Blaise Pascal | |
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 Painting of Pascal made by François II Quesnel for Gérard Edelinck in 1691 | |
| Born | 19 June 1623 |
| Died | 19 August 1662 (aged 39) Paris, France |
| Nationality | French |
| Era | 17th-century philosophy |
| Region | Western philosophy |
| School | Cartesianism Jansenism Fideism |
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Blaise Pascal (/pæˈskæl/ pask-AL, also UK: /-ˈskɑːl, ˈpæskəl, -skæl/ -AHL, PASK-əl, -al, US: /pɑːˈskɑːl/ pah-SKAHL;[3][4][5][6][7] French: [blɛz paskal]; 19 June 1623 – 19 August 1662) was a French mathematician, physicist, inventor, philosopher, writer and Catholic theologian. He was a child prodigy who was educated by his father, a tax collector in Rouen. Pascal's earliest mathematical work was on the conics sections; he wrote a significant treatise on the subject of projective geometry at the age of 16. He later corresponded with Pierre de Fermat on probability theory, strongly influencing the development of modern economics and social science. In 1642, while still a teenager, he started some pioneering work on calculating machines (called Pascal's calculators and later Pascalines), establishing him as one of the first two inventors of the mechanical calculator.[8][9] He also worked in the natural and applied sciences, where he made important contributions to the study of fluids, and clarified the concepts of pressure and vacuum by generalising the work of Evangelista Torricelli. Following Galileo Galilei and Torricelli, in 1647, he rebutted Aristotle's followers who insisted that nature abhors a vacuum. Pascal's results caused many disputes before being accepted. Pascal also wrote in defense of the scientific method. In 1646, he and his sister Jacqueline identified with the religious movement within Catholicism known by its detractors as Jansenism.[10] Following a religious experience in late 1654, he began writing influential works on philosophy and theology. His two most famous works date from this period: the Lettres provinciales and the Pensées, the former set in the conflict between Jansenists and Jesuits. The latter contains Pascal's Wager, known in the original as the Discourse on the Machine, a probabilistic argument for God's existence. In that year, he also wrote an important treatise on the arithmetical triangle. Between 1658 and 1659, he wrote on the cycloid and its use in calculating the volume of solids. Throughout his life, Pascal was in frail health, especially after the age of 18; he died just two months after his 39th birthday.[11] Early life and educationPascal was born in Clermont-Ferrand, which is in France's Auvergne region, by the Massif Central. He lost his mother, Antoinette Begon, at the age of three.[12] His father, Étienne Pascal (1588–1651), who also had an interest in science and mathematics, was a local judge and member of the "Noblesse de Robe". Pascal had two sisters, the younger Jacqueline and the elder Gilberte. In 1631, five years after the death of his wife,[2] Étienne Pascal moved with his children to Paris. The newly arrived family soon hired Louise Delfault, a maid who eventually became an instrumental member of the family. Étienne, who never remarried, decided that he alone would educate his children, for they all showed extraordinary intellectual ability, particularly his son Blaise. The young Pascal showed an amazing aptitude for mathematics and science. Essay on ConicsParticularly of interest to Pascal was a work of Desargues on conic sections. Following Desargues' thinking, the 16-year-old Pascal produced, as a means of proof, a short treatise on what was called the "Mystic Hexagram", "Essai pour les coniques" ("Essay on Conics") and sent it—his first serious work of mathematics—to Père Mersenne in Paris; it is known still today as Pascal's theorem. It states that if a hexagon is inscribed in a circle (or conic) then the three intersection points of opposite sides lie on a line (called the Pascal line). Pascal's work was so precocious that Descartes was convinced that Pascal's father had written it. When assured by Mersenne that it was, indeed, the product of the son and not the father, Descartes dismissed it with a sniff: "I do not find it strange that he has offered demonstrations about conics more appropriate than those of the ancients," adding, "but other matters related to this subject can be proposed that would scarcely occur to a 16-year-old child."[13] Leaving ParisIn France at that time offices and positions could be—and were—bought and sold. In 1631, Étienne sold his position as second president of the Cour des Aides for 65,665 livres.[14] The money was invested in a government bond which provided, if not a lavish, then certainly a comfortable income which allowed the Pascal family to move to, and enjoy, Paris. But in 1638 Richelieu, desperate for money to carry on the Thirty Years' War, defaulted on the government's bonds. Suddenly