The Calculus Diaries - Jennifer Ouellette [37]
Buffon performed the same experiment using a sewing needle and a checkerboard—hence the name Buffon’s needle. Drop the needle onto the checkerboard, and one of two things happens: Either the needle crosses or touches one of the lines, or it doesn’t cross any lines. (This assumes parallel lines or squares spaced about one inch apart, and the use of a needle one inch long.)
Buffon dropped the needle over and over again, keeping track of how the needle randomly landed each time. His found that the probability that a dropped needle (or tossed coin) would cross a line is approximately 2 divided by π. He divided the number of crossing needles by the total number of needles, and realized that the more times one drops the needle, the closer one would approach the value of the probability—that is, the closer one would come to the value of π.
There are many online versions of this experiment, wherein the player can repeat the “toss” as many times as desired: five hundred, a thousand, even a hundred thousand times. Once again, the more times you repeat the experiment—the more times you roll the dice at the craps table, or spin the roulette wheel—the more closely you will approach the calculated probability. There may be winning or losing streaks in the short term, but the more you play, the more predictable things become. It’s just a quirky little oddity that the value relates to π.
With an infinite number of tosses, the value will be exactly π—that is the limit of that infinite series of tosses. The mathematician Pierre-Simon de Laplace definitively proved this in 1812. This is also the essence of what Mary Malone discovers in The Amber Spyglass. A seemingly random scattering of needles (or yarrow sticks) over a sheet of lined paper can nonetheless give you a very precise number in the end. Such is the power of calculus.
4
The Devil’s Playground
Mechanics is the paradise of mathematical science because here we come to the fruits of mathematics.
—LEONARDO DA VINCI
It is a bright and sunny Sunday afternoon inside Disneyland’s California Adventure theme park. Visitors meander blithely through the broad “streets,” nibbling on ice cream and occasionally pausing for photo ops with life-size characters from popular animated features like Monsters, Inc., The Incredibles , or Lilo & Stitch. They seem oblivious to the ominous shadow cast by the Tower of Terror, looming nearly two hundred feet above the ground, or the screams emanating from within the structure. Blackened scorch marks decorate the crumbling facade, where lightning supposedly struck in 1939, with tragic results.
Of course, nothing in Disney’s many theme parks is real. Those are screams of exhilarated delight, not abject terror, piercing the grim walls. Inspired by the classic TV series Twilight Zone, the Tower of Terror is Disney’s theatrical twist on the classic free-fall ride. We’ve been waiting in line for nearly forty-five minutes to experience those few fleeting moments of thrills and chills.
Inside we encounter the faded glory of a bygone era: Sagging overstuffed furniture, layers of dust, cracked plaster, and glass chandeliers laced with fake cobwebs grace the “lobby.” We gradually shuffle our way to a boarding dock for mock elevators, where an employee dressed as a bellhop ensures we are all tightly strapped into our seats. Our elevator rises midway to the top and stops, and we are treated to Rod Serling’s disembodied voice regaling us with the saga of a dark and stormy night on October 31, 1939, when five hotel guests stepped into an elevator and were launched into . . . the Twilight Zone!
Before we can snicker at the cheesy effects, our elevator makes a sudden gut-churning drop back to the ground floor and then shoots up all the way to the top of the structure (ostensibly the thirteenth floor), the acceleration pushing us into our seats.