An interesting and largely unanswered question concern the acquisition of our ability to understand and perform mathematics. We appear to innately possess an concrete grasp of only a handful of small values, and yet we frequently engage in transactions for quantities that reach into the hundreds or thousands.
Our ability to perform these computations no doubt speaks to the substantial development in our capacity for abstract reason, but there is plenty of evidence that the mechanism is far from perfectly rational. For example, our approximated mental addition and subtraction are marked by a curious pattern of errors: we tend to overestimate the answer when adding and underestimate when subtracting. And of course, the fact that computers long ago outclassed us in the domain of basic calculation and yet still struggle to do something as simple (for us) as identify the subject of a picture suggests that our minds are not ideally suited for arithmetic.
In an alternate theory, our mathematical reasoning co-opted the neural architecture that serves similar cognitive processing. Evolution tends to take the easiest route, and building on top of a module that already exists is much more efficient than producing a novel one. A paper in last week’s Science supports this theory, as it shows that a brain region responsible for eye movement is directly involved in mental arithmetic.
The group of researchers, led by Andre Knops in Stanislas Dehaene’s lab at INSERM scanned subjects with fMRI while they performed two tasks. In one, they simply gazed at a fixation cross until prompted to quickly look to the left or to the right. In the second, they were presented with two numbers and asked either to add them or subtract them and then to choose from among seven alternatives the closest outcome.
Standard analysis showed that, among other regions, the posterior superior parietal lobule (PSPL) was active during both tasks. In both earlier neurological research and single-cell studies in non-human primates, this area has been found to be involved in selecting the spatial target of an impending shift in visual attention. The theory is that it performs the vector additions necessary to guide the oculomotor system towards a point in space.
The researchers went beyond merely identifying increased activation in this area, however, by performing pattern classification with a machine learning algorithm. They trained the algorithm with the neuroimaging data from the eye-movement trials. Then, when they fed data from the arithmetic trials into the algorithm, it was able to distinguish between whether the subject was performing addition or subtraction on that trial.
In other words, the patterns of activity within the PSPL was highly similar both when the subject was about to look to the left and when he was performing mental subtraction. Likewise for looking right and addition. Because the experiment used eye-tracking software to monitor the subjects in the scanner, these results were not affected by actual eye movements.
The pattern classification method goes beyond tradition neuroimaging methods to determine not just which areas are involved in some experiment but also how they are involved. As this study shows, that can be very useful for understanding the relationship between older innate abilities and newer learned ones. Our brains are powerful calculators, just not in the way we usually use the term.
Knops, A., Thirion, B., Hubbard, E., Michel, V., & Dehaene, S. (2009). Recruitment of an Area Involved in Eye Movements During Mental Arithmetic Science, 324 (5934), 1583-1585 DOI: 10.1126/science.1171599
