As much as that story made me reflect on the loneliness of the acquired savant, I took joy in the next several cases I studied. I particularly liked the story of Alonzo Clemons of Boulder, Colorado. As an infant, he suffered a brain injury in a fall, and though he could scarcely speak in complete sentences, Clemons could sculpt out of clay any animal he saw in uncanny detail, using no tools other than his hands. In fact, all he needed to do was glance at the animal once, and then he stored the image photographically in his mind and could complete an entirely accurate sculpture. His desire to sculpt started shortly after his head injury. As a child, he would take the shortening out of the cupboards in his family home and set to work compulsively sculpting animals; finally, someone bought him some clay. To this day, wherever he goes, he carries with him a duffle bag with several bricks of clay, just in case he sees something he has to sculpt. After reading his story, I was really glad my injury didn’t rob me of the ability to communicate. I didn’t choose to communicate often, but something inside me was compelled to share what I knew.
Clemons worked on his sculptures for twenty years in solitude. But when the film Rain Man, which was inspired by the remarkable abilities of the savant Kim Peek, came out, the public became more interested in Clemons’s work. He now shows his art and has been featured on many TV shows, including 60 Minutes and the Discovery Channel’s World of Wonder.
Not far from Clemons, in Denver, lives another man who acquired savant abilities. Derek Amato was forty when hijinks at a backyard barbecue changed his life. Someone tossed a football near the in-ground pool, and then the game became catching the football over the water. On one toss, Amato dove into the shallow end of a pool and struck his head on the pool’s floor. “I remember the impact being very loud. It was like a bomb had gone off. And I knew I hit my head hard enough that I was hurt. I knew I was hurt badly,” he said in a Science Channel documentary. He felt like blood was pouring out of his ears, though it was not. He was admitted to the hospital with a serious concussion and soon noticed some memory loss and hearing loss.
A few days after the barbecue, he was released from the hospital, and he sat down at a keyboard at a friend’s house and began to play. Though he’d played a little guitar, he had never played piano before, but suddenly he was a virtuoso. It was original music. And it was beautiful. He continued until about two the next morning, afraid the ability would be short-lived. He and his friend couldn’t understand what was happening. “It was no ‘Mary Had a Little Lamb,’” Amato said.
“As I shut my eyes, I found these black-and-white structures moving from left to right, which in fact would represent, in my mind, a fluid and continuous stream of musical notation,” Amato later wrote in a blog post on the Wisconsin Medical Society’s website. “I could not only play and compose, but I would later discover that I could recall a prior played piece of music as if it had been etched in my mind’s eye.”
In an interview on the Today show, Amato admitted that there were downsides to the injury. “I deal with the fluorescent-light issues,” he told Matt Lauer. “I collapse sometimes out of the blue. And the migraines and the headaches are intense. And my hearing is half gone.” He called the lingering symptoms “a price tag on this particular gift.” When I heard him say that on the video, I thought of my own OCD, PTSD, and other problems. I agreed with him that though these issues presented a challenge, I wouldn’t trade my new abilities for life without them.
Orlando Serrell is another interesting acquired savant. In 1979, when he was ten years old, he was playing baseball, and while he was making a run for first base, a baseball struck him on the left side of the head. He fell to the ground and remained there for a few moments, then got up and continued to play. “I didn’t tell my parents, therefore, I had no medical treatment for the accident,” he wrote on his website. He did have a headache for a long while following the incident, he said. Soon, he noticed he had developed the ability to do calendrical calculations; he could tell you the day of the week associated with any date. If you said, March 28, 1957, he would answer, correctly, Thursday. He can also tell you what the weather was and what he was doing on any given day since his accident. In 2002 he was invited by NBC’s Dateline to undergo a brain scan at Columbia University, and he appeared in a special on savants. His case made me want to know exactly which parts of my brain had been affected by my injury.
