By Berit Brogaard and Kristian Marlow
Mark Aarøe Nissen is a 22-year-old math student at Aarhus University, Denmark, with extraordinary memory abilities. He has competed in memory sports for several years. He can recite the number Pi to more than 20,000 decimal points, recall thousands of names, faces and historical dates and remember the order of a pack of cards.
For those of us who can barely remember the items on a grocery list, these extraordinary memory skills might seem savant-like. Mark laughs as we make this suggestion. “That’s nonsense. I am not a savant,” he insists. “It’s not something that just comes to me. I use advanced systems and algorithms to accomplish what I do.”
When Mark first began remembering Pi he took the digits and converted them into shapes. He used shapes of objects from the real world: humans, animals, fruits. “The number 13 used to be the shape of an apple and 32 used to be fire,” Mark explains. Once he had memorized the shapes, he planted them in imaginary but familiar landscapes: His childhood home, the university, downtown Aarhus in Mark’s hometown, that vacation spot down at the Reviere at the south coast of France.
Today Mark remembers exactly ten thousand shapes each representing a four-digit number. When he needs to recall a number he walks through the landscape and then he sees the shape and the number pops into his mind. For example, he might see an apple and the number 13 pops into his mind. Finding his way through the landscape is simple, he says. “It’s just like following a route you know, for instance, the route from your home to your workplace.”
Emotions play an important role in recalling numbers, cards and names. Mark actually spots the emotion first and then constructs the shapes from what he is feeling. This technique is extremely powerful, Mark tells us, because the emotion in some sense is intrinsic to the shape. For example, if you see a waterfall of milk in the kitchen, that will trigger a feeling of absurdity. If you see broken glass in the living room, that will give rise to a feeling of discomfort.
In order to imagine Pi Mark has a particular route through the landscape that initiate an emotion in him which then gives rise to a mental image.
Concerned about our inability to remember simple grocery lists Mark quickly adds that his method also can be used to remember lists. Next time you go to the store, leave the iPhone at home, he says. Suppose you want to remember a grocery list that has the following items on it: milk, a bottle of red wine and oranges. Now place the milk in the kitchen, the wine in the living room and oranges outside. Then add the different feelings and associations. In the kitchen you might see a waterfall of milk. This may give rise to a feeling of absurdity or pleasure. In the living room you can imagine that the bottle of red wine cracks on the floor. This will trigger a feeling of instability. As you are walking through the aisles of the store, you start your mental journey in the kitchen. There you are hit with a feeling of absurdity and see a waterfall of milk. As you walk into the living room you suddenly have this uncomfortable feeling of instability. You see the broken glass on the floor and remember to pick up wine. You continue this way until you are done.
When Mark competes in memory sports he uses a headset that blocks out sounds. Some use special glasses to block out peripheral visual input but Mark doesn’t find that necessary. He naturally goes into his own world of emotions, shapes and landscapes.
Mark has once attempted to beat the current European record in reciting Pi to the greatest decimal point. The current record is held by Daniel Tammet, the author of the bestseller Born on a Blue Day: Inside the Mind of an Extraordinary Autistic Savant. Tammet won the European championship with 22,514 decimal points on International Pi Day (March 14) in 2004.
Regrettably, Mark didn’t succeed. After reaching the 17,108th decimal point, he wrote 48 when it should have been 84. He immediately realized that he had made a mistake and stopped the process. We asked Mark why he thought he made the mistake. “Concentration,” he replied. “After hours and hours of writing down digits of Pi, your brain just stops focusing. It’s a bit like hitting the wall in a marathon.” The wall occurs around 20 miles as a physiological response to carbohydrate deletion. Most new marathon runners have heard of it but don’t expect it. “Marathon wall. Yeah, well. If I see one I will break through it or climb over it,” they will say. Then after 20 miles they start to realize what it really means to hit the wall. The legs start tingling until they become almost numb. Then the pain sets in. Red hot lead inside the legs. For Mark it wasn’t quite that bad. But it only takes a fraction of a second to lose concentration and screw up.
Both Mark and Tammet have some way to go before they reach the superhuman abilities of Chao Lu, who holds the Guinness world record in reciting Pi dating back to 2005. Lu recalled 67,890 digits of pi in 24 hours and 4 minutes with an error at the 67,891st digit, saying it was a 5, when it was actually a 0. Most of us have experienced fatigue after a few hours of standardized testing. It’s a bit difficult to contemplate the mental and physical fatigue Lu must have gone through during this day-long recall exercise.
