A Case of Acquired Savant Syndrome and Synesthesia Following a Brutal Assault Berit Brogaard January 12, 2011
0. Introduction “Everything that exists has geometry”, says JP, who acquired amazing mathematical abilities after a mugging incident in 2002. He was hit hard on the head, and he now experiences reality as mathematical fractals describable by equations. Light bouncing off a shiny car explodes into a fractal overlaying reality, the outer boundaries of objects are tangents, tiny pieces that change angles relative to one another and turn into picture frames of fractals during motion, and the boundaries of clouds and liquids are spiraling lines. Before the incident JP was no whiz at math. He copied most of the answers on his geometry exam in high school and never had much interest in the subject matter. He went to college but never finished. He worked in sales for a few years and then moved onto a furniture store that sells furniture manufactured by his father. The mugger’s stroke ostensibly changed the architecture of JP’s brain. After an introspective period lasting three years, he started drawing what he saw right in front of his eyes. The results were amazing, a series of hand-drawn approximations of mathematical fractals, the first of their kind. Mathematicians and physicists were taken aback: Some of JP’s drawings depict equations in math that hitherto were only presentable in graph form. Others depict actual electron interference patterns. This is the first scientific report on JP's condition. A functional MRI is in progress. The present report is based on existing medical data and non-invasive testing and interviewing. I offer an assessment of his condition. I then suggest that his case provides a counterexample to Stanislas Dehaene’s hypothesis that people with savant syndrome are more adept at understanding mathematics or performing difficult operations, not because they were equipped with a distinct brain architecture, but because they have more training owing to their inherited or acquired passion for the subject matter (Dehaene 1999, 2001). Finally, I suggest that JP’s case may offer some clues about the biological basis of complex mathematical operations in people with synesthesia and savant syndrome.
1. Acquired Synesthesia and Savant Syndrome Following a Mugging Incident: A Case Report On Friday September 13, 2002 JP, who was 32 at the time, and his date left a restaurant. Two guys were behind them. Shortly thereafter JP was hit on the back right side of his head between the ear and the beginning of the vertebra, "where it feels like the cranium is attached to something else". JP lost consciousness for a second and the next thing he remembers is that he was on the ground on his knees. At first, he didn’t realize he was being attacked. He was hit 1
again on the right side of the head. At this point he realized that he was being attacked. He reached out for the guy’s legs, yanked them away under him, bid the guy’s leg and grabbed his crotch and squeezed as hard as he could. The guy screamed and the other guy started kicking JP. They wanted his jacket. They thought his wallet was hidden there. He gave them his jacket. The guys left. Later in the emergency room, JP was examined and X-rays were taken. He was diagnosed with a bleeding kidney and a concussion and sent home to rest for a few days. From that moment JP realized that something was unusual. Reality was fragmented. All the edges of things were sliced into small pieces or tangents. When he moved or watched an object move, patterns would form. The little light bouncing off of a car window or the car’s shiny paint on a sunny day would explode into an array of triangles. He thought that maybe he was going crazy. He stayed inside his house for three years, isolated. He would leave only if it was absolutely necessary. This was his "introspective time", he says. Two regular MRIs were done during the subsequent three years, one to check that JP didn’t have a brain tumor and the other to check an area of his neck that had suffered from the incident. He subsequently had Platinum metal plates inserted in his neck. In 2005 JP thought he would try to draw what he saw when light bounces off of a car window. He drew a sloppy picture of a “circle” made out of triangles and instinctively called it “Pi”. "You can't draw a perfect circle", JP explained to his mother, "all you can do is fill in more and more areas". "Hence Pi goes to infinity" his mother said. That’s when it clicked. JP realized that what he was seeing in the light flashes in car windows or the shiny paint of cars on a sunny day was Pi. The first drawing of Pi was sloppy. Someone who saw the drawing mentioned that it actually could be quite amazing if only he used a ruler and a compass. JP then made a drawing of Pi with a ruler and compass (Fig 1, 2). The result was amazing. He didn’t know what it meant. But he instinctively knew it was important. He later realized his drawing represents an equation and proved it (Fig 3). Pi is the ratio of the perimeter, Pn, of a regular polygon with n sides circumscribed around a circle with diameter d to d, as n increases to infinity. With n = 6 (a hexagon), we get 3. With n = 360, we get 3.141552779, and with a higher n, we get an even better approximation. Regardless of how high we set n, we will never quite get Pi, because Pi is a limit. As JP points out, the problem of getting the exact value of Pi is similar to the problem that Mandelbrot had with measuring the perimeter of a coastal line. The smaller the yardstick you use the longer the perimeter, and if you were to keep making the yardstick smaller, you’d have an infinite perimeter. This is also known as the “Yardstick Problem”.
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Figure 1: Pi drawing as it was being drawn
Figure 2: Pi © Jason Padgett
Sometime after JP begun drawing, he had started working in a furniture store, and he was eager to show his drawings to people. He realized that while people thought his drawings were fascinating, most people didn’t understand what he said about them. A mathematician told him that he had to learn to speak the language of mathematics if he wanted to make himself understood. He then went and took a trigonometry class and a couple of calculus classes at a local community college. This made him realize that his drawings depicted approximations of 3
mathematical fractals. In 2010 JP won Best International Newcomer in the Art Basel Miami Beach competition.
Figure 3: Last page of the proof that the drawing represents Pi
2. Synesthesia and Savant Syndrome JP never received an official diagnosis of his condition. An assessment of his symptoms, however, suggests that he has synesthesia, savant syndrome, OCD and atypical function of areas in the occipitotemporal intersection.
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Synesthesia: Synesthesia is a relatively rare neurological condition in which stimulation in one sensory or cognitive stream involuntarily leads to associated experiences in a second unstimulated stream (Cytowic 1989). The most common form of synesthesia is grapheme-color synesthesia, in which numbers or letters are seen as colored. But lots of other forms of synesthesia have been identified. One of the marks of visual synesthesia is that images are either seen as projected out onto the world or in the mind's eye (Dixon et al. 2004). Another mark of synesthesia is that synesthetic experience show test-retest reliability (Baron-Cohen 1987, Eagleman 2007): Colors, shapes or other attributes identified by the subject as representative of her synesthetic experiences in the initial testing phase are nearly identical to colors, shapes or other attributes identified by the subject as representative of her synesthetic experiences in a retesting six months later. Though JP’s synesthetic experiences are unusual, they satisfy the test-retest criterion. He consistently reports that light sparkling off solid things explodes into mathematical fractals overlaying reality. Other common triggers of his synesthetic experiences include water draining, water dripping into water and an airplane disappearing into a cloud. JP sees the fractals projected out in front of his eyes with little changes over the years and hence appears to satisfy the criteria for (acquired) projector synesthesia. Acquired synesthesia is rare. A case has been reported in which a woman acquired synesthesia following a stroke (Beauchamp and Ro 2008) but in far the most cases synesthesia is an inherited developmental condition. Visual synesthesia has other typical characteristics besides the experience of overlaying or imagery and test-retest reliability. Evidence indicates that lower color synesthesia is closer phenomenally to visual perception than it is to visual imagery. fMRI studies of synesthetic experience and imagery do not reveal any difference between the two: Striate (V1) areas and the color complex V4/V8 are activated in visual imagery in normal people (Cattaneo et al, 2009, Tong 2003) and in color synesthesia (Aleman et al, 2001, Nunn et al 2002, Hubert et al 2005, Sperling et al 2006). However, a recent study indicates that brightness and brightness contrast are greater in visual synesthetic images than in normal visual imagery.1 The study involved 85 color synesthetes and 233 controls. Both controls and synesthetes were shown a colorful photograph and were then instructed to close their eyes and visualize the image (Fig. 4). After opening their eyes they were shown a series of copies of the original photo with varying brightness or brightness contrast. The subjects were instructed to choose the one photo that they judged to be most similar to the original in terms of brightness or brightness contrast. Synesthetes were furthermore asked to choose a photo as exemplary of their synesthetic images in terms of brightness or brightness contrast. It was found that in 82% of synesthetes the brightness or brightness contrast of synesthetic images was greater than the original photographs and in 74% of controls the brightness or brightness contrast of visual images was lower than in the original photographs. 1
The initial data were presented at NYU at the workshop “The phenomenology of synesthesia” on November 20, 2010.
