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Authors: Richard Preston
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manner of speaking, pi is undescribable and cannot be found.
The earliest known reference to pi in human history occurs in a Middle Kingdom papyrus scroll, written around 1650 B.C.E . by a scribe named Ahmes. He titled his scroll “The Entrance into the Knowledge of All Existing Things.” He led his readers through various mathematical problems and solutions, and toward the end of the scroll he found the area of a circle, using a rough sort of pi.
Around 200 B.C.E ., Archimedes of Syracuse found that pi is somewhere between 3 10 /71 and 3 1 /7. That’s about 3.14. (The Greeks didn’t use decimals.) Archimedes had no special term for pi, calling it “the perimeter to the diameter.” By in effect approximating pi to two places after the decimal point, Archimedes narrowed down the suspected location of pi to one part in a hundred. After that, knowledge of pi bogged down. Finally, in the seventeenth century, a German mathematician named Ludolph van Ceulen approximated pi to thirty-five decimal places, or one part in a hundred million billion billion billion—a calculation that took Ludolph most of his life to accomplish. It gave him such satisfaction that he had the thirty-five digits of pi engraved on his tombstone, which ended up being installed in a special graveyard for professors in St. Peter’s Church in Leiden, in the Netherlands. Ludolph was so admired for his digits that pi came to be called the Ludolphian number. But then his tombstone vanished from the graveyard, and some people think it was turned into a sidewalk slab. If so, somewhere in Leiden people are probably walking over Ludolph’s digits. The Germans still call pi the Ludolphian number.
In the eighteenth century, Leonhard Euler, mathematician to Catherine the Great, empress of Russia, began calling it p or c. The first person to use the Greek letterwas William Jones, an English mathematician, who coined it in 1706. Jones probably meantto stand for “periphery.”
It is hard to ignore the ubiquity of pi in nature. Pi is obvious in the disks of the moon and the sun. The double helix of DNA revolves around pi. Pi hides in the rainbow and sits in the pupil of the eye, and when a raindrop falls into water, pi emerges in the spreading rings. Pi can be found in waves and spectra of all kinds, and therefore pi occurs in colors and music, in earthquakes, in surf. Pi is everywhere in superstrings, the hypothetical loops of energy that may vibrate in many dimensions, forming the essence of matter. Pi occurs naturally in tables of death, in what is known as a Gaussian distribution of deaths in a population. That is, when a person dies, the event “feels” the Ludolphian number.
It is one of the great mysteries why nature seems to know mathematics. No one can suggest why this should be so. Eugene Wigner, the physicist, once said that the miracle in the way the language of mathematics fits the laws of physics “is a wonderful gift which we neither understand nor deserve.” We may not understand or deserve pi, but nature is aware of it, as Captain O. C. Fox learned while he was recovering in a hospital from a wound that he got in the American Civil War. Having nothing better to do with his time than lie in bed and derive pi, Captain Fox spent a few weeks tossing pieces of fine steel wire onto a wooden board ruled with parallel lines. The wires fell randomly across the lines in such a way that pi emerged in the statistics. After throwing his wires on the floor eleven hundred times, Captain Fox was able to derive pi to two places after the decimal point—he got it to the same accuracy that Archimedes did. But Captain Fox’s method was not efficient. Each digit took far more time to get than the previous one. If he had had a thousand years to recover from his wound, he might have gotten pi to perhaps another decimal place. To go deeper into pi, it is necessary to use a machine.
The race toward pi happened in cyberspace, inside supercomputers. In the
The earliest known reference to pi in human history occurs in a Middle Kingdom papyrus scroll, written around 1650 B.C.E . by a scribe named Ahmes. He titled his scroll “The Entrance into the Knowledge of All Existing Things.” He led his readers through various mathematical problems and solutions, and toward the end of the scroll he found the area of a circle, using a rough sort of pi.
Around 200 B.C.E ., Archimedes of Syracuse found that pi is somewhere between 3 10 /71 and 3 1 /7. That’s about 3.14. (The Greeks didn’t use decimals.) Archimedes had no special term for pi, calling it “the perimeter to the diameter.” By in effect approximating pi to two places after the decimal point, Archimedes narrowed down the suspected location of pi to one part in a hundred. After that, knowledge of pi bogged down. Finally, in the seventeenth century, a German mathematician named Ludolph van Ceulen approximated pi to thirty-five decimal places, or one part in a hundred million billion billion billion—a calculation that took Ludolph most of his life to accomplish. It gave him such satisfaction that he had the thirty-five digits of pi engraved on his tombstone, which ended up being installed in a special graveyard for professors in St. Peter’s Church in Leiden, in the Netherlands. Ludolph was so admired for his digits that pi came to be called the Ludolphian number. But then his tombstone vanished from the graveyard, and some people think it was turned into a sidewalk slab. If so, somewhere in Leiden people are probably walking over Ludolph’s digits. The Germans still call pi the Ludolphian number.
In the eighteenth century, Leonhard Euler, mathematician to Catherine the Great, empress of Russia, began calling it p or c. The first person to use the Greek letterwas William Jones, an English mathematician, who coined it in 1706. Jones probably meantto stand for “periphery.”
It is hard to ignore the ubiquity of pi in nature. Pi is obvious in the disks of the moon and the sun. The double helix of DNA revolves around pi. Pi hides in the rainbow and sits in the pupil of the eye, and when a raindrop falls into water, pi emerges in the spreading rings. Pi can be found in waves and spectra of all kinds, and therefore pi occurs in colors and music, in earthquakes, in surf. Pi is everywhere in superstrings, the hypothetical loops of energy that may vibrate in many dimensions, forming the essence of matter. Pi occurs naturally in tables of death, in what is known as a Gaussian distribution of deaths in a population. That is, when a person dies, the event “feels” the Ludolphian number.
It is one of the great mysteries why nature seems to know mathematics. No one can suggest why this should be so. Eugene Wigner, the physicist, once said that the miracle in the way the language of mathematics fits the laws of physics “is a wonderful gift which we neither understand nor deserve.” We may not understand or deserve pi, but nature is aware of it, as Captain O. C. Fox learned while he was recovering in a hospital from a wound that he got in the American Civil War. Having nothing better to do with his time than lie in bed and derive pi, Captain Fox spent a few weeks tossing pieces of fine steel wire onto a wooden board ruled with parallel lines. The wires fell randomly across the lines in such a way that pi emerged in the statistics. After throwing his wires on the floor eleven hundred times, Captain Fox was able to derive pi to two places after the decimal point—he got it to the same accuracy that Archimedes did. But Captain Fox’s method was not efficient. Each digit took far more time to get than the previous one. If he had had a thousand years to recover from his wound, he might have gotten pi to perhaps another decimal place. To go deeper into pi, it is necessary to use a machine.
The race toward pi happened in cyberspace, inside supercomputers. In the
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