Though Mark can recite pi to the 20,000th decimal points, his favorite memory discipline is not reciting Pi but counting cards. “I can easily beat BlackJack,” he says, “it mainly requires counting cards and then bidding in the right way. It’s not that hard.” When Mark told us this, we both immediately tried to convince him to join us at some casinos to make some quick cash, but he didn’t go for it. “For me, this is a sport, not a way to make money,” he replied sternly. It seems that this memory superhero will only use his powers for good.
Realizing we weren’t going to get Mark to join us on a tour de Casinos, we wanted to know whether we could pick up these skills ourselves. Whether everyone can do what Mark does, however, is a difficult question. Mark believes everyone can improve their memory by using good memory techniques, but there may be differences in people’s abilities. “And even if you do have the underlying abilities,” Mark kindly explains, “don’t expect to beat Blackjack at the the river casino tomorrow. It takes hours and hours of practice. You wouldn’t have the time to do it.”
For Mark, however, it wasn’t just practice. Interest also played a crucial role. He has always been obsessed with memorizing things. He found memory sports exciting even as a small child. Most of his peers were interested in soccer and outdoor play. Mark was more of a geek. Though he played soccer (all Danes do), he was intensely focused on his memory games and when he didn’t attend soccer practice he would tend to sit in his room figuring out how to memorize things, such as long strings of numbers or the cards in a deck of cards.
Mark’s second favorite memory game is binary number games. Binary number systems are the systems used in programing language. Put a bunch of zeros and ones next to each other and you get a very large number. These languages may be hard to learn, but they are easy to remember, says Mark. You can remember more using a binary system. When Mark sees three binary numbers, he knows exactly what number it is. So there is a sense in which he can remember three times as many binary numbers as he can remember numbers in the ten-digit system.
Ugh, "genius" again
Despite his extraordinary memory skills Mark hesitates to call himself a savant. He doesn’t really believe that there are all that many true savants, as the word is normally construed. “In most cases it’s a matter of learning the right techniques, not about the surfacing of some inner genius, as the media would have it.” Mark thinks terms like “savant” and “genius” often are misused. “People are fascinated by the apparently mysterious abilities people have. So people decide to make some money off of this fascination.”
Antwerp philosopher Carolyn Dicey Jennings concurs: “To me, there is little worse praise than ‘genius’," she says. “The root of the word, shared with 'genie', signifies a magical, impossible to understand element, brushing aside the hard work under the miraculous rug of some innate talent, some God-given gift.”
Carolyn herself is a humble person. She grants that she hasn’t been called “genius” a whole lot. But that doesn’t make her feel much better “since now I can never reach their stature. How could one climb what is divine? When someone uses the word ‘genius,’ they are asking you to kneel. I find this request revolting. Whatever happened to determined effort? To the strength of the collective? Whatever ‘genius’ is, it has nothing to do with these. And so I not-so-humbly request: look to the hours, attend to what is added, praise the support that has enabled this accomplishment. Do not reduce us all by giving it away.”
As Mark expresses his doubts about self-proclaimed savants and the people who exploit the folk’s fascination with them and Carolyn asks us to look at the hours and raise the support that has enabled the prolonged effort, we start to feel a little bit guilty.
But it’s not primarily authors like us that Mark and Carolyn are critical of. Mark thinks self-proclaimed savants practice their uncanny skills more than we think. “Daniel Tammet uses techniques that are very similar to those other people competing in memory sports use,” Mark says. “It’s not magic.”
We reminded Mark that Tammet isn’t just a savant but also a synesthete. There is no algorithm you can follow to become a synesthete. However, Mark thinks Tammet’s synesthesia is self-taught. “He probably intentionally associated color, shape and texture with numbers and after doing this for many years, it became automatic. Memory, too, is responsible for automatization of this connection.”
This also applies to Tammet’s amazing language skills, Mark says. As shown in the famous documentary The Boy with the Incredible Brain, Tammet learned Icelandic in a week. But even language skills require memory, Mark reminds us. Learning a language fast is a matter of memorizing certain grammatical rules and lexical entries. People who are used to competing in memory sports can do this very fast.
Joshua Foer, the author of Moonwalking with Einstein: The Art and Science of Remembering Everything, agrees with Nissen that Tammet uses memory techniques similar to those of other memorists. When Foer asked Tammet to multiply three numbers with three numbers, Foer reports that he could see Tammet’s hands move on the table. “He does something very strange with his hands and that’s normal for people who multiply numbers in their mind,” says Mark.
Mark mentions that Tammet used to compete in disciplines where you have to remember faces. “He remembered a lot of faces in a very short time, which is unusual for a person with autism,” Mark says, “Of course, autism is really a spectrum disorder, so having this ability doesn’t rule out that he has some autism spectrum disorder.” Mark, however, would like to know why Tammet keeps it a secret that he used to compete in face recognition games. “He had a different name back then. About ten years ago he changed his name from Daniel Corney to Daniel Tammet and announced that he was an autistic savant. Joshua Foer later tested him on remembering faces and suddenly he couldn’t remember any faces. That’s just a bit weird."
The Number Sense
The sentiments expressed by Carolyn Dicey Jennings and Mark Nissen are not new. French psychologist and cognitive neuroscientist Stanislas Dehaene, who has conducted influential research on how the brain processes numbers, thinks that the biological basis of mathematical savant skills is obsession with numbers.
According to Dehaene, there are two kinds of number manipulations that we all engage in. In most of our daily tasks we make approximations. When driving down the highway during rush hour and we decide to change lane, we don’t count the cars in each lane and then make a decision. We simply note that there are fewer cars in the other lane and then we make a move, sometimes to the dismay of fellow drivers. Non-human animals can do this almost as proficiently as we can.
We don’t really use much exact mathematics in everyday life. When we learn to do exact calculations and other exact manipulations of numbers in school, we learn it by memorizing certain basic facts and algorithms.
Our brains don’t normally consciously represent this type of exact math. The reason for this, Dehaene says, is that our brain normally converts number words (one, two, three, ...) and Arabic numerals (1, 2, 3,...) into conscious representations of quantities of things. The brain processes 3 as a quantity of three things. Of course, we don’t read the word “three” and then three bananas show up in our heads. It may be very schematic. But the way we understand numbers is similar to the way we visualize quantities of things.
It is easy for us to visualize small quantities. Think of three bananas. Piece of cake. Five. Not too hard. Ten. Now it’s starting to get difficult. 104. Impossible. The larger the number is, the fuzzier the representation. So, there is a clearer representation of 3 in the brain than there is of 104.
This way of representing numbers is a product of evolution, says Dehaene. The best survivors were those who could provide good approximations of numerical difference and sameness. Our ancestors didn’t need exact numbers in order to decide whether to fight or run when faced with danger. Whether they were faced with 103 or 106 dangerous animals would not affect their decision to escape.
The way that the human brain represents numbers, Dehaene says, severely limits its mathematical potential. Owing to our evolutionary history, we do not have the potential to do exact calculations very fast, though memory can contribute to the speed of calculations.
Dehaene acknowledges that many people with savant syndrome appear to present a counterexample to this theory of how the brain processes numbers. If savants have the ability to calculate numbers accurately with lightning speed, then his theory does not apply to them.
Dehaene, however, believes the difference in abilities between people with savant syndrome and normal individuals is a function of a difference in training and interest. Savants have more training than most of us. They have learned a few tricks. What differs between them and us is that they are more obsessed with numbers and devote more of their time to study numbers and math than “normal individual”. As Dehaene puts it in his book The Number Sense:
Talented people succeed largely because they devote a considerable time, attention and effort to their topic of predilection. Through training, they develop well-tuned algorithms and clever shortcuts that any of us could learn if we tried, and that are carefully devised to take advantage of our brain’s assets and get around its limits. and get around its limits. What is special about them is their disproportionate and relentless passion for numbers and mathematics – a passion which is occasionally of pathological origin, as clearly seen in retarded autistic children with calculation skills. Training experiments indicate that, with a similar amount of training, normal subjects can also enhance their memory and calculation speed (The Number Sense, 2001: 14)
Dehaene thus agrees with Mark that people like Daniel Tammet, who can calculate as fast as a calculator, appear to be doing magical calculations because they have memorized algorithms and have a strong interest in practicing. If this is true, savants are not all that different from the rest of us.
Why don’t we all walk around as living calculators?
