One sense less, one more equation

Author: Marta Bueno Saz received her BSc and MSc in Physics and her BA in Pedagogy from the University of Salamanca. Her research is currently focused on neuroscience. She became fully blind soon after completing her degrees.

The cerebral cortex is a limited resource. Evolution has employed some impressive tricks to increase the amount of cortex available, such as folding it, therefore getting more surface in the same volume, or putting different things in the left and right hemisphere instead of duplicating them, thus enlarging its capacity to accommodate specific functions such as talking, reading or doing arithmetic operations or geometric rotations.

Now, let’s think of a blind person, what happens with the visual cortex? The answer is that a portion of its neural network is recruited for math. Brain plasticity is amazing and when a cortical region doesn’t do its duty, instead of getting relegated, is reused for other tasks, often very different to the original ones. This fact has been brought out in the investigation carried out by the team of Marina Bendy ¹. The goal of her research is to check if the numerical processing, which activates frontal and parietal lobes, is conditioned by the visual experience. It is well known that these two regions, as well as the intraparietal sulcus, are involved in the resolution of mathematical tasks. However, little was known about how the visual experience was determining the mathematical thinking.

We could theorize that for many math-related processes, sight has a crucial importance, e.g. equation solving, imagining numbers with is characteristic script –those Arabic signs–, operate with them, reading the statement of a problem, representing points in a Cartesian axis or even dare to attack higher mathematical issues. All of them seem to be very visual questions, but they are not, sight is not a sense that determines mathematical reasoning.

In this research an experiment with both people with congenital blindness and people without visual problems was performed. The sighted subjects were put a blindfold so that they were on equal circumstances. The activity consisted in the resolution of equations, orally asked, with different difficulty levels. It was observed with neuroimaging methods that the brain areas sensitive to these numerical tests were the same in both groups, frontal and parietal cortex and intraparietal sulcus. Therefore, mathematical thinking is not affected by visual experience. This conclusion would have justified an article by itself, but it was not the only novel finding in the research. The big surprise was that in blind people –but not in the control group– the visual cortex was activated during the “blindfolded” equation solving.

This unexpected conclusion, the activation of a portion of the visual neural network in blind people to address mathematical tasks, leads us to reflect about the character of the information input channel. Taking into account the abstract nature of mathematics it is easy to assume that a direct perception of what we want to know is not relevant, that is, in order to appreciate the details in a picasso it would be mandatory to see it, and to perceive all the information associated to the concept “apple” it would be appropriate to see it, smell it, touch it and even taste it. Hence, whatever sense we use to give entrance to the mathematical information, this doesn’t determine its subsequent processing. Sight can be used but hearing and touch (as in braille) are also valid. It’s true that the sensory modality implies differences. For instance, many objects –one hundred or more– can be simultaneously perceived through sight in one second, while the number of objects you can sense by hearing or touch is limited to ten or less in the same amount of time. A larger quantity of data can be processed by training the hearing ability, but this requires a sequential presentation. Still, the brain regions involved in mathematics are the same, regardless of the sensory modality giving access to the information.

Furthermore, some people believe blind people can have an outstanding competence in several fields of mathematics, such as geometry. The spatial ability of a sighted person is based on the brain analysis of a two-dimensional image, the projection of a three-dimensional world in the retina, while the spatial ability of a blind person is based on the brain analysis of the information acquired through other senses, such as touch and hearing. In both cases the brain creates flexible methods of spatial representations based in the information. Alexei Sossinsky ² writes “At first, the blind person who regains his sight does not distinguish a square from a circle: he sees only their topological equivalence. In contrast, he immediately sees that the torus is not a sphere”. Sossinsky points out that sighted people make mistakes due to that confusing and inadequate two-dimensional projection on the retina, while a blind person has a non-deformed, three-dimensional intuition of the space.

Back to the visual cortex neuron recruitment for mathematical aspects in blind people, will this connective enlargement imply any advantage? There’s no evidence of that, but it has been observed that the more complex the mathematical task is, the greater activity is shown by this region of cortical expansion.

It was already known that in blind people, part of this visual cortex is intended to answer to auditory and tactile stimuli, but the scope of the functional reorganization remains subject to study. In one hand, some examples of the plasticity in the visual cortex retain aspects of the original visual functions. For instance, the cortex region activated when a sighted person sees a moving object closely matches the response in blind people when a sound-emitting device is moving. Equally, the same neural network is activated when a person search something with his sight and when a blind person tries to locate a specific sound ³. On the other hand, the visual cortex in the blind population participates in high-level language tasks such as word remembrance and statement understanding ⁴. It was also found that this visual cortex responses to language coexist with the numerical response. Therefore, the results obtained by Bendy and her team suggest that the previously observed language-oriented plasticity is a part of a larger pattern that recruits part of the visual system in blind people to perform both language and mathematics superior cognitive tasks. The same goes for touch, since Cohen et al. ⁵ observed that these visual cortex areas showed synaptic activity when blind people read braille, but not when sighted people did it. The same brain areas involved in tactile discrimination were activated in both groups, but the visual cortex is also activated in the blind population; that is, sighted people actually only touch braille, but blind people also sees it. There’s a series of vacant neural processors, and they get recycled to solve complex tasks.

It is very tempting to assign a “pluripotent” role to the visual cortex in blind people and acknowledge it an extra processing function, but no research has shown rigorously this sort of superpowers. However, brain plasticity is highlighted again. We can learn during all our lifetime and the neural connectivity looks for unexpected paths to do it.

From outside the world of mathematics, there exists the common place that the notation of this discipline is very technical, and it is thought that this could create an insurmountable barrier for blind people. The truth is, that this forest of graphs, symbols, matrices and other thicket is a more accessible terrain, in some respects, to blind people. One reason is that in mathematics you read less because this writing is more compact. As Norberto Salinas, another blind mathematician, says “in math, you read a couple of pages and you have a lot of food for your brain”, Also, blind people often have a trained, useful imagination that can be applied to many tasks, including the mathematical ones.

Finally, the idea is to emphasize the concept of neurodiversity and its derivatives. In this text we have seen that the lack of a sense restructures the neural connectivity. In other cases, brains would be different and would develop other pieces in order to solve the puzzle. To respect and value neurodiversity is the essence of the inclusion.