“There are three types of mathematicians, those who can count and those who can’t.”

Bad joke? You bet. But what makes this amusing is that the joke is triggered by our perception of a paradox, a breakdown in mathematical logic that activates regions of the brain located in the right prefrontal cortex. These regions are sensitive to the perception of causality and alert us to situations that are suspect or fishy — possible sources of danger where a situation just doesn’t seem to add up.

Many of the famous etchings by the artist M.C. Escher activate a similar response because they depict scenes that violate causality. His famous “Waterfall” shows a water wheel powered by water pouring down from a wooden flume. The water turns the wheel, and is redirected uphill back to the mouth of the flume, where it can once again pour over the wheel, in an endless cycle. The drawing shows us a situation that violates pretty much every law of physics on the books, and our brain perceives this logical oddity as amusing — a visual joke.

The trick that makes Escher’s drawings intriguing is a geometric construction psychologists refer to as an “impossible figure,” a line-form suggesting a three-dimensional object that could never exist in our experience. Psychologists, including a team led by Catya von Károlyi of the University of Wisconsin-Eau Claire, have used such figures to study human cognition. When the team asked people to pick out impossible figures from similarly drawn illustrations that did not violate causality, they were surprised to discover that some people were faster at this than others. And most surprising of all, among those who were the fastest were those with dyslexia.

Dyslexia is often called a “learning disability.” And it can indeed present learning challenges. Although its effects vary widely, children with dyslexia read so slowly that it would typically take them a half a year to read the same number of words other children might read in a day. Therefore, the fact that people who read so slowly were so adept at picking out the impossible figures was a big surprise to the researchers. After all, why would people who are slow in reading be fast at responding to visual representations of causal reasoning?

Though the psychologists may have been surprised, many of the people with dyslexia I speak with are not. In our laboratory at the Harvard-Smithsonian Center for Astrophysics we have carried out studies funded by the National Science Foundation to investigate talents for science among those with dyslexia. The dyslexic scientist Christopher Tonkin described to me his sense of this as a sensitivity to “things out of place.” He’s easily bothered by the weeds among the flowers in his garden, and he felt that this sensitivity for visual anomalies was something he built on in his career as a professional scientist. Such differences in sensitivity for causal perception may explain why people like Carole Greider and Baruj Benacerraf have been able to perform Nobel prize-winning science despite lifelong challenges with dyslexia.

In one study, we tested professional astrophysicists with and without dyslexia for their abilities to spot the simulated graphical signature in a spectrum characteristic of a black hole. The scientists with dyslexia —perhaps sensitive to the weeds among the flowers— were better at picking out the black holes from the noise, an advantage useful in their careers. Another study in our laboratory compared the abilities of college students with and without dyslexia for memorizing blurry-looking images resembling x-rays. Again, those with dyslexia showed an advantage, an advantage in that can be useful in science or medicine.

Why are there advantages in dyslexia? Is it something about the brains of people with dyslexia that predisposes them to causal thinking? Or, is it a form of compensation, differences in the brain that occur because people with dyslexia read less? Unfortunately, the answer to these questions is unknown.

One thing we do know for sure is that reading changes the structure of the brain. An avid reader might read for an hour or more a day, day in and day out for years on end. This highly specialized repetitive training, requiring an unnaturally precise, split-second control over eye movements, can quickly restructure the visual system so as to make some pathways more efficient than the others.

When illiterate adults were taught to read, an imaging study led by Stanislas Dehaene in France showed that changes occurred in the brain as reading was acquired. But, as these adults developed skills for reading, they also lost their former abilities to process certain types of visual information, such as the ability to determine when an object is the mirror image of another. Learning to read therefore comes at a cost, and the ability to carry out certain types of visual processing are lost when people learn to read. This would suggest that the visual strengths in dyslexia are simply an artifact of differences in reading experience, a trade-off that occurs as a consequence of poor reading in dyslexia.

