Note to readers: Every now and then, I am intrigued enough by one of the proposals presented to me for a guest column that I decide to publish it. This is one of those times. As a former (but long-time non-practicing) student of mathematics, I bring to you the thoughts of two very distinguished educators and authors, PhDs both, who also happen to be baseball fans. In the essay that follows, they consider the possibilities of the power of the parabola in the success of the St. Louis Cardinals.
By Sujata Bhatia, Harvard University and Patrick Chura, University of Akron
From the foul lines to the angles of the bases, one would assume that the game of baseball is about straight edges, squares and diamonds. But the parabolic arch on the field of Busch Stadium hints otherwise.
Probably we are introduced to parabolas during high school. In math class, we learn that the parabola is an open-ended “U” with arms that reach toward infinity. In physics class, we earn that parabolas are fundamental to projectile motion. Throw a ball and it will trace a parabola. Bounce the ball along the ground, and a series of diminishing parabolas will result. A parabola is the shape comets make when they orbit the sun. NASA calls such a path an “escape orbit” because an object that achieves such a trajectory can travel forever.
We might even get to talk about parabolas during English class. In “Walking,” the last essay Henry David Thoreau ever wrote, Thoreau said he wanted his beloved daily walks in the woods to follow the contour of “a parabola… opening westward.” Thoreau chose the parabola for its philosophic properties, seeing it as a perfect middle way between opposing cultural forces. It symbolized not only the type of beauty he wished his walks to have, but the shaping and altering effects he wished his life to have.
The parabola also has a lot to do with the game of baseball. Though we’re used to thinking of the baseball diamond as the epitome of lines and angles, the game is really defined by curves. For the All-Star Game in 2009, the St. Louis Cardinals tapped into the deep science of the sport by combing into the outfield grass of the new Busch Stadium a beautiful replica of Eero Saarinen’s 630-foot parabolic masterpiece, the St. Louis Gateway Arch. Cardinal PR rep Mark Taylor said that the figure “was so well received by the media and fans that the team decided to keep it as a signature feature of the ballpark.”
The Cardinals have had great success on this field, so it’s worth considering whether the club’s innovative take on “field geometry” helps them win. As many fans know, the flight path of a hit baseball is parabolic. And according to accepted research in environmental psychology, so is the ideal path taken by an outfielder to intercept the ball’s flight. Catching a fly ball requires the calculation of a subconscious geometric equation that relies on the ability to predict parabolic motion. This ability is what brings outfielder and fly ball together in one of the game’s key kinetic processes—a process that, in essence, illustrates the joining of a parabola with a parabola. Making the necessary split-second calculations on a playing surface that is inscribed with the parabolic shape could make the Cardinal players more efficient. A Cardinal outfielder, whether he is looking straight ahead or upward toward a batted ball, always has the arc of a parabola—a shape replicating the game’s dynamic geometry—in his field of vision.
Of course, the visiting team plays on the same field. But playing at Busch Stadium for a handful of games a year is not the same as taking regular practice and playing 81 regular season games there. Part of the home field advantage is the psychological reinforcement that comes with familiarity, allowing the environment to enhance the judgment of home players in comparison to opponents who do not internalize it to an equal degree.
Psychologists claim that humans are always responding to environmental variables, and the Busch Stadium parabola seems a major one. The long-term imprinting of this field design could work for the Cardinals in many ways. Using the constant locational cues made possible by the parabola, Cardinal outfielders can position themselves more accurately for hitters and set themselves for throws to the bases with more confidence. Being familiar with the arc of the parabola can help guide throwing lines and the ball’s trajectory.
A similar parabolic consciousness might even make Cardinal hitters more comfortable at the plate. Second base and home plate bisect the parabola and lie along a geometric sweet-spot called an axis of symmetry. This could give hitters an added reference point for guiding the ball toward gaps. Painting a straight white line to halve the field from home plate to centerfield would violate the rules of the game, but the curved parabola accomplishes the same thing another way.
So we shouldn’t be deceived by the perpendicular lines of the baseball diamond; the game is all turns, arches, bends and bows. The swing of the batter, the path of the fielder, the flight of the baseball, even the red seams on the ball are all curving arcs. By making a parabola the signature feature of their field, the Cardinals have unleashed the real beauty of baseball. And the more we think about it, the more we suspect that this eye-catching innovation actually helps the Cardinals win.
On Wednesday night, on the field where St. Louis had a 55-28 record this year, the Cardinals won the deciding game of their division series against Pittsburgh. If they continue to win, other teams might eventually re-think their own field geometry. And we’ll be comparing the arms of the parabola to the arms of a triumphant athlete, reaching upward toward infinity.
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