Struck by Genius: How a Brain Injury Made Me a Mathematical Marvel

by Padgett, Jason

  When I got my photos developed, they weren’t that great. They weren’t as sharply focused or filled with wave patterns as the images I’d seen with my own eyes. Real life is so much better for me than photos; I think it’s because motion creates additional effects in my perception that can’t be captured by a camera. Flipping through a magazine one day on campus, I learned about some photography software called Genuine Fractals (now renamed Perfect Resize 7.5). This Photoshop plug-in allowed you to increase the resolution of a photo and reopen it in improved focus at almost any scale. I thought that sounded one step better than what I had, but I wished there were software that could capture precisely what I saw. Perhaps one day I could create it.

  It didn’t take my teachers long to discover I was no ordinary student. Though I was going to school only part-time so I could begin working again at Planet Futon, I was serious about my courses. I sat in the front of each classroom and raised my hand often. I noticed my professors looking at me oddly during my daily purification rituals and when I engaged them in class, and it was obvious that they found me not only unusual but perhaps exceptional—simultaneously deficient in mathematical terminology and fundamentals and extremely advanced in my theorizing. I made the effort to answer a lot of questions and ask new ones. There was a guy in one of my classes who clucked every time I did, but I wasn’t going to let him get to me.

  I started to be encouraged by the faculty members’ inquisitiveness. They had questions for me, too, about how I thought and how I arrived at various answers. I got the feeling that despite my nontraditional methodology, I was coming up with the right answers and maybe even some surprising questions. I started sharing my drawings after class.

  My introductory algebra teacher, Tracy Haynie, asked us to draw a nautilus from triangles based on a lesson in our textbook. The exercise required us to simply find the correct-size triangles to place in the outline of the shell in a flat, two-dimensional way, but I was inspired immediately when I saw it. I realized I could build a three-dimensional spiral nautilus like the one I’d loved in childhood if I applied the Pythagorean theorem. I drew the first triangle and then, using the equation a2 + b2 = c2, I recursively put c back in the equation as a, kept b as one, and grew it out, kind of like how Mandelbrot formed his set. Placing each new triangle, calculated this way at a right angle to the first, grew out a perfect nautilus.

  Haynie was fascinated enough to ask the other students to draw a seashell using the Pythagorean theorem, as I had. Mine was seventeen times larger than what she had them draw, but many of them were excited by the exercise and now we were all talking about it.

  One day I was walking down the hall, struggling with my rolling suitcase and with my arms full of drawings. I was facing a troublesome hallway door that pulled inward (making my foot or elbow method unworkable). It also had a handicapped buzzer, but that was out of order. Haynie appeared out of nowhere, swooped in, and opened the door for me. I can’t tell you what this simple act of kindness, followed by meaningful conversations about the OCD that kept me from touching door handles, meant to me coming from an instructor. She even said, “I think I have a little touch of that,” and I believed her, since she kept her classroom so neat and tidy. Her reaction was so, well, human, it made me want to work even harder.

  I felt very much at home and inspired by Haynie’s class and her kindness toward me that I even brought my daughter, then eight, with me one day. She learned to graph a function with the rest of the class. It was really important to me that Megan think of college as a great place to go. I wanted her to apply herself when the time came. I didn’t want her to lose time or go down the wrong road as I had when I was younger.

  At the end of the semester, Haynie asked me for one of my illustrations. “One day you might be famous and this drawing will be worth lots of money,” she said with a smile. I could feel my cheeks flush red. Later she sent me an e-mail saying that there weren’t many students she remembered as well as she remembered me and telling me what a joy I had been to teach back in 2006. She still has my drawing. Thanks to her careful attention and inspiring teaching, I came to love school.

  Another teacher, Meredith LaFlesh, saw my potential and zeroed in on me during her rotations in the math lab, tutoring me in trigonometry and filling in the blanks in my math vocabulary. I realized how fortunate I was to be connecting with great teachers and I tried to make the most of their generous attention. One night, freshly inspired by LaFlesh’s instruction, I set out to create a formula describing pi and arrived at the following:

  I showed up early the next day and knocked on her door as soon as the light in her classroom flickered on. The legally blind LaFlesh put on her glasses—a pair with a very high degree of magnification—and studied my work. She typed the equation into her scientific calculator and brought it to within an inch of her eyes.

  “This is correct!” she said, leaning back in her chair and looking at me with awe. “How did you do this?” I explained that I visualized pi as a shape in space and worked backward to find the formula that accurately represented it. I saw pi as a function of a circle subdivided by triangles where x equaled the number of triangles. As x approached infinity, f(x) approached pi. She shook her head in wonder and had me work through each stage of the back-to-front calculation on the blackboard.

  My reputation with the students began to improve as well. They were getting used to the fact that I was always raising my hand in class. A few of them told me I was asking the questions everyone else was too shy to ask. Even the nonstop partiers, who I suspected were always hung over in class, eventually warmed up to me, seeking me out at the math lab to ask me to explain the week’s assignments with my drawings. I found myself counseling them, telling them I had been just like them when I was their age and that they ought to stay in more often and concentrate on their studies. I felt like I was talking to my younger self.

  I loved the math lab. It was not only a place to go for supplemental help, but also a place where students could discuss and even debate important lessons. I tried to get past how grossed out I was by having to log in on a touchscreen computer—I wiped the glass off to do so and, later, the keyboard. Then there was the issue of the curious way questions were asked in the lab. There was a bowl in the front of each desk almost overflowing with marbles. Beside it was a silk daisy. You needed to pick up the daisy by the stem and stick it upright in the bowl to signal you needed help. I was so scared of this dust collector that I picked it up using one of my wipes every time. I tended to spill a bunch of marbles out of the bowl when I put the daisy in, as did my fellow students. Every time this happened, some people applauded. I usually felt so embarrassed for whoever had spilled the marbles—kind of the way I do when a waiter drops a glass in a restaurant. I never had such empathy before, but now it’s literally a tightening in my chest. So the silence of that environment was punctuated by the spilling of marbles and huddled students discussing math.

  I made some good friends there. One of my new admirers was so enthralled by my drawings he decided to show my illustration of pi to a tenured professor we ran into in the hallway. I hadn’t yet been in any of this professor’s classes, though I hoped to be soon, as he was one of the most respected teachers at the school. The professor looked it over and announced, “This is correct, but only someone who hasn’t been taught how to think would calculate pi this way . . . who’s the student? I have to meet him!”

  “It’s me,” I said in a little mouse of a voice as I stood beside my friend. The professor smacked his hand to his head and bounced up and down a couple of times and said, “This is genius!” Then he shook my hand and asked me all about myself in the few minutes before the next class period. I walked away elated.

  All the positive feedback I was getting in school made me realize that something really extraordinary was going on with me—that it was not just all in my head, so to speak. I started to hang around the student newspaper office to tell them about my unusual case. What I really wanted
to do was share some of my drawings with the student community through the paper so I could teach more people about math from a visual point of view. The staff was very interested, and one reporter taped hours and hours of conversation. A story never appeared, however, and the newspaper ended up closing.

  There were definitely some people at school who didn’t understand me or get where I was coming from. There was the clucking fellow student in my trigonometry class, but he dropped out. He was quickly replaced in the math lab by a student who was very religious and looked at me warily whenever I described the world in geometric terms or by using the laws of physics. I don’t disrespect people’s beliefs, but he really had a problem with my secular approach. The instructors broke up our animated debates a couple of times.

  There was also one instructor in the math lab who clearly was having a little fun with me. He called me the Math-Lab Janitor, because of the way I sanitized my workspace each day, and joked that the room had never been so clean. He would come by my desk over and over when I was working and put his finger on the Enter button of my scientific calculator just to watch me swab it down immediately with a baby wipe. I tried to smile through it and keep from telling him how truly terrified I was by those germs that he found so funny.

  Perhaps the most difficult hurdle was the class on the use of calculus in physics. I was really excited to begin, as I felt this was where the lectures would get into the fine detail of why things are the way they are.

  In the beginning, my biggest challenge was setting up the equations for the word problems; basically, changing a story into symbols. There were so many different variables and symbols that I didn’t yet know, I worried that I’d never pass the class. When they were finally set up and it came down to doing the calculations, I was much more at ease.

  It was a large class, and the instructor grumbled whenever I raised my hand to ask a question or make an observation. Although the majority of my teachers encouraged participation, there were a few sticklers who just wanted to make it through the syllabus without interruption or tangential inquiry.

  One day we got into a discussion about instantaneous velocity, and I brought up that I had a problem with how calculus required the assumption that things approach infinity in order to get the result. I didn’t think that was the correct way because that gave you only an approximation, in my humble opinion. I would much rather have calculated it this way:

  True instantaneous velocity = change in position/Planck time.

  I called the professor sir, and I tried to be polite, but he was clearly annoyed. He said something like “Grrr. Yes,” granting my point but clearly wanting to move on. It was correct, and he acknowledged that, as bothered as he was by the interruption.

  I continued to remain engaged in my classes despite these hurdles. However, one teacher dealt me a near-fatal academic blow.

  A new professor was working in the math lab. While discussing a math problem with him, I explained that I needed to visualize it as shapes first before I went to the next step. He looked at me with a really perplexed face and said, “Well, there’s something wrong with your brain, then.”

  I felt a dagger go deep into my heart. My ears started to get warm with shame and I tried to explain how ever since my injury, I’d automatically associated shapes with numbers. Now they were encoded in my mind, I continued, and helped me with memory and calculations. Have you ever heard of synesthesia? I asked him.

  “You need a new brain. Numbers are not shapes,” he retorted.

  I was silenced. I was so shocked and ashamed that I wished I could run and hide behind the blanketed windows of my home. But then shame gave way to anger. I gathered my books and drawings and went to the head of the math department. The man was one of my calculus teachers, the best of the bunch, and he listened intently as I described the insulting conversation I’d just had.

  “He belittled me,” I said. “He wouldn’t even listen to me so I could show him my system would still yield the right answer.”

  He had sympathy for me and said he was wrong and that it shouldn’t have happened. “But before you file a report, I need to tell you something,” he said. “He just found out he has cancer.”

  I was stunned. I felt so sorry for him. I thought of the loss of my own beloved stepfather to the disease and immediately changed my mind about filing a report.

  His words still stung me, though, and I realized that although math abilities came easily to me now, the path ahead of me in legitimizing these abilities and getting a formal education was going to be a challenging one. The euphoria I felt in returning to school was tempered with caution now and perhaps that was for the best. I resolved to continue to work as hard as I could, unaware I’d have a new reason to be joyful in the coming weeks.

  Chapter Ten

  The Hermit and the Hermitage

  LUNCH TRAYS WERE clanging, people were speaking to my left and my right, and announcements were coming over the public-address system, but I didn’t hear a thing. I was sitting at the cafeteria table at Tacoma Community College and drawing intensely, deeply absorbed in getting every line perfect. I was in the zone and had noticed that when I needed to work, I was able to project the safe, quiet space I’d created for myself during my years of isolation around me like a protective bubble. I was surprised, as I’d never had this ability before, and in the old days, I would have been holding court at one of the tables, describing last night’s debauchery or planning that night’s.

  I barely noticed when a young woman sat at the last seat available, two places to my right. From bits of conversation I heard over the din, I became vaguely aware that she knew the other young woman directly to my right and that they had a German class together. I finished my drawing, checked my watch, and saw that I had a few minutes left before class. I decided to talk to the woman nearest me. I began to show her my drawings, but it was her friend who told me she thought they were amazing; she said that her father was an engineer and had drafted similar patterns and blueprints while she was growing up. She asked me how I managed to draw them. I told her I used a ruler and sometimes a compass.

  “My dad had tools like that too!” she said excitedly, then looked down, a shy person catching herself in a moment of enthusiasm.

  I stared at her a little longer than I ordinarily would have, since her eyes were averted, and I immediately wanted to know more about him and more about her as well. I felt an unfamiliar but instant intimacy at her comparing my work to her dad’s.

  I asked her where she was from—her accent was charming.

  “I’m from Russia.”

  “I’m from Alaska!” I responded, feeling a strong connection that I wasn’t sure was just about the neighboring geography.

  “Do you know Alaska used to be part of Russia?” she asked.

  “Yes, I do.”

  Her name was Elena Afanasyeva and she was a dual major, business and finance. Elena looked like a snow maiden, with porcelain skin and pale blond hair cut in a bob. Her eyes were lit with intelligence, and her voice was gentle and soft. She seemed genuinely interested in my work. I tried not to stare at her. I realized I’d been alone too long.

  I may have been a very confident guy in my glory days but it had been years since any woman had responded to me like that. In the past, I was now aware, my interactions with women were largely based on physical attraction, aided by some clever conversation that certainly didn’t rise to the level of the things that occupied my mind now.

  I was not that man anymore—the one to whom relationships, albeit mostly superficial ones, came so easily—and I was adrift. I felt shy and I worried that Elena would see right through me and know the wreck I’d been since the mugging. With my physical difficulties—my neck and back were still affected by the beating I took—I had not worked out in years. I knew I was getting ahead of myself, but I could see that she was fascinated by my drawings, and I allowed myself to think for a second that if she was that interested in the only thing I really cared about
now, we might actually have a chance to be more than friends. In fact, I was glad I was currently single and alone. The loneliness had been hard to bear, but it meant I was available. It was as though fate had put me in a holding pattern for just this moment.

  Snapping out of my reverie, I realized it was almost time for me to get to my next class. I knew I wanted to see her again but I couldn’t bring myself to ask her out in the few minutes I had left, and I brooded over my atrophied social skills all the way down the hall. Right as I was about to kick open the door to the classroom, something told me to turn around, and I ran back to the courtyard and gave Elena my number on a small slip of paper. She looked at me like, Are you kidding me? I left feeling dejected, and then three days later, the phone rang.

  Megan handed me the receiver and it was Elena; she wanted to know if I would like to go to a soccer game that some of her South American friends, also international students at our school, were putting together in a few hours. Wow, would I ever, I thought. But with my daughter standing right in front of me, I felt I had to explain who’d picked up the phone and tell Elena a little more about myself first. “Can my daughter come? She’s with me today. I think she’d enjoy watching the game.”

  “Of course” came the faint reply.

  I needed to know from the start that Elena would be okay with my daughter. I didn’t know until she told me later that it was a shock at first and that she worried I had too much history for her to deal with.

  I’d thought for years that I would never resume a normal social life and it was hard to let go of that fear, but something in Elena’s voice on the phone was so comforting and warm that it was easy for me to segue from asking her how school was going to discussing other light topics. Though I felt guilty about it, I decided not to take Megan to the game. If things went well, Elena would meet Megan eventually. For that day, I wanted to be able to focus all my attention on Elena. I arranged for Megan’s favorite sitter and went on to meet Elena at a bus stop near the school. She was joined by her best friend, a Chilean student named Carolina. As the soccer game commenced, I found myself sharing all I could with Elena in the stands—about what happened the night of the mugging, about my drawings, about the geometry I saw all around me. I was afraid I might be overwhelming her, but I thought it was important that she knew who I was from the start. To my delight, she smiled and nodded a lot and asked plenty of her own questions about my theories. Bonus: she was really bright and had a quirky, sharp sense of humor that was some blend of American and Russian sensibility I found really intriguing.