My colleagues and I suggested that one reason people with dyslexia may exhibit visual talents is that they have difficulty managing visual attention. It may at first seem ironic that a difficulty can lead to an advantage, but it makes sense when you realize that what we call “advantages” and “disadvantages” have meaning only in the context of the task that needs to be performed.

For example, imagine you’re looking to hire a talented security guard. This person’s job will be to spot things that look odd and out of place, and call the police when something suspicious —say, an unexpected footprint in a flowerbed— is spotted. If this is the person’s task, would you rather hire a person who is an excellent reader, who has the ability to focus deeply and get lost in the text, or would you rather hire a person who is sensitive to changes in their visual environment, who is less apt to focus and block out the world?

Tasks such as reading require an ability to focus your attention on the words as your eyes scan a sentence, to quickly and accurately shift your attention in sequence from one word to the next. But, to be a good security guard you need an opposite skill; you need to be able to be alert to everything all at once, and though this isn’t helpful for reading, this can lead to talents in other areas. If the task is to find the logical flaw in an impossible figure, then this can be done more quickly if you can distribute your attention everywhere on the figure all at once. If you tend to focus on the visual detail, to examine every piece of the figure in sequence, it could take you longer to determine whether these parts add up to the whole, and you would be at a disadvantage.

A series of studies by an Italian team led by Andrea Facoetti have shown that children with dyslexia often exhibit impairments in visual attention. In one study, Facoetti’s team measured visual attention in 82 preschool children who had not yet been taught to read. The researchers then waited a few years until these children finished second grade, and then examined how well each child had learned reading. They found that those who had difficulty focusing their visual attention in preschool had more difficulty learning to read.

These studies raise the possibility that visual attention deficits, present from a very early age, are responsible for the reading challenges that are characteristic of dyslexia. If this theory is upheld, it would also suggest that the observed advantages are not an incidental byproduct of experience with reading, but are instead the result of differences in the brain that were likely present from birth.

If this is indeed the case, given that attention affects perception in very general ways, any number of advantages should emerge. While people with dyslexia may tend to miss details in their environment that require an attentional focus, they would be expected to be better at noticing things that are distributed more broadly. To put this another way, while typical readers may tend to miss the forest because it’s view is blocked by all the trees, people with dyslexia may see things more holistically, and miss the trees, but see the forest.

Among other advantages observed, Gadi Geiger and his colleagues at MIT found that people with dyslexia can distribute their attention far more broadly than do typical readers, successfully identifying letters flashed simultaneously in the center and the periphery for spacings that were much further apart. They also showed that such advantages are not just for things that are visual, but that they apply to sounds as well. In one study, simulating the sounds of a cocktail party, they found that people with dyslexia were able to pick out more words spoken by voices widely-distributed in the room, compared with people who were proficient readers.

Whether or not observations of such advantages —measured in the laboratory— have applications to talents in real life remains an open question. But, whatever the reason, a clear trend is beginning to emerge: People with dyslexia may exhibit strengths for seeing the big picture (both literally and figuratively) others tend to miss. Thomas G. West has long argued that out-of-the-box thinking is historically part and parcel of dyslexia, and more recently physicians Brock and Fernette Eide have advanced similar arguments. Sociologists, such as Julie Logan of the Cass Business School in London agree. Logan found that dyslexia is relatively common among business entrepreneurs; people who tend to think differently and see the big picture in thinking creatively about a business.

Whatever the mechanism, one thing is clear: dyslexia is associated with differences in visual abilities, and these differences can be an advantage in many circumstances, such as those that occur in science, technology, engineering and mathematics. In physics we know that an engine is capable of productive work only when there are differences in temperature, hot versus cold. It’s only when everything is all the same that nothing productive can get done. Neurological differences similarly drive the engine of society, to create the contrasts between hot and cold that lead to productive work. Impairments in one area can lead to advantages in others, and it is these differences that drive progress in many fields, including science and math. After all, there are probably many more than three kinds of mathematicians, and society needs them all.