Get Better at Math by Disrupting Your Brain

The paradox of performance improved by perturbation


We tend to believe that our brains work as well as they can.

Thus, we assume that if you are good at math, it means that your brain is superior to the brains of those who find math more challenging. Of course, we have come to realize that people are better at some things than at others. Being better in math does not mean being smarter at everything. But we assume that, at least within a given domain, better behavioral performance implies superior brains, because we take it for granted that the brain is working as well as it can to optimize behavior.

However, a growing number of instances in clinical neurology and a growing body of research in cognitive neuroscience reveal that this assumption is incorrect. (Many are discussed in “The Paradoxical Brain,” a new book edited by Narinder Kapur and coming out next year from Cambridge University Press.) 

For example, if the brain optimizes behavior, disruption of normal brain activity ought to lead to a loss of function, and never to enhancement. And yet, in some instances, disruption of brain activity with noninvasive transcranial magnetic stimulation or transcranial direct current stimulation -- both methods that use devices outside the skull to affect the workings inside -- can result in a paradoxical behavioral improvement.

Take a recent example: In the November 23 issue of Current Biology, researchers led by Roi Cohen Kadosh of Oxford University report that noninvasive brain stimulation can promote the “number sense.”

Nearly one in every five people has a developmental disability that makes it difficult for them to process and understand numbers, and others acquire similar difficulties from a stroke, traumatic brain injury or a degenerative disease like Alzheimer’s disease. Therapies for disorders in numerical competence are lacking.

Cohen Kadosh’s team concluded that noninvasive brain stimulation may be a valuable therapeutic intervention in patients with numerical disabilities. Substantially more work is needed before this conclusion is actually supported by data. Studies in patients are critically needed, because the results in normal subjects may be very different from those obtainable in patients. Regardless, the findings are extremely interesting and reveal fundamental and surprising aspects about human brain function.

How the study worked: Over six days, 15 adult subjects were asked to learn the association between nine arbitrary symbols without knowing the quantity that had been assigned to them. The learning phase lasted for nearly two hours each day, and for the first 20 minutes of each daily session, subjects were exposed to transcranial direct current stimulation of their parietal lobes.

The parietal lobes are thought to be critical regions in the processing of magnitudes and the representation of numbers. Individuals who have difficulties with numbers have been found to have anomalies of the right parietal lobe, and the right parietal lobe is also thought to be critical for the development of numerical understanding during childhood.

At the end of the learning phase, the subjects’ newly created number sense was measured using various tests. The goal of the study was to assess whether modifying activity in the parietal lobes affected the acquisition of number competence.

If the brain functions by optimizing behavior, it might be possible to worsen numerical competence by disrupting parietal function, but it should not be possible to enhance it that way. However, that is precisely what Cohen Kadosh's team found. Remarkably, this improvement was still present six months after the training.

What are we to make of this? It has become increasingly apparent that complex brain functions -- such as coordinated movement, memory, language, or mathematical thinking -- depend critically on dynamic interactions between brain areas. This is the concept of “functional connectivity networks” — distributed brain regions transiently interacting to perform a particular neural function.

Abnormalities in the interactions of network components play a critical role in common and devastating disorders ranging from epilepsy to depression. Damage to specific networks can lead to distinct neurological syndromes. Furthermore, both the deficits and recovery after damage are a function of the architecture and adaptability of these networks.

Behavior after damage, or after the modulation of activity in a given brain area, reflects the capacity of the brain and its networks to adapt to the disruption. The final behavioral consequence of a brain injury may be worsened performance, but also, paradoxically, improved performance, or even recovery from the deleterious consequences of a pre-existing insult or disease.

Consistent with such notions of distributed, plastic brain networks, we have learned that the effects of noninvasive stimulation depend on the connections between the regions we are targeting and the rest of the brain. The stimulation changes local brain activity, but also changes activity in distant structures.  It is thus possible to use noninvasive stimulation to systematically explore “paradoxical facilitation” -- disruption that leads to improved performance -- in healthy subjects and in patients with a variety of neuropsychiatric conditions. We can even consider trying to use it -- cautiously -- for neurological or psychiatric therapeutics, just as Cohen Kadosh’s team propose for numerical competence.  

Certainly the pursuit of such potential therapeutic applications of non-invasive brain stimulation is exciting and promising. Already, studies in recent years showed that noninvasive stimulation can improve attention in normal subjects, and this phenomenon can be applied to patients with a stroke and enable them to recover from “neglect,” the inability to pay attention to one part of their world. Similarly, studies found that it is possible to promote motor learning in normal subjects by coupling noninvasive brain stimulation with practice, and similar approaches are showing promise in promoting recovery of motor function after a stroke.

Clinical medicine aside, these types of results offer important insights into normal brain function. In 1620, the Spanish playwright Lope de Vega wrote in the dedication of “La Viuda Valenciana” (The Widow from Valencia): “La gala del nadar es saber guardar la ropa” (The pride of swimming is knowing how to guard the clothes). This plays on a Spanish proverb dating back to the Middle Ages: “No se puede nadar y guardar la ropa” (You cannot swim and guard the clothes).

Indeed, jumping in a river or a lake for a swim, while keeping a watchful eye on your own clothes to prevent them from being stolen, must not have been easy. The proverb is still in widespread use in Spain and indicates the need to commit to a task, give it your all, without holding back.

However, as Lope de Vega points out, true accomplishment lies in achieving both: swimming and guarding the clothes at the same time. It appears that our brain is designed to do just that. There are many examples that illustrate the fact that our nervous system works with a “functional reserve”. Under certain circumstances we are quite capable of better performance, faster reactions, stronger force generation, more efficient learning.  A critical question, though, is what the cost of such 'supra-normal' performance might be.

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