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

by Padgett, Jason

  I didn’t know much about academic procedures and I was far from being able to write a journal article on my thoughts and submit it for peer review, but this little step in taking my thoughts public was a real change for me. I found that society interested me again—if only in the context of having a conversation with people about math. I had some great responses, which encouraged me, and some real trolls, who insulted me and made me realize online forums aren’t the best place to seek feedback. But it was still a big step for me to post my thoughts.

  After that brief and mixed-results excursion into public discourse, I doubled up on my reading and ignored the pull of the outside world. Historically speaking, I was in good company—Archimedes was allegedly so engrossed in pi that he failed to notice when Roman soldiers captured his home city of Syracuse. Before he was beheaded, he yelled, “Don’t disturb my circles!” I understood how he felt.

  The term pi, which is the sixteenth letter of the Greek alphabet, was first used to describe the irrational number in a 1706 paper by the mathematician William Jones. The concept of pi has existed for four thousand years, and it can be used as a litmus test to indicate where humans were technologically at any given time. As Petr Beckmann wrote in A History of π, “The history of π is a quaint little mirror of the history of man.” I read that Simon Newcomb, the astronomer and mathematician who accurately measured the speed of light in the nineteenth century, had been quoted as saying humankind’s fascination with pi vastly transcends practical need. “Ten decimals are sufficient to give the circumference of the earth to the fraction of an inch,” he said, “and thirty decimals would give the circumference of the whole visible universe to a quantity imperceptible with the most powerful telescope.” But as humankind advanced, so did the utility of pi. Since ancient times, it has been important in construction and architecture. Now, everything from manufacturing machine parts to navigation and global positioning makes use of the constant in engineering formulas. Its infinite trail stretches out before us like a road map to the future, driving us forward. If pi really is tied to the Planck length, I imagine this finding could prove even more useful, for everything from space travel to supercomputing to things we have not yet imagined. If explorers from another world one day found our lifeless planet and excavated the ruins, I fantasized they would conclude, “Throughout their history, humans sought the end of pi.”

  Realizing this made me want to perfect pi—to get it to the closest possible measurement of all. I went deeper within myself than I ever had before to attempt this. I became a virtual hermit as I pursued my study of pi. I knew I was obsessed. However, I had read that obsession was key to savants’ capabilities and supposed this was how I was going to be from now on. I didn’t try to change my behavior. I was growing to like the new me.

  Even in the beginning of my pi quest, when I was energized by my newfound artistic abilities, I understood the contradictions in my behavior. I was creatively extroverted—practically evangelistic about my visions, in fact—but physically introverted and still flinching at the sound of footsteps. I rarely felt up to tackling my fear, but my daughter, Megan, inspired me to try. Early one evening in 2005, I noticed that my seven-year-old was staying cooped up in the living room with her friend Dylan rather than playing outdoors. My fear for my own safety extended to my precious child, and I never even let her go out into the yard. It occurred to me that she was feeling the same isolation I’d created for myself. I dug out my telescope from the closet and shouted from the entryway:

  “C’mon, guys, we’re going outside to look at the stars.”

  “Are you sure, Daddy?” Megan was surprised to see me even approach the front door.

  “Absolutely; come on.”

  I was almost finished setting up the tripod outside when my neighbor from two doors down approached.

  “Excuse me, you’re stepping on my irises,” she said.

  “That’s a good joke!” I responded, thinking she was referring to the irises of her eyes and the high-powered lens of the telescope. I was becoming really good at reading body language and having empathy, but verbal cues were not my strong suit.

  “It’s not a joke. You’re in my flower bed!”

  “Oh, I’m sorry . . . I’ll move down five feet or so. I live right there.”

  “What do you mean, you live right there? No one lives there,” the woman said, sweeping her hand toward my house. The roof was partially caved in—due to a fallen tree branch—and pigeons were flying in and out of the attic.

  “No, really, I’ve lived here for the last six years,” I replied. The neighbor walked back home, incredulous.

  My time outside my house was brief; I was pulled back in to my studies of pi. My isolation reinforced by my obsession with this number, I continued to learn its history and practice drawing my visions and equations by hand. I began to lose all sense of time and found myself practically hypnotized by the pursuit. I concluded that when scientists used computers to illustrate a formula, they forfeited the opportunity to witness each individual step, and much of the information about the underlying math and how it actually worked was lost. I may not have been a mathematician, but not a step was lost on me in my geometric bunker.

  I almost didn’t remember the old barhopping, good-time Jason now as I hunched over my drawing tablet or sat for hours in front of the computer, soaking up all that I’d missed during my formal education and chasing pi’s infinite trail out into space. I began to take solace in my isolation because I had found my passion, my constant companion: my research.

  After pi revealed itself to me in a way that could be drawn, the other images came to me, one after another. The floodgates opened and I could finally express what was going on in my newly fertile mind. I could see geometric representations for equations related to relativity, for example, and to the photon double-slit experiment and to particle fusion and to the way prime numbers live for me at vectors within a sphere. Nothing was a simple equation; it had to have form.

