Free Pascal's Wager by James A. Connor Page B
Authors: James A. Connor
would have been sad for Blaise and embarrassing for Père Mersenne.
At once, Mersenne sent word about the younger Pascal’s success to his contacts throughout Europe. Scientists and intellectuals as far away as Poland heard about the young geometer. Meanwhile, Descartes, too, heard about the pamphlet, and on a visit to Mersenne, the monk showed him a copy. Descartes, who was then forty-four and still angry about Étienne’s criticism of his own geometry, was not impressed, and instead grumped like a grandfather with a bad tooth. “I do not find it strange that he has offered demonstrations about conics more appropriate than those of the ancients,” he said, “but other matters related to this subject can be proposed that would scarcely occur to a sixteen-year-old child.”
[1642]
The Arithmetic Machine
I propose to consider the question—Can machines think?
—A LAN T URING
B y 1642, the Pascals were well settled into the local scene in Rouen. That year, Gilberte, living in Clermont, gave birth to a son, Étienne, named for her father. Also during that year, the fearsome Cardinal Richelieu succumbed to his many diseases and died. Within a year, his master, Louis XIII, would follow. The English civil war between the Cavaliers and Roundheads began in 1642, and Galileo Galilei died of illness and old age, still under house arrest. Closer to home, the violence of the Pascal family’s first days in Normandy had subsided, and Étienne had begun his work in earnest as the chief tax collector of the region. His biggest problems had become mathematical. With the uprising, the registers had been destroyed, the office was a mess, the state of collections was disorganized, and Étienne had to spend long, laborious hours calculating, calculating, and calculating. He worked into the night every night, and soon the exhaustion that hung about this new honor was like a funeral wreath. Étienne grew snappish and complained about his health. “For four months now, I have not gone to bed more than six times before two o’clock in the morning,” he wrote to Gilberte.
Blaise, then barely nineteen, volunteered to pitch in, but he was quickly buried by the mountain of work, and since his health was ephemeral, he found himself in some distress. His head hurt. The problem was complicated by the complexity of the French currency. One French livre equaled 20 sols; one sol equaled 12 deniers, so that the steps up and down the currency were uneven and therefore not easily tabulated. One livre was therefore 240 deniers—which was unnecessarily complex. Each set of calculations, therefore, was exquisitely tedious, just the kind of work that sucks the life out of one’s soul. There had to be an easier way.
Out of pure necessity, Blaise cast about for a solution, and found it in a machine. Blaise saw fairly quickly that the kinds of calculations that his father’s work required were mechanical and could be done by a machine. But what kind of machine? The machine he came up with, the Pascaline, was the first calculating machine in the modern style. The centuries have refined the mechanism, but the basic concept underpinning the logic of Pascal’s device and the logic of an electronic computer are not that different. In essence, Pascal set up a series of gears that moved one way—forward but not backward. Inside of a long narrow box, he fixed eight cylinders, with the numbers from zero to nine printed on each one. Each cylinder had two sets of numbers, however, one descending, at the top of the cylinder, and the other ascending, at the bottom. Therefore, the top numbers were used for subtraction, while the bottom numbers were used for addition. The user would choose one operation over the other by sliding a metal bar over the unused portion of the cylinder, to highlight the calculation at hand. Underneath the row of cylinders, set horizontally across the top of the box, was a sheet of metal that hung vertically, perpendicular to the row of
At once, Mersenne sent word about the younger Pascal’s success to his contacts throughout Europe. Scientists and intellectuals as far away as Poland heard about the young geometer. Meanwhile, Descartes, too, heard about the pamphlet, and on a visit to Mersenne, the monk showed him a copy. Descartes, who was then forty-four and still angry about Étienne’s criticism of his own geometry, was not impressed, and instead grumped like a grandfather with a bad tooth. “I do not find it strange that he has offered demonstrations about conics more appropriate than those of the ancients,” he said, “but other matters related to this subject can be proposed that would scarcely occur to a sixteen-year-old child.”
[1642]
The Arithmetic Machine
I propose to consider the question—Can machines think?
—A LAN T URING
B y 1642, the Pascals were well settled into the local scene in Rouen. That year, Gilberte, living in Clermont, gave birth to a son, Étienne, named for her father. Also during that year, the fearsome Cardinal Richelieu succumbed to his many diseases and died. Within a year, his master, Louis XIII, would follow. The English civil war between the Cavaliers and Roundheads began in 1642, and Galileo Galilei died of illness and old age, still under house arrest. Closer to home, the violence of the Pascal family’s first days in Normandy had subsided, and Étienne had begun his work in earnest as the chief tax collector of the region. His biggest problems had become mathematical. With the uprising, the registers had been destroyed, the office was a mess, the state of collections was disorganized, and Étienne had to spend long, laborious hours calculating, calculating, and calculating. He worked into the night every night, and soon the exhaustion that hung about this new honor was like a funeral wreath. Étienne grew snappish and complained about his health. “For four months now, I have not gone to bed more than six times before two o’clock in the morning,” he wrote to Gilberte.
Blaise, then barely nineteen, volunteered to pitch in, but he was quickly buried by the mountain of work, and since his health was ephemeral, he found himself in some distress. His head hurt. The problem was complicated by the complexity of the French currency. One French livre equaled 20 sols; one sol equaled 12 deniers, so that the steps up and down the currency were uneven and therefore not easily tabulated. One livre was therefore 240 deniers—which was unnecessarily complex. Each set of calculations, therefore, was exquisitely tedious, just the kind of work that sucks the life out of one’s soul. There had to be an easier way.
Out of pure necessity, Blaise cast about for a solution, and found it in a machine. Blaise saw fairly quickly that the kinds of calculations that his father’s work required were mechanical and could be done by a machine. But what kind of machine? The machine he came up with, the Pascaline, was the first calculating machine in the modern style. The centuries have refined the mechanism, but the basic concept underpinning the logic of Pascal’s device and the logic of an electronic computer are not that different. In essence, Pascal set up a series of gears that moved one way—forward but not backward. Inside of a long narrow box, he fixed eight cylinders, with the numbers from zero to nine printed on each one. Each cylinder had two sets of numbers, however, one descending, at the top of the cylinder, and the other ascending, at the bottom. Therefore, the top numbers were used for subtraction, while the bottom numbers were used for addition. The user would choose one operation over the other by sliding a metal bar over the unused portion of the cylinder, to highlight the calculation at hand. Underneath the row of cylinders, set horizontally across the top of the box, was a sheet of metal that hung vertically, perpendicular to the row of