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Fig 4. Example of contrast variation photos. Left, original, 50%, 75%. Right, 25%, 50%, 75%.
JP's synesthetic experiences exhibit a similar feature. While JP has normal hue processing, he describes many of his synesthetic images as exploding from flashes of light and excessive brightness.
Savant Syndrome: Savant syndrome is a condition in which a person has a talent that is so developed that he can perform what may seem like impossible mathematical, linguistic or artistic tasks. According to Darald A. Treffert, savant skills occur in a very narrow range of abilities (Treffert 2009). Far the most typical ones are: Music: Piano performance or composition with perfect pitch. Example: Blind Tom, a blind autistic slave in Georgia in the nineteenth century, was an amazing pianist and performer. Art: Drawing, painting, or sculpting. Example: Stephen Wiltshire drew an extremely accurate sketch of a four square mile section of London, including twelve major landmarks and two hundred other buildings after a twelve minute helicopter ride through the area. Calendar calculation: The ability to name the day of the week that a certain date or event will or did occur in any particular year or to name all the years when a specific holiday will fall on a specific date. Example: for any chosen calendar day, the human computers and autistic twins Kay and Flo Lyman can report what they ate for dinner, what they did on that day, what weekday it was, what their favorite TV-host wore on that day, and so on. 6
Mathematics: Lightning calculation, geometrical acumen or computation of multi-digit prime numbers, in the absence of other special arithmetic abilities. Example: Oliver Sacks’ autistic twins John and Michael computed prime numbers with more than 6 digits (Sacks 1985). Spatial skills: Distance measurements or construction of complex structures with painstaking accuracy. Example: the real rain man Kim Peeks was able to provide map directions between any two cities (Peek 2005).
Savant skills tend to be right-brain or bilateral skills. For example, mathematical skills likely involve bilateral processing in the intra-parietal sulcus (Dehaene 1999, 2001, 2007, Dehaene et al, 1998, 2004, Piazza et al 2007, Eger et al 2009, Hubbard et al. 2009), and spatial reasoning skills involve right-hemisphere processing in superior temporal cortex, the regions on the right that corresponds to the language area on the left (Karnath et al. 2001).
Figure 5: Hand-drawn fractal 4/7th done © Jason Padgett The leading hypothesis is that savant syndrome is caused by a lesion or birth defect in the left hemisphere that results in overcompensation by the right hemisphere (Pesenti et al. 2001). An alternative, but related, hypothesis is that we all have the skills of savants but that they are dormant because of the dominance of the left hemisphere in most people (Snyder et al. 2003, Young et al. 2004). In some people with savant syndrome the dominance is weakened by an absence of information transfer between hemispheres. For example, an MRI scan of the artistic savant, Kim Peek, who lent inspiration to the fictional character Raymond Babbitt, played by Dustin Hoffman, in the movie Rain Man, revealed an absence of the corpus callosum, the anterior commissure and the hippocampal commissure, the parts of the neurological system that transfer information between hemispheres (Wisconsin Medical Society, Islands of Genius).