I was glad to finally come across the case of a female with savant syndrome, as the condition is even more rare in women. According to experts, when it comes to savant syndrome, men outnumber women by about six to one. Why? Researchers are still trying to figure it out, but some theories suggest that it may have something to do with the way the brain develops in the womb. Also, the savant syndrome is often associated with autism, and autism is more common in males.
The lone female savant I came across was a child named Nadia. In the 1970s, she drew beautiful pictures of horses, and her drawings were so fine they were compared to those of Rembrandt and Leonardo da Vinci. But she lost her drawing abilities when she learned to speak, according to the British psychologist Lorna Selfe.
I cobbled together what I was learning about acquired synesthesia and savantism to get a better picture of what was going on in my own mind. The stories of people with such gifts were comforting to me, though I hadn’t yet come across anyone with what I suspected I had, both acquired synesthesia and acquired savantism. The experiences of savants and synesthetes still didn’t explain what was happening in my life. Even Tammet had had what I considered the good fortune to be born the way he was. I doubted he could truly relate to my conflicted feelings about my new identity. My alternating shock and euphoria about the emergence of my new sensory perceptions added a layer to the experience I’m not sure people who’ve had synesthesia or savant syndrome their whole lives can imagine. Would I ever feel at home in my own skin and have that sort of acceptance and grace about my abilities?
Though I looked to Tammet and other fellow synesthetes and savants with extraordinary gifts for clues and guidance, I was left with the feeling I would have to forge my own path.
Chapter Seven
The Edge of a Circle
IN MY ISOLATION, I felt the profound change of the shape of my own world. My life used to be a mile wide and an inch deep: I covered a lot of ground running around, but I barely scratched the surface of things with my superficial pursuits. Now, it was an inch wide and a mile deep. I was practically immobile, working from my spot at the computer most days. I focused on the tiniest thing and pondered it incessantly, plumbing this narrow but very deep space.
It was during this time of major shifts in my perception—started by my trauma and made greater by this silent laboratory of sorts—that I found my intellectual passion. I became fascinated with pi, that irrational, infinite number that corresponds to a circle’s circumference divided by its diameter. To me, that irrational number became a fundamental building block of everything around me, a signifier of nature’s perfect symmetry, repeated over and over throughout our world. I saw it everywhere I looked with my new brain: in light reflected off glass, in the corona of a street lamp, even in the virtual scaffolding of a rainbow.
My fascination with pi began in 2005. On a rare foray outside, I noticed the light bouncing off a car window in the form of an arc, and the concept came to life. Like most visual phenomena now, it was hardly just light bouncing off glass but an extraordinary geometric display: a ball of light was where the beam hit the glass. Rays fanned out from it like the spokes of an illuminated bicycle wheel or the radii of a circle. They were iridescent and I was rapt and lost in the potential infinity of it all. It looked like a laser light show my favorite bar might have put on in the old days, only a million times better. Staring at the display, I felt an overwhelming sense of stimulation and inspiration. To the new me, so entranced by math and physics for the first time, it was a revelation.
I was literally fist-pumping and saying, “Oh my God! This is amazing!” over and over
that day when I first understood that what I was seeing was a representation of pi. It clicked for me because the circle I saw was subdivided by the light rays and I realized each ray was really a representation of the radius dividing the circle into pieces. I realized that if I added up the areas of all these pieces, which were sort of like slices of a cake, they would equal the circle’s area. Measuring that value would be a much easier way to figure out the value of pi than the difficult “circumference of a circle divided by its diameter” method I had once struggled to understand in school. In my Internet searches about circles and diameters and radii, I had learned that pi was a confounding problem because the circumference divided by the diameter was irrational: rather than corresponding to a clean fraction, the number stretched out to infinity in decimal form, with no repeating pattern. If you divide 1 by 3, you get 0.33333333, with 3s repeating forever. Divide 1 by 7 and you get the infinitely repeating pattern 0.142857142857142857. Divide a circle’s circumference by its diameter and you get a number that begins 3.14159265358 and just keeps going. Mathematicians are still calculating new digits of pi, out into the quadrillions, and no one has yet found a real repeating pattern. No wonder it had always been so hard to understand.
