Struck by Genius: How a Brain Injury Made Me a Mathematical Marvel (8 page)

Then I could finally hug my daughter.

Chapter Six

A
S A CHILD
, I had a vast seashell collection. My prized piece was a brown polka-dot nautilus that had been varnished. How many hours had I stared at this store-bought addition to the other shells, most of which I’d found on vacation beaches with my family? I had liked it because it was so clean and glossy. In childhood imaginings, staring at that shell, I saw myself going round and round the spirals like a slide, the spiral never ending and the sound of the ocean echoing in the white halls of my seashell amusement ride. I wondered about my favorite shell’s previous life under the sea and the creature that had inhabited it. How deep underwater had it lived? What had it eaten? Where had it been in its travels? How had it died? How could it be so utterly perfect living in the murky depths until some fisherman or a crashing wave tossing it ashore had led it to me?

One day, I was bingeing on information again, glued to my chair, sitting in front of the computer in my house for the fourth straight hour. I’d been searching for the repetitive geometric forms I was seeing before my eyes when a nautilus shell appeared in the retrieved entries on my screen. I clicked on it immediately. There was something at once familiar about the spiraling natural form. I’d seen it in my childhood prized possession, but I’d also seen it in my morning coffee as I stirred; I’d watched it every day as the water in the sink went down the drain. And one of the new images I saw repeatedly was a spiral out in space. I often wondered about its seemingly infinite reach and how smaller parts of it echoed the larger parts. But I hadn’t connected that outer-space shape to the nautilus, much less to other things I was noticing in nature, until now. As I read on, I learned that these shapes were known as fractals, a word I’d never heard before. Fractals are the fundamental, repetitive geometric building blocks of everything in the known universe, from seashells to the leaves and trees and mountains and even to lightning. The pull of this newfound discovery was strong. It seemed to signal to me that my visions could be something more than the hallucinations of a brain-injury survivor. It felt like the beginning of a way back to sanity.

It all seemed to relate to something I’d seen during one early-morning grocery-store run. There was a leafy tree with a branch overhanging the roadway. The leaves became virtually see-through in the glow from my headlights. Each leaf seemed to have its own trunk and branches running through it, mirroring the tree as a whole. I stared in wonder, and then I held my own hand up. I was captivated and quickly flicked on the car’s overhead light to be sure. The veins of my hands branched out under my pale skin like those of the leaves. The tiny wrinkles on my hand also seemed to be a repetitive pattern. My fingers seemed an echo of my arm, my arm an echo of the trunk of my own body.
Why have I never noticed this before?
I thought. I now had respect for the smallest things and was filled with a sense of wonder about the world at large, despite my ongoing fear of it. And as quickly as it had come on, my epiphany passed, overtaken by the paranoia that someone would recognize me with the car light on and try to harm me. I flicked the light off and continued driving.

I learned all I could about the fractal nature of the seashell and began researching the budding branch of mathematics known as fractal geometry. It was a very young discipline, developed in the 1970s by IBM researcher Benoit Mandelbrot and popularized in the 1980s after the publication of his book
The Fractal Geometry of Nature.
Why is fractal geometry so much more amazing than the stuff most of us learned in school? Textbook Euclidean geometry is what’s used to measure or create smooth shapes—think of the clean edges of a high-rise building, the sleek lines of a countertop, or the symmetrical arch of a bridge. But it tends to fall short when one attempts to measure or reproduce the rough shapes found in nature, such as clouds, craters, or those coastlines I mentioned earlier. Mandelbrot’s fractal geometry finally gave us a way to explore and understand the natural roughness in the world around us.