  I bought several artist’s drawing tablets and boxes of new pencils and spent every moment—at the breakfast table or my desk—working on putting these visions on paper.

  One of the earliest things I did was plot the way I saw prime numbers: out in space, in front of me. I drew a circle and began filling it with sequential, boxed numbers, setting off the primes by coloring in their spaces with a red or blue pencil. Instead of tracing this in the air while trying to describe it verbally, I could show people something concrete about what I was thinking. Though it was still unusual for me to see people, on those occasions when I did, I found them nodding at my explanations. Even if they didn’t understand it completely, most said it was beautiful and had an interesting pattern.1

  My synesthetic visions were solved and unsolved, explaining mathematical concepts to me but not explained by mathematical concepts (at least, none that I was aware of). I began to think of them as a different way into known concepts, as though I were seeing math from a fresh angle. To me, they were so provocative that they made things relevant for the first time in my life and made me want to know about the realm they came from.

  I also tried my hand at a shape that artists, mathematicians, physicists, and others have been drawing for thousands of years. Some describe it as sacred geometry, while others use scientific terms like grid and lattice. I like to call it a Planck lattice—it’s my interpretation of the structure of space-time, and it helps me to explain quantized energy and the relationship between energy and mass described by Einstein’s theory of special relativity.

  Each side of every small equilateral triangle in this diagram represents a Planck length. I started with a single point and drew triangles outward until a lattice appeared. I realized that every point in space-time needed to be one or whole multiples of the Planck length away from all the others. This requirement, in my opinion, automatically creates the gridlike structure of space-time that Albert Einstein described.

  Another theme that inspired me to draw was the
idea of wave-particle duality, a concept introduced by Einstein in 1905. He had previously described light as made of photons. However, he knew that light sometimes acted like a wave instead of a stream of particles. I wanted to capture that moment of transition, when light is both particle and wave. This is what I saw in my mind when I imagined it. I also saw this in my mind’s eye when thinking about parallel universes. I realized there were so many discrete numbers of places you could be, and each one of those had a certain probability. A photon can follow all possible paths, just as the center point of this drawing could. This image arises in my imagination now whenever I think of probability, even when I’m making mundane decisions about which actions to take during an ordinary day.

  It occurred to me that not only did light move as waves or particles across the space-time grid, so did I—what little I moved those days. I spent many hours absorbed in translating my ideas into drawings from that point onward. The artwork allowed me to express my rich new inner life. It also gave me a sense of connectedness, in that I was now at least reading about other people and trying to take part in a conversation, even if my continuing fear of face-to-face human contact kept me from leaving the house. In so many ways, my art was saving me.

  Chapter Eight

  Inflection Point

  DRAWINGS OF MY visions and ideas were now piled high all around me in every room. I was drifting off to sleep in front of the TV one late April night in 2006 when a local news bulletin startled me into a raw, uncomfortable consciousness. The anchor reported that a human skeleton had been found over the weekend by two young boys cutting trails in the woods, and I recognized the location as a stretch of evergreens only one hundred yards from my brother’s front door. After all this time, could it be possible that the answer to my brother’s disappearance had been that close?

  I dialed the station’s hot line, and the switchboard forwarded my call to the police department in Kent, a town near where my brother had lived at the time of his disappearance. I told the receptionist what my brother was wearing the night he disappeared—an Alaska Helicopters Inc. jacket and a Los Angeles Raiders baseball cap—and after an excruciating silence, she confirmed that this description matched the clothes discovered with the remains. Before the news even sank in, I phoned my mother and father, one right after the other. They cried into their receivers.

  The mystery of my brother’s vanishing was both solved and unsolved; I learned that a garrote was found next to the body and that the hyoid bone was missing from John’s neck, consistent with strangling, but the police investigation was inconclusive. With no active criminal investigation going on, the specter of suicide hung over my family, though I refused to believe it. The uncertainty was more comfortable than the conclusion, and after all, I’d learned to coexist with the inexplicable.

  I accompanied my mom to identify the remains. It was so hard to see my brother reduced to skeleton form. I stared for a long time at the contours of his skull and recognized it as very similar to my own; now that I’d grown so thin, I could see my bone structure when looking in the mirror. The similarities in the outlines and the angles were stunning to me. I tried to focus on that geometry instead of the horror before me.

  John’s death made me realize how far I’d drifted from my family. Perhaps it was time to reconnect. Though I’d felt renewed kinship with my parents over our mutual loss of John, I still couldn’t bring myself to reach out to them beyond our initial coming-together for the funeral. I couldn’t break my isolation.

  My brother’s death only reinforced my fear of the outside world and assured me that I was on the right side of my walls, where I remained. It had been three and a half years since I first retreated into the dark refuge of my home. Months of quiet study followed my brother’s death, during which memories of him interrupted my thoughts regularly.