Part of the trouble is that no one has a way to accurately measure the circumference or area of a perfect circle. Instead, mathematicians have to approximate. One way of calculating the value of pi dates back to the Greek mathematician Archimedes. Around 250 BC, he tried to find the area of a circle by placing one polygon inside a circle and another polygon outside the circle. He calculated the perimeter of the two polygons and theorized that the value of pi lay between those two numbers. Then he kept increasing the number of sides of the polygons—working his way up to ninety-six sides—so the areas of the two polygons got closer to equaling each other. Using this method, he calculated that the value of pi was between 3 10/71 and 3 1/7. The ancient Greeks didn’t use decimals, but his fractions were the equivalent of about 3.1408 and 3.1429, respectively—not too far off the figure we use today.
I had never been taught about Archimedes or this visual approach, but now that I had arrived at the realization independently, I wanted to run through the streets announcing my profound discovery. I wanted to tell everyone this was a great secret revealed. Suddenly an idea I’d known in school only as “that 3.14 number” took on a relevance it had never had for me in a textbook or lecture.
I raced home and began my research further into pi that very day. As I read academic papers and popular-science articles online, I started to feel that pi literally defined everything—not just the ratios in a circle, but all of creation. It pertained to so many naturally occurring spheres, from pebbles to planets. And in more complex mathematics, like calculus, it helped define slope. I thought about the spirals of my seashell and draining water and coffee swirls. My own pupils were circles. Where would we be without the invention of the wheel? Circles were everywhere I looked and they felt fundamental to existence.
I began trying to describe what I saw to the rare visitor or person who telephoned. I said things like “Have you ever seen those boats where you push the lever forward from stop to fast? Push that lever all the way up and think of it as an obtuse, greater-than-ninety-degree angle, say a hundred-and-seventy-nine-degree angle, a really large one. Move that lever back down to a right angle, then slowly bring it down to an acute, less-than-ninety-degree angle until you collapse it in on itself. Think that every click along that lever makes a certain triangle. And every triangle is defined by pi at a certain value.” While this visual helped me a great deal and seemed very on point, my audience remained confused.
I wished I could give everyone the eureka moment I had had that day with the car—a circle subdivided by glistening, illuminated triangles. But when I tried to describe my inspiration, people told me that it would have been just an arc of light or a halo or a reflection to them. I couldn’t believe it was so mundane to them when for me it was a peak experience. I searched for the words to best represent this. I would wave my hands in the air, tracing what I’d seen with a pointed finger. All I got in return were blank stares. I realized that things would never be the same for me—all my life I would see down deep into the structure of things while everyone I knew was still skating on the surface. It was as though I’d been fitted with some sort of microscopic, x-ray-vision contact lenses. I searched for the words to capture its beauty and, more than that, the truth I believed its structure represented, but I was stammering.
Finally, I picked up a pencil and tried to sketch it.
I had never been able to draw in the past, but I was now pretty adept. The pencil didn’t feel like a foreign object in my hand but an extension of me and my mind. I felt compelled to draw and did almost nothing else. I found I was better able to represent things on paper than I had been. The joke in my family until now had been that when we played Pictionary, my doodles were always the worst! For one round of the game in which I had to represent the god Zeus, my scratch marks were little more than a carrot shape for a mountain and a zigzag for a lightning bolt above it.
I was amazed by my sudden facility with a pencil. It was as though someone else were clutching my fist and guiding my hand. This was another ability I’d never had before, and I had to set the pencil down for a moment to take it all in. What really made it come together, however, was when, in a rare conversation during my continued self-imposed isolation, a friend suggested that I add a ruler and a compass to my toolbox. I began to draw forms very close to the beauty I’d witnessed.