Mandelbrot came up with the concept of fractals while at IBM, where, amid all the number crunching and analysis, he began noticing repeating patterns within the data. He applied a simple mathematical formula, which has since become known as the Mandelbrot set, to the patterns he detected. I know that not everybody is as enthralled with fractal geometry and math as I am, but I can’t help but share the actual formula. I think even math-averse people would have to admit that it looks surprisingly simple:
z
_n+1
= z
_n
²
+ C.
Where it gets tricky is that it involves complex numbers (a complex number is made up of two real numbers and one imaginary number). And to complicate things even more, every time you solve for
z,
you plug that new value back into the equation recursively and build it out, so the results never end. It can go on literally to infinity.

Things really got exciting when Mandelbrot put the powerful computing technology at IBM to work, letting the computers apply the formula over and over and over again—more times than any human possibly could. Next, he used the new technology to plot out a visual representation of the formula. The result? A breathtaking image of a fractal so intricately detailed that I could look at it on my computer and hit the zoom button ten times—or, if my computer would let me, a thousand, a million, or even a billion times—and see smaller and smaller subsets of similar but not quite identical patterns. Because of the Mandelbrot set’s intricate patterns and never-ending nature, experts have said that the set may be the most complex of all mathematical objects.

The Mandelbrot set has captured popular imagination, outside of the realm of mathematics, for many reasons. For one thing, when plotted out, it’s a very beautiful image. In a 2010 TED talk, Mandelbrot explained that depending on the specific numbers he plugged into the formula, the computers spit out shapes of “such complication, such harmony, and such beauty.” He was absolutely right. I stared at the paisley- and ice-crystal-like images I found online and was awestruck and inspired. For some people, the Mandelbrot set is a glimpse into the infinite nature of the universe. Others see it as a way to find order in our chaotic world. Still others consider it a representation of the similarity shared by everything and everyone on this planet.

For me, it was a reflection of what was going on in my own mind—on a smaller scale, of course. Perhaps my mind wasn’t processing what it saw on the same infinite scale Mandelbrot found, but I do think that what I experience is somehow a reflection of his work. Just as the Mandelbrot set reflects the universal order of things in nature (it has been referred to as “God’s thumbprint”), I believe what I’m seeing is the very essence of ourselves and our universe.

One day I watched a documentary called
The Colours of Infinity.
It featured Mandelbrot and was hosted by the great science and science fiction writer Sir Arthur C. Clarke, who may be best known for cowriting the screenplay for the film
2001: A Space Odyssey.
Of course, I loved learning more about fractals, but what was most astounding to me was an interview with Michael Fielding Barnsley of Great Britain. A mathematician and author, he founded a company called Iterated Systems Incorporated and works on fractal models that can be applied to technology and even medicine. It occurred to me for the first time that while my visions were nice to look at, they might also have useful applications.

The deeper I looked into the application of fractals, the more I felt that what I was seeing wasn’t so alien after all. Mandelbrot himself said in the documentary that humans might have discovered his set at any point in human history, given its organic nature and the simplicity of the math behind it. However, it wasn’t until the powerful computers of the late twentieth century were able to plot millions of results that anyone could see it in all its complexity. Still, fractals can be seen in everything from ancient carpets from the Far East to Islamic tile work to Western stained-glass windows. In Mandelbrot’s TED talk, he mentioned that even the Eiffel Tower in Paris had a fractal aspect to it. He suggested that its creator, Gustave Eiffel, was “intuitively” familiar with fractals. Had artists and architects through the ages seen the things I was now seeing? I knew that before my injury, I had noticed repeating patterns in the ragged edges of coastlines and in ice crystals, but now I was seeing repetitive geometric images in my own mind. Learning about fractals and the Mandelbrot set validated my belief that my new visions were giving me a firsthand look at the secrets of the universe. And yet this breakthrough, this glimmer of hope, still happened in darkness, behind the blankets I’d tacked up to my windows.

One month turned into one year, a year into two, two years into three, my darkened hovel lit only by the persistent, incandescent visions in my mind, the TV, and the computer monitor. Had someone peered in, he or she would have seen a man very much alone in his thoughts and research, a hermit who had almost no connection to the outside world. After three years, I’d given up hope my brother would ever return. I was missing now too, in my own way, having turned deep inside myself. It was hard to tell if I’d emerge from this self-imposed exile, but I was too obsessed with these new patterns in the universe to really care. This was my life now—I was drawn deep into the infinite and fractal spiral of my own mind.