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The brain can also transfer information indirectly through subcortical areas. It is unknown whether any information was transferred between hemispheres in Kim Peek’s brain. However, in most cases the dominance of the left hemisphere is weakened by a lesion to the left hemisphere. Savant syndrome is typically accompanied by severe developmental disorders, usually autism. In the largest study of savant syndrome today, 41 out 51 subjects had been diagnosed with autism (Treffert 2009). But there are also cases in which savant syndrome occurs without any associated disability and cases in which it is acquired later in life, following central nervous system injury or disease (Lythgoe et al, 2005, Treffert 2009). For example, Daniel Tammet (DT), a young man with savant syndrome, can perform mathematical calculations faster than most people can on a calculator (Bor et al. 2007). Though there is some evidence that DT has some degree of autism, this is far from obvious, and it certainly is not the cause of any disability. DT is capable of living a quite normal life with his male partner, while also appearing on television and participating in science experiments. He can speak 10 languages, some of which he learned in the course of a few days. DT may be an example of a person with acquired savant syndrome, as he reports that his extreme mathematical abilities kicked in after a series of seizures he had when he was four.
Figure 6: Prime number vectors ©Jason Padgett
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JP fits the standard characterization of savant syndrome. His savant skills fall into three groups: Artistic, mathematical and spatial. JP had taken some college courses before the incident: accounting, micro- and macro-economics. But he never took a college math course. In fact, he never finished college. His last math course prior to the incident was a geometry course in highschool where he copied most of the answers on the final exam. Prior to the attack JP scored less than 100 on a standard IQ test and had no artistic abilities. He couldn’t even draw a decent picture in the popular game Pictionary. Despite his lack of prior training, JP is the only person in the world to have ever handdrawn meticulously accurate approximations of mathematical fractals using only straight lines. He can predict the vectors for prime numbers in his drawings, and his drawing of hf = mc2, which contains all the style elements of his earliest drawings, is remarkably similar to an actual picture of electron interference patterns, which he found years after first drawing the pattern (see Fig 7, 8). Like other individuals with savant syndrome and highly specialized artistic skills, JP reached top scores on spatial ability tests, a standard component of many IQ tests, after the incident.
Figure 7: Actual picture of electron interference patterns
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Figure 8: hf = mc2 © Jason Padgett
Obsessive-Compulsive Disorder: The DSM IV criteria for obsessive-compulsive disorder (OCD) require sufferers to have either intruding thoughts or images that provoke anxiety, or repetitive behaviors or mental acts that help to prevent anxiety. It is furthermore required that the sufferer sees the thoughts or behavior as excessive and unreasonable. JP has been officially diagnosed with OCD, a common finding in people with savant syndrome (Treffert 2009). He is obsessed with numbers and fractals. His occupation with the subject-matters is deeper, more involved and extends for longer time each day than typical hobbies. When he tries to think or concentrate on something else, his mind immediately goes back to thinking about numbers and fractals. Sometimes he finds himself counting steps or intensely studying the shapes of the leaves on a tree. Drawing what he sees soothes him. JP is also obsessed with germs. He cannot stand when people breathe on him or touch him. If people breathe on him, it feels hot and causes convulsion. He immediately feels the need to wash. JP used to be extremely social and is still able to be social but now he has a constant need to withdraw. The mugging incident left JP with a form of chorea that involves involuntary, irregular muscle twitches and muscle jerks. Other causes such as tumors and spinal cord injuries were ruled out as a cause of the muscle twitches, leaving chorea as the most likely condition to cause the twitches. JP’s OCD may be indirectly associated with the muscle twitches. OCD correlates with hyper-production of the neurotransmitter dopamine in the basal ganglia and decreased production of serotonin (Kim et al. 2003). As chorea sometimes correlates with elevated dopamine levels (Newman et al. 1985), JP’s high dopamine levels could be a cause of the muscle twitches.