  Some of the memories were bittersweet. One summer day when I was about nine and John was eleven, we were in the Alaska woods and a car came tearing through a dirt road toward us, kicking up a huge cloud of dust. We had already made dozens of dead-end trails in the forest around the cabin, fitting the paths with tripwires made of fishing line and digging half-foot holes in the ground that were camouflaged with leaves to trap any bad guys who might approach. John hurriedly shaved the leaves off a six-foot fireweed to fashion a spear and launched it at the car, which came screeching to a halt. Out came one very angry, very drunk lumberjack. We boys ran like hell down one of our trails, dissolving into fits of giggles when the tree cutter fell like an oak himself, tripped by one of our wires. Then he got up and got close enough to grab John by the ankle. He screamed at us for some time but eventually returned to his car. We high-fived each other and celebrated our ability to protect ourselves; the trap had worked, on the whole. We thought we were immortal at that moment, totally unaware of the dangers that awaited us in the future.

  My mom married a man named Bob and we eventually moved out of our cabin to a gigantic wooden home in the wilderness in the town of Girdwood. The home was built on ten-foot stilts due to the depth of the snow. We would go through about twenty cords of wood each season there—we would split and stack them ourselves. The road nearest the town is considered the most dangerous in the state of Alaska, and it’s also one of the most important routes for commerce and defense: the Seward Highway. The road goes through a national forest, continues for about five miles to our former hometown, and then passes through Chugach State Park for ten miles. After that, it goes through the skiing village of Bird and the village of Indian, and then it reenters the forest. Finally, it passes along the Gulf of Alaska and has vistas so stunning they are fatally distracting. Collisions there are almost always head-on.

  My best memory of the house was hiding up in my loft, enjoying the sound of rain on the roof or feeling the awe of the sound of snow sliding off it and down to the ground. First you would hear crack! Then: whoosh! Then: boom! Boom! and as many booms as it took to get all the large chunks of snow off the slope at the top of the house.

  Living in the wilderness proved to be too boring for John; he was so bored, he decided to call in a false fire alarm one day. I admit I aided him in that foolishness. When he handed me the phone after calling in the fire, I whimpered, “Help!” The operator sent emergency vehicles in a flash over treacherous terrain, only to find us cowering and already feeling guilty about what we’d done.

  But there had once been a real fire at our place. We had carelessly thrown a bunch of newspapers we’d used to catch paint drippings into the fireplace, and they ignited the twenty-foot chimney. My mom, Toni, is now a frail lady, owing to the losses in our lives, but back in the day, you could give her an emergency and watch some sort of superhero reserve come into play. She’s still remarkable and I seek her advice a lot. I remember her evacuating us and simultaneously fighting the fire with an extinguisher, getting us to safety and saving the house in the process.

  I remembered the time a bully in our town began riding his motorbike up our driveway really aggressively, harassing us with countless revs of his engine just under our windows. John had no problem when I dug a trench in the road out in front of our house and filled it with gasoline and put in a fuse. I waited to hear the sound of the approaching speed demon, and as soon as I did, I set it ablaze. He came screeching to a halt in front of the wall of flames and never bothered us again. Sometimes I laughed to myself through tears at these memories. I had been a survivor at a very young age.

  And then my time in Alaska ended. Our father called to ask if John and I would like to visit him in his new home in Seattle. I said yes. For some reason, John said no. When I reflect on it now, I think the divorce must have been more disturbing to John than it was to me. He was older and more aware of events, and in the way that firstborns often bear the brunt of things in a family, he took everything much harder than I did.

  My plane approached Seattle, and the Space Needle might as well have been a giant exclamation point. I couldn’t believe the city, with its perfect
balance of nature and development: the wide expanses of the blue sound, the glittering new buildings of downtown, all interspersed with green spaces. I’d been living in the woods, after all. At the summer’s end, my father and his new girlfriend, Pam, asked me if I wanted to stay and go to school there. I didn’t hesitate to say yes. That was the beginning of something wonderful and new for me—a second chance in a way—but it was also the beginning of a rift between me and my brother.

  Later, John did move to Seattle, but he was different, and things were never the same between us. John would like a girl, and she would like me better; we’d play a board game and I would win; I made friends more easily; and Pam chose me as her favorite. And worse, I was blissfully unaware there were hard feelings until I was about sixteen. By then John was exhibiting signs of bipolar disorder, though we didn’t know what it was at the time.

  What we were aware of was that John had withdrawn deep inside himself. He was distrustful of people and developed an abiding interest in animals, almost as a substitute. He would walk around in a trench coat filled with martial-arts weapons and sugar gliders, these tiny rodent pets he kept with him all the time. He always had the right leg of his pants rolled up to the knee—even in cold weather—to display a tattoo he’d gotten: a ferret in an attack position, standing on its hind legs. He grew violent. More than once, I had to pretend to pass out when he had me in a chokehold, to get him off me. John fought violently with Pam.