Interruptions from the outside world were few and far between. My visits from Megan were always a high point, but my main companions in my seclusion were my memories, the TV, and the computer. They offered a safe connection to the outside world. My viewing and surfing habits were quite different than they’d been before, however. While I’d always had an interest in science fiction, I had never turned my attention to pure science. I used to watch football every Sunday and make a real occasion of it, popping corn and camping out on the sofa for hours with family and friends. Now I didn’t care at all about my favorite teams. I found myself obsessed with any programming having to do with scientific research. Science fiction remained an interest too, but I was now more curious about the reality of science than the fantasy, with one exception.

I would set the alarm for three o’clock each morning, though sometimes I was already—or still—up, to watch my favorite TV show,
Farscape.
An Australian program that lasted four seasons, it featured the adventures of a character called John Crichton, an astronaut. He was part of a group trying to escape from corrupt authorities, called Peacekeepers. Crichton had accidentally flown through a wormhole and wanted to make his way back to Earth. At one point, to help Crichton get home, aliens implanted in his brain the ability to do higher math and physics. I was hooked. I had no delusions that my new abilities came from aliens, but like my hero, I was suddenly overwhelmed by what I knew and understood.

I too felt like a stranger in a strange land trying to find his way back home. That character, with whom I felt I had so much in common, was my only friend during a very lonely time. I was devastated when the series was canceled.

Then one night, about three years into my isolation, in the blue glow of the television, I stumbled on a program about a man named Daniel Tammet—a synesthete and autistic savant from England who was able to recite pi from memory to 22,514 places. This was even better than my scuttled hero John Crichton because Tammet was a real human being and he was interested in the same things I was. With his studious appearance and fair coloring, he even resembled the new me. At one point Tammet said he could do math so well because he could see it in shapes before his eyes.

I leaped from my chair and began jumping around the room. “That’s it! That’s what’s going on with me. Oh my God! Someone else can see what I see!”

I rushed to my computer and Googled
Daniel Tammet,
savant syndrome,
and a word I’d never heard before:
synesthesia
. I quickly learned that synesthesia is a sort of blending of the senses that can take many forms. Some people with synesthesia see colors when they look at numbers or letters—for example,
A
might be orange,
B
might be violet, and
C
might be lime green. Others see colors when they hear music. Still others may taste words or smell colors. In Tammet’s case, he saw numbers as colors and shapes and said this helped him to remember them and calculate with great ease.

When I looked up savant syndrome, I found that, by definition, a savant is someone with a lot of knowledge about a particular subject or field. But the term often gets used to describe a person whose unusual aptitude for a specific subject or skill comes along with decreased abilities in other areas. Most savants, like the extremely high-functioning Tammet, are born that way. Not me. I was quickly realizing that my situation was far more rare. Experts called it sudden-onset savant syndrome or acquired savant syndrome. I read all I could for many hours into the morning. Then I slept deeply, for the first time in months, with my face on the keyboard. The worry and confusion of the past three years had finally lifted a little.

Knowing I had a brain injury was pretty frightening. But sensing that I might have acquired synesthesia and savantism as a result was oddly exciting. Except I had no idea what those things were. After three years out of work, I definitely couldn’t afford the required testing and medical advice, nor did I want to emerge from my house, so I set out to learn all I could on my own. I continued to mine that mother lode of all knowledge, the Internet.

I learned that at that time, there were only thirty documented cases of acquired savant syndrome on the entire planet, and none of the savants also had synesthesia. Could I be the only one in the world? I’d felt such pangs of recognition in seeing Tammet describe his own naturally occurring synesthesia and savantism, I was sure I must be right in thinking I had these syndromes. But I was not sure I wanted to be this new self, regardless of its rarity and its attractions.