corresponded to the real 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.