But if the majority of us can learn to speed calculate insanely high numbers, why don’t we all walk around as living calculators? Why can’t we beat Daniel Tammet’s European record in reciting Pi from memory to 22,514 digits in five hours and nine minutes? Why don’t we challenge the computing twins Kay and Flo, who can tell you what their favorite television host was wearing on any date you give them, to a memory game?
Daehene offers part of the answer. Most of us are too busy doing all kinds of other things or we simply lack the interest in excelling in this kind of activity much to casino owners’ fortune. We may have various interests and obsessions but most of us are not obsessed with numbers, complex geometrical patterns or the color of the television host’s shirt over the past 3,000 days.
There is another important difference between normal individuals and savants. While most of us can, and sometimes do, learn to imitate savants by using algorithms to speed calculate, we tend to continue to be aware of the method they are using. While the skill can become more automatic over time, normal individuals do not normally reach a result without knowing how they reached it. They are conscious of the method and the steps required to get to the result.
At least in some cases, the brains of people with special mathematical abilities make calculations that are not themselves consciously accessible, even though the result is. Tammet reports that he is not conscious of how the mathematical calculations he performs are carried out in his brain. He provides the input and receives the output in the form of a colorful three-dimensional figure that he can translate into a number.
Likewise, acquired savant Jason Padgett receives information about the elaborate mathematical patterns he is seeing and drawing through vision but he is not aware of the calculations his brain is making before producing the mathematical geometrical shape. He turns his eyes toward something and receives the output in the form of a complex mathematical shape. As Jason puts it, “my conscious brain is a receiver of the result of the calculation made by my unconscious brain.” Even Mark Nissen, who denies being a savant, uses imagery to access numbers stores far outside of his conscious awareness.
There are, of course, physical and biological limitations to our brain’s abilities to calculate. But the main limitations of the human brain appear to be limitations to our conscious abilities and limitations imposed by dominant brain regions. We cannot consciously make hugely complex calculations in our heads or perform calculations that spit out a fractal in our field of vision.
It is unlikely that savants are born with a special mathematical organ that predisposes them to be fast calculators. But even if savant syndrome is not genetically encoded and is not the result of a special math faculty, it is probably something over and above extensive training and good memory. The fact that savant syndrome can be acquired after a hard hit on the head suggests that the right kind of brain organization is needed for savantism to develop. But owing to the plasticity of the brain, it is plausible that brain regions common to all of us can develop into “special math organs”.
Which regions of the brain have this potential? The most likely answer is that its the regions that normally prepare us for action, sometimes called “the vision for action pathway,” or dorsal stream. The brain’s action pathway compute exactly how far we have to move to reach to an object. It calculates the path your arm has to make to reach to the object. It calculates the size of the grip aperture. And so on. But while we usually are aware of the movement taking place, we are not aware of these complex calculations. We cannot answer questions about the size of our grip aperture or the precise path our hand has to take to reach to an object--we can merely demonstrate it.
Even when we are not consciously aware of changes in object size, we still adjust our hand apertures to fit the object. If an object suddenly changes location, corresponding adjustments in hand velocity and trajectory are made in less than 100 ms, which is not enough time for the human brain to consciously represent the adjustment of object location or the corresponding change in hand velocity and trajectory.
Studies have further shown that when study participants are asked to use a minimally demanding vocal response (Tah!) to signal their awareness of a change in object location, modification of movement occurs significantly faster than the vocal response. Adjustments of trajectory and hand aperture occur within 100 ms, whereas the vocal response occurs after 420 ms. This may be why if we think too much about our action in killing a fly we behave more slowly than if we just reacted to the fly.
It seems then that the action pathway is a brain region that can make calculations before we even have a chance to become aware of them. Most of these calculations never reach our conscious awareness. People with special math skills have a way of tapping into the unconscious mathematical calculations. Like most of us, they are not typically aware of the calculations taking place but sometimes the calculations reach conscious awareness in different ways. For example, in Jason Padgett’s case, they reach his consciousness in the form of complex mathematical patterns. In Mark Nissen's case, they reach consciousness by being recallable through emotions and images.
Mark is in some sense right. We all have the superhuman abilities inside us but we cannot always tap into them. Sometimes they remain hidden from sight forever, sometimes they remain hidden until someone beats us up or we bang our head against a corner of a swimming pool. It may not be as glamorous as a radioactive spider bite but even these superhuman abilities have their own origin story.