By now, it is an accepted tenet of linguists, neuroscientists, and developmental psychologists: Syntax, the framework of language, is hardwired in our brain. Even newborns possess the capacity for language. We do know the anatomical locations of language capacity, but we still have only rudimentary ideas as to what makes a gifted writer stand out from the rest of us, neurobiologically speaking.
So, I was delighted to read a fascinating post in the Israeli newspaper Ha’aretz by the neuroscientist Alumit Ishai of the University of Zurich about a related mental activity: mathematical calculation. In it, she summarizes the work of Professor Dehaene of the University of Paris, on this subject. I had been acquainted with Dehaene’s work only by a fortunate coincidence. One of the delights of a visit to London is heading down Charring Cross and rummaging through the wonderful used book shops lining up the street. And there, I found a well-worn Penguin book called “The Number Sense” by Dehaene. At the time, I did not know much about the subject, much less about the author, but the subject and the writing were captivating. I later learned that Professor Dehaene was well known for his work in cognitive neuroscience.
Dehaene recounts a wonderful story that illustrates how scientists with an inquiring mind become fascinated with an enigmatic phenomenon, and begin following the trail like a hound dog.
About 20 years ago, he met Mr. N, who had had a left hemisphere stroke. As expected, the patient’s right arm was paralyzed, his speech was slow, and he lost his reading capacity. So far, nothing unexpected. But Mr. N also suffered from acalculia, or the lost capacity to calculate. He could recite from memory series like 2, 4, 6, 8 but could not count from 9 downward, could not distinguish between odd and even numbers, or to identify the numeral 5. When asked to add 2+2, his answers varied between 3 and 5. In his world, numbers where not precise, only approximations; his year had 350 days and 5 seasons, and a dozen eggs were 6 or 10 eggs.
Dehaene asked some simple questions; how do we determine whether one number is larger than another. What he found was that if the subjects were presented with the numerals 4 and 7, all of them responded fast and correctly chose 7. But the when numerals were either farther apart (for example 2 and 9) or closer together (like 5 and 6), the response time increased and the error rate increased. He also observed that it was easier, measured by response time, for his subjects (some of them students majoring in math) to distinguish between 2 and 3 than between 7 and 8. His conclusion: When we see or hear numerals, the brain maps them on a “straight line” in ascending order, but this mapping becomes blurred as the numerals exceed 3 or 4.
Fascinating anthropological correlates
The Mundurukú people of the Amazon basin do not have words in their language to describe numbers larger than 5. In fact, the word for 5 is “one hand”. But they do have a numerical intuition: They know for instance, that 50+30 is greater than 60. Closer to home: Numbers are described differently in different languages, for instance, English and Chinese, or Mundrukú for that matter.
And now we can take the leap from the “soft” sciences of anthropology and linguistics to neurobiology.
The seat of mathematical sense
Using fMRI imaging of the brain, Dehaene and his collaborators, among other groups, found that performing simple mathematical tasks, like subtracting 4 from 13, generate increased neuronal activity in the parietal lobe, and more specifically in an area called the intraparietal sulcus, or IPS; (sulcus=inner fold). But this area is not exclusively “mathematical”. What else happens in this area? For starters, the representation of the fingers is located here. How many of us still sometimes count using fingers?
That’s not all. The IPS contains a series of functionally distinct subregions that have been intensively investigated using both single cell neurophysiology in primates and human functional neuroimaging. Its principal functions are related to perceptual-motor coordination (for directing eye movements and reaching) and visual attention, careful and focused listening, imagining, retrieval of stored information, spatial sense, and music. Is this the reason why many mathematicians are excellent musicians and composers?
Anybody who listens deeply to a Bach sonata or variations cannot help but recognize how “mathematical” his music is. Another tantalizing observation: Albert Einstein’s IPS is said to be (based on a post-mortem examination) unusually deep and curved, creating a much larger cortical surface, which in turn could accommodate more neurons and infinitely more connections between them. The rest of the brain was unremarkable, anatomically speaking. This observation was made decades before anybody had the foggiest idea about the functions located in this region. By the way, Einstein related in his memoirs that he used to “imagine” his mathematical equations. For instance, his famous E=mc2 came to him one day when he visualized himself riding a rocket.