When I first tried to render the vision, I drew a perfect circle with a smooth perimeter, which was not what I had seen. The circle I saw was not perfectly curved—the circumference of it was jagged. It was more of a polygon with countless sides and filled with triangles, only approximating a perfect circle. So, as I drafted circle after circle at my desk, I began filling them with triangles. As I added more triangles I realized I was filling in more and more area at the circle’s edge.
“You can only fill in more and more triangles,” I said to my mom during one late-night phone call about this quest.
“Hence, pi goes to infinity,” she responded.
Her statement made everything click, and I realized how this insight was reflected in the circles I saw all around me and had been attempting to draw. What if the base of these triangles became smaller and smaller? First I filled a circle with 60 triangles, then 180:
Then 360:
All the way up to 720, when the width of the pencil’s lead wouldn’t allow for any more lines:
One day my daughter, Megan, was halfway through an episode of Pokémon when she hollered a question to me: “Dad, how does the TV work?” I explained that each image is made up of hundreds of little rectangular pixels, and when the pixels change color, they change the larger picture too. Just then a commercial for Overstock.com, with its giant O logo, came on, and Megan said, “That’s impossible, Dad. How do you make a circle out of rectangles?”
It was like a bomb went off in my mind. In a matter of minutes, I was no longer just a receiver of geometric imagery or a researcher; I was a theorist.
Ever since the mugging, curved objects in my line of sight had lost their smooth edges. They looked jagged and inexplicably discrete from their surroundings, and while I had spent years puzzling over the distortion, its significance had eluded me, and my drawings hadn’t cracked the code. That afternoon I found the right words.
“Circles don’t exist,” I told her.
The deceptively simple observation hijacked my thought process. I described the basics of the familiar concept to Megan: “When you see a circle on the television, the edges appear to be curved only because the pixels are so tiny relative to the scale of your perception. The smaller the pixels, the smoother the edge becomes, but it never becomes perfectly smooth because the pixels can be made smaller and smaller, on to infinity.” I didn’t want to get too technical with Megan, but this realization reminded me of Mandelb
rot’s fractal geometry, which emphasized the roughness in the world around us. In my head, I was quickly moving beyond the fundamentals.
Pi was becoming my mathematical soul mate. I began to obsess over it the way I did the cleanliness of my hands. Other mathematicians had discovered the utility of pi long before I stumbled on it. It is believed that ancient Egyptians knew about it and used it in the construction of the pyramids, as evidenced by those structures’ proportions. Pi has even been found in the Mandelbrot set. Its value lay in mathematics—not just in geometry but also in calculus applications and computing algorithms. The record for calculating pi (as of this writing)—which has been an obsession of people around the world ever since pi was first discovered—was achieved in March 2013 by Ed Karrels of Santa Clara University, in California. He computed the number to eight quadrillion places using a supercomputer. Though the sophisticated calculations of pi humbled me, I realized all of us were seeking the same thing.
However, I thought even the most sophisticated attempts to calculate pi were not taking it down to the quantum level—not one that I was able to find from my humble home computer station, anyway. So I began contemplating a hypothetical correction using one of the concepts for which Max Planck was awarded the Nobel Prize: the Planck length, an infinitesimally small unit of measurement equal to 1.62 × 10−35 meters. Just to clarify, that’s millions, billions, trillions, and even quadrillions times smaller than anything that can be seen with the naked eye. The Planck length is the scale of length measurement where the usual rules of gravity break down and quantum mechanics comes into play. It’s also the smallest possible building block of space in the universe that can be observed (or exist relative to us). If the triangles I placed in my circle were each on the scale of a Planck length—would that not be a more perfect pi? I later posted my theory about this on a physics forum online because I was so sure I was the first to discover it.
Struck by Genius: How a Brain Injury Made Me a Mathematical Marvel Page 8
