I could mention my first introduction to Godel’s theorem about the essential incompleteness of mathematics; or my first encounter with the Banach-Tarski theorem in topology showing that a sphere the size of a pea can be decomposed into a finite number of pieces and put back together to get a sphere the size of a basketball; or Russell’s paradox about the set of all sets that do not belong to themselves; or any number of counterintuitive results in probability theory. All of these mathematical ideas excited me in high school and college, but I will concentrate instead on the thrill I felt in elementary school when I saw that the power of simple arithmetic was sufficient to vanquish a bully, my fifth-grade teacher. It still evokes the same emotions in me that it did decades ago.Indeed being proved right is one of the most seductive possible experiences, luring many of us to pursue knowledge as a calling. Unfortunately it also lures many of us into arrogance, or at least it did me. Full of my own intellectual victories over teachers, textbooks and peers, I was at 19 a pompous, insufferable jerk. But I have mostly gotten over it, and I learned a huge amount along the way.
I was about 10 years old and enthralled with baseball. I loved playing the game and aspired to be a major league shortstop. (My father played in college and professionally in the minor leagues.) I also became obsessed with baseball statistics and noted that a relief pitcher for the then Milwaukee Braves had an earned run average (ERA) of 135. (The arithmetic details are less important than the psychology of the story, but as I dimly recall, the pitcher had allowed the opposing team to score five runs and had got only one batter out. Getting one batter out is equivalent to pitching one-third of an inning, one-27th of a complete nine-inning game––and allowing five runs in one-27th of an inning translates into an ERA of 5/(1/27) or 135.)
Impressed by this extraordinarily bad ERA, I mentioned it diffidently to my teacher during a class discussion of sports. He looked pained and annoyed and sarcastically asked me to explain the fact to my class. Being quite shy, I did so with a quavering voice, a shaking hand, and a reddened face. (A strikeout in self-confidence.) When I finished, he almost bellowed that I was confused and wrong and that I should sit down.
An overweight coach and gym teacher with a bulbous nose, he asserted that ERA’s could never be higher than 27, the number of outs in a complete game.
For good measure he cackled derisively.
Later that season, The Milwaukee Journal published the averages of all the Braves players. Since this pitcher hadn't pitched again, his ERA was 135, as I had calculated. I remember thinking then of mathematics as a kind of omnipotent protector. I was small and quiet and he was large and loud. But I was right and I could show him. This thought and the sense of power it instilled in me was exciting. So, still smarting from my earlier humiliation, I brought in the newspaper and showed it to him. He gave me a threatening look and again told me to sit down. His idea of good education apparently was to make sure everyone remained seated. I did sit down but this time with a slight smile on my face.
We both knew I was right and he was wrong.
Tuesday, July 7, 2015
The Thrill of Being Right
The Aspen Ideas Festival asked a bunch of famous intellectuals, "What Insight or Idea has Thrilled You?" Mathematician John Allen Paulos answered with this story: