Struck by Genius: How a Brain Injury Made Me a Mathematical Marvel by Jason Padgett, Maureen Ann Seaberg Page A
Authors: Jason Padgett, Maureen Ann Seaberg
Ads: Link
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
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
Similar Books