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Atypical Responsiveness in Occipitotemporal Areas: JP sees the boundaries of objects as sliced up into pieces or tangents and the boundaries of liquids and clouds as spiraling lines (Fig. 8). He never sees a smooth path. This condition resembles apperceptive agonosia in that his brain processes the boundaries of objects differently from most people. JP’s brain never creates a smooth line on the basis of the tangent lines he experiences. Upon further scrutiny, however, it is clear that this condition is not a form of visual agnosia. In apperceptive agnosia, subjects are unable to use standard Getalt grouping principles (e.g. similarity, continuity or symmetry) to generate a boundary that will reveal the object’s identity (Milner et al 1991, McIntosh 2004, Karnath et al. 2009). They are unable to detect a visual boundary between object and background. Because they cannot establish an edge between object and background, they cannot draw what they see.
Figure 9: Quantum Seashell © Jason Padgett
JP’s condition is not even remotely similar to apperceptive agnosia. He is clearly able to use Gestalt grouping principles to establish the frontier between object and background. Even though the boundaries of objects are fragmented, they stand out bright and solid from the background. The boundary he sees differs from the boundary we see but he can draw this boundary in ever so many details. Nor is JP’s agnosia a kind of associative agnosia. Associative agnosia is a disorder in which early stage perceptual processing is intact but high-level perceptual processing is impaired. Associative agnosia patients have lesions to the parts of the posterior cerebral artery supplying blood to the temporal lobe and to parts of the visual cortex but have no lesions to areas of the parts of the brain involved in cognitive processing (the prefrontal cortex, parts of the limbic system (hippocampus) and the basal ganglia). So, they have visual sensations and 11
cognitive processing but they are unable to recognize what kind of object is in front of them. For example, they cannot say on the basis of vision whether the object in front of them is a cat or a dog. JP’s ability to recognize what kind of object is in front of him is intact, ruling out associative agnosia as the condition associated with his perception of object boundaries. As the occipitotemporal intersection is involved in object and object boundary formation, JP is like to have damages to this region. Areas in the occipitotemporal intersection are implicated in most visual form disorders rooted in the visual cortex. In most cases, however, larger areas of the occipital or temporal lobe are involved, likely due to the fact that most studies of visual form disorders have looked at patients with brain lesions owing to carbon-monoxide poisoning or a stroke. One region that stands out as a possible target area for JP’s lesion is the lateral occipital complex (LOC). Lateral occipital complex is the lateral-posterior area of the occipital lobe (visual cortex), just abutting the posterior area of the motion-sensitive area MT/V5. LOC shows preferential activation to images of objects, compared to a wide range of texture patterns (Malach 1995, Grill-Spector et al. 1998, Wong et al. 2009, Pourtois et al. 2009). As LOC generates the same response for objects regardless of their shape, it may be considered an intermediate link in the chain of processing stages leading to object recognition in visual cortex. LOC is also known as ‘visual memory’. It is responsible for object persistence for a few seconds after the stimuli was been removed (Wong et al. 2009) and is involved in rotation-invariant shape processing (Silvanto et al. 2010). As JP does not see object boundaries as smooth and invariant over time, it is possible that the assault in 2002 caused injury to LOC.
3. The Memory Theory Reconsidered JP is an interesting case, not least because he is the first described case of both acquired synesthesia and savant syndrome. Furthermore, it seems that JP’s case can give some clues as to the biological basis of savant syndrome. These clues seem inconsistent with Sanislas Dehaene’s theory that the biological basis of mathematical savant skills is number obsession. According to Dehaeni, the inferior parietal cortices are bilaterally involved in estimated number processing, whereas exact calculations and other exact manipulations of numbers are a matter of memorizing certain basic facts and algorithms (Dehaene 1999, 2001, Daehene et al, 1998, 2004). The human brain, Dehaene suggests, converts number words and Arabic numerals into analogical quantity representation organized by numerical proximity. The larger the number is, the fuzzier the representation. So, there is a clearer representation of 3 in the inferior parietal cortices than there is of 104. The analogical quantity representation is a product of evolution. The best survivors were those who could provide good approximations of numerical difference and sameness. Dehaene provides four pieces of evidence for this theory. First, animals represent numbers in an analogical way. Second, infants represent numbers in an analogical way. Third, in adults, infants and animals the calculation time is longer when numbers are either very large or close in proximity. Fourth, the intraparital sulcus on both sides
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is crucially involved in the representation and acquisition of knowledge about numerical quantities and their relations. 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 (Dehaene 1999, 2001). If savants have the ability to calculate numbers accurately with lightning speed, then his theory does not apply to them. Because savantism is not an isolated phenomenon found in one “freak individual”, the abilities of savants should make us question the accuracy of Dehaene’s theory more generally. Dehaene, however, has a reply to this kind of worry. He thinks 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 that 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: 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 short-cuts 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 (2001: 14) The suggestion is that people like DT, who can calculate as fast as a calculator, appear to be doing magical calculations because they have memorized a few algorisms and have a strong interest in practicing. While I think Dehaene’s theory ultimately fails, I do think that there is some truth to his claim that normal individuals can acquire the ability to speed calculate. For example, almost anyone can learn to multiply numbers at lightning speed by using algorithms. A simple algorithm for multiplication is an algorithm I call the “crisscross method”. An illustration is offered below (Fig. 10, 11, 12):
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Step 1 7x8(56) 7x2 (14) 9x8 (72)86 9x2 (18)
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Figure 10: The crisscross method for fast multiplication, two digits. Result: 6278
Within a few days of practice two-digit numbers can be multiplied in a couple of seconds using this method. The crisscross method does not even require particularly good memory skills. Almost any person can learn the 64 facts of single digit multiplication by heart (not including 0xn, 1xn). With very simple addition skill added to the mix and normal working memory, the crisscross method is straightforward. We can multiply n-digit numbers using an extension of the two-digit version (Fig. 11, 12). I tested how long it would take three average undergraduate students to reach prodigious calculation speed (< 5s) without paper and pencil for n =3. Two of the three reached that level within 5 hours. One gave up.
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Figure 11: The crisscross method for fast multiplication, three digits. Result: 15,129
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Figure 12: Additional steps in 4-, 5- and 6-digit multiplication. Results: 1,522,756 and 152,399,025 and 1.524138e+10 (15,241,383,936 = > 15 trillion)
It would be a simple task to formulate analogous methods for division. Calendar calculations at lightening speed are also easier to perform than it may at first seem. Suppose in 2010 your brand new acquaintance tells you he is turning 40 on Saturday. You quickly divide 40 by 7, get 35 and a rest of 5. Knowing that 2002 was a leap year you quickly calculate that he has gone through 9 leap years in his life. You subtract 7 from that number and get 2. The algorithm now is to add the 5 and the 2, then add 1 to that and count backwards from Saturday. That yields a Friday. Within seconds of meeting him, you tell him he was born on a Friday. By memorizing a few dates and matching weekdays for each month of the current year, you can use the same method to speed-calculate the weekday of any date within this or the last century. So, Dehaene is indeed right that normal individuals can achieve lightening speed calculation abilities by learning a few algorithms and undergoing training. 15
However, while calculation speed is achievable with practice and algorithms, mathematical savants can perform other tricks than speed calculation. Daniel Tammet can recite Pi from memory to 22,514 digits in five hours and nine minutes, the computing twins Kay and Flo can tell you what they had for dinner on any date you give them within seconds of asking them, Sacks’ autistic twins John and Michael could compute six-digit prime numbers in a few seconds. JP’s case too appears to be a counterexample to Dehaene’s memory theory. JP had no math and no interest in math prior to the brutal assault in 2002. He never finished college. He is only now acquiring simple training in mathematics, and his drawings were made many years prior to that. There is no way in which JP could have learned how to draw meticulously accurate approximations of mathematical fractals or predict prime number vectors prior to the incident or his first drawings.
Figure 13: Wave Particle Duality © Jason Padgett
There is another important difference between normal individuals and savants. While normal subjects can, and sometimes do, learn to imitate savants by using algorithms to speed calculate, these subjects 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. The brains of savants with special mathematical abilities, on the other hand, make calculations that are not themselves consciously accessible, even though the result is. Tammet is not conscious of how mathematical calculations 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 16
translate into the number result of the calculation. But the calculation itself is not accessible to him. Likewise, JP receives information about fractals 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 terms of a mathematical fractal. As JP puts it, his conscious brain is a receiver of the result of the calculation made by his unconscious brain. 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 the dominant left hemisphere. We cannot consciously make hugely complex calculations in our heads or perform calculations that spit out a fractal in our field of vision. How then can we explain the difference between the brain function of normal speed calculators and mathematical savants? Dehaene is right that it is unlikely that savants are born with a special mathematical organ that predisposes them to be fast calculators. The fact that savant syndrome can be acquired after a hard hit on the head, as it was in JP’s case, suggests that if the brains of savants differ from the brains of normal individuals, then they differ in structure not in substance. Dehaene, however, seems to think that if savant syndrome is not genetically encoded and is not the result of a special math faculty, then it is “just” the result of extensive training and fairly good memory. This reasoning, however, is not sound. Owing to the flexibility 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? JP’s case can give us some clues here. From being terrible at drawing, JP developed the ability to draw extremely well, an ability that requires visual representation and control of immediate, or “online”, action (Amedi 2008). Like other savants, JP typically completes his drawings in a piecemeal fashion. Furthermore, he is significantly better at providing spontaneous answers to mathematical puzzles than providing answers after reflecting on them and, importantly, geometrical images just “come to him”. This suggests that the relevant brain regions are regions that (ii) govern immediate or “online” actions, (ii) compute representations that represent details as opposed to entire scenes, (iii) facilitate and guide fine motor skills, (iv) enable fast calculations below the level of conscious awareness, and (v) allow for unusual feedback to visual areas. We know that the posterior region of the parietal cortex is involved in integrating sensory input, primarily from the tactile and visual system, and delivering this information to the motor system. The integration is in a constant flux, that is, parietal representations of the world are constantly changing. The constant change is beneficial when immediate or “online” action is required. Spontaneously reaching to and grasping an object without delay requires fast integrations of sensory input. Optic ataxia is a condition in which the subject suffers damage to the posterior parietal cortex. Behaviorally, the condition is manifested as a deficit in reaching and grasping under visual guidance. For example, patients with optic ataxia make large pointing errors when asked 17
to quickly point to stimuli in their visual field (Milner, et al. 1999). The condition improves when a delay is introduced between the task representation and the pointing movement. When the damage to the parietal lobe is bilateral, individuals with optic ataxia typically have difficulties performing ordinary activities such as drawing, writing, eating or filling a glass. Optic ataxia is the mirror condition of visual agnosia in which the identification of objects is impaired whereas online action usually proceeds normally. It was these two conditions that gave rise to David Milner and Melvyn Goodale’s famous theory of the two visual streams (Goodale and Milner 1992, Milner and Goodale 1995, 2008). Milner and Goodale suggested that there are two anatomically and functionally dissociated visual streams: the ventral stream and the dorsal stream. The ventral stream, which is responsible for vision for perception, starts in the lower visual areas of the occipital lobe and runs through the temporal lobe. The dorsal stream, on the other hand, which is responsible for vision for action, starts in the lower areas of the occipital lobe but then runs through the parietal lobe. Unlike visual representations computed in the ventral stream, visual representations computed in the dorsal stream do not give rise to visual awareness. Dorsal stream areas compute exactly how far the subject has to move her hand to reach to an object, the path the arm has to make to reach to the object, the size of the grip aperture, and so on. But while subjects usually are aware of the movement taking place, they are not aware of these complex calculations. They cannot answers questions about the size of their grip aperture or the precise path their hand has to take to reach to an object, they can merely demonstrate it. Even when subjects are not consciously aware of changes in object size, they still change their hand apertures to fit the object (Gentilucci et al. 1995). If an object suddenly changes location, corresponding adjustments in arm velocity and trajectory are made in less than 100 ms, which is not enough time for the human brain to consciously represent the change in object location or the corresponding change in velocity and trajectory (Paulignan et al. 1991). Studies have further shown that when subjects are asked to use a minimally demanding vocal response (Tah!) to signal their awareness of a change in object location, correction of movement occurs significantly faster than the vocal response. Corrections of trajectory and hand aperture occur within 100 ms, whereas the vocal response happens after 420 ms (Castiello, Paulignan and Jeannerod 1991, Castiello and Jeannerod 1991). Studies of pointing and saccadic eye movement further indicate that subjects can correct saccadic eye and pointing movements faster than they can consciously perceive a change in object location (Goodale, Pelisson and Prablanc 1986, Pelisson et al. 1986). In one study, subjects were asked to point as fast and accurately as possible to stimuli occurring in the dark (Pelisson et al. 1986). In the first series of trials, the target leaped from an initial position to a randomly selected position. In the second series, the target made a second jump in the same direction as the initial jump. Subjects reported that they were unaware of the second jump, and they were unable to predict its direction, but while saccadic eye and pointing movements were initially aimed at the target’s position after the first jump, both were immediately adjusted to fit the target’s new location. Even though the participants had no conscious awareness of the two jumps, they were clearly seeing and acting on both jumps. The findings indicate that the subjects updated movement trajectory and target location without conscious awareness of the update. 18
There is some reason to think that the representations computed by parietal brain regions never, or rarely, correlate directly with conscious awareness. Even when ordinary individuals quickly judge that 100 is larger than 77 on the basis of representations of the number line in the intraparietal sulcus, they are not aware of a number line. Their judgment occurs spontaneously via feed-forward to frontal areas. In some cases of synesthesia, the number line is consciously represented. But this is consistent with the hypothesis that synesthesia arises via lack of inhibition of feedback from the parietal cortex to occipitotemporal brain regions. Awareness of the number line corresponds to representations in brain regions that are anatomically and functionally dissociated from the parietal brain regions. The complex of posterior “dorsal stream” areas, spatial recognition areas in the superior temporal lobe and areas in the intraparietal sulcus may be a candidate to be the infamous “math organ” researchers have been searching for for centuries. There is nothing mysterious about this organ. Normally, a part of this complex of brain regions functions in just the way described by Dehaene. It makes approximations about the relative sizes of quantities. But the hypothesis set forth here is that the parietal lobe sometimes develops in such a way as to allow unusual, complex calculations to take place and the result to reach conscious awareness via synesthetic representations.
4. Concluding Remarks After a mugging incident in 2002 that involved a hard hit on the back of the head, JP has developed what appears to be synesthesia and savant syndrome. JP reports that observations of clouds, liquids and solid objects give rise to visual images of mathematical fractals. He draws what he sees and is the first in the world to draw mathematical fractals by hand. He has furthermore developed the ability to talk about the equations describing the fractals. Prior to the incident JP had an IQ below 100 and dropped out of college. He had no interest in mathematics. I have argued here that JP’s case provides a counterexample to Dehaene’s theory that mathematical savant skills are the result of extensive training and fairly good memory. I have furthermore suggested a possible biological basis for mathematical savant skills. I proposed that mathematical savant skills may be a result of overcompensation in the parietal lobe, which allows complex mathematical calculations to take place below the level of conscious awareness. These calculations would not normally be cognitively accessible. However, I hypothesize that, owing to the lack of inhibition of feedback to visual areas, the calculations are cognitively accessible via synesthetic representations.
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