The Calculus Diaries - Jennifer Ouellette [36]
NEEDLE IN A HAYSTACK
We round out our wild Vegas weekend with several hours of good old-fashioned poker—a game of skill and strategy, as opposed to pure random chance, wherein the casino takes a cut of the pot instead of relying on a built-in house edge. What have I learned? “Craps” is an apt moniker. Also? I can’t bluff worth a damn at Texas hold ’em. But in the end, we emerge from the weekend with our wallets relatively unscathed.
Relaxing over cocktails at the Bellagio that evening, I ponder the fact that probability theory and gambling are also linked to fortune-telling and one of the most famous “natural” numbers, π. In Philip Pullman’s The Amber Spyglass, fictional Oxford physicist Mary Malone finds she can communicate with the mysterious, conscious particles collectively named Dust using the yarrow-stick casting methods of the I Ching (it’s also possible to use coins). For those who scoff that a physicist would never express any appreciation for a “supernatural” method of divination, consider this: When he was knighted, Neils Bohr included the yin-yang symbol in the design for his coat of arms, to reflect his appreciation for the I Ching’s ingenious use of probabilistic concepts.
Mary Malone’s divination method has a real-world counterpart in one of the oldest problems in geometrical probability, known as Buffon’s needle. This experiment was the brainchild of a French naturalist and mathematician named Georges-Louis Leclerc, Comte de Buffon. Born and raised on the Côte d’Or, the young George-Louis started off studying law before getting side-tracked by mathematics and science. It’s not clear that he ever earned a degree, because he was forced to leave the university after getting tangled up in a duel. He then toured Europe, only returning when he heard his father had remarried—not so much out of familial devotion as concern over collecting his inheritance.
Buffon fils is best known for writing the Histoire naturelle, a whopping forty-four volumes of encyclopedic knowledge that covered everything known at that time about the natural world. A full hundred years before Charles Darwin’s Origin of Species, Buffon noted the similarities between humans and apes and mused on the possibility of a common ancestry, concluding that species must have evolved since that common point. He never proposed an actual mechanism for this evolution, but his tome was translated into numerous languages and certainly influenced Darwin, who described Buffon—in the foreword to the sixth edition of Origin—as “the first author who in modern times has treated it in a scientific spirit.”
Buffon’s quirky contribution to probability theory lies in a paper he published in 1777 entitled, Sur le jeu de franc-carreau [On the Game of Open-Tile]. He first considered a small coin—an ecu, for all you crossword puzzle buffs—thrown randomly on a square-tiled floor. It was all the rage in Buffon’s social circles to place bets on whether the coin would land entirely within the bounds of a single tile or across the boundaries of two tiles right next to each other. Buffon had a bit of an advantage over his peers thanks to his mathematical interests. He realized he could figure out the odds of the wager using calculus, making him the first person to introduce calculus into probability theory.
Buffon noted that the coin would land entirely within a tile whenever the exact center of the coin landed within a smaller square—and that smaller square’s side was equal to the side of a floor tile minus the diameter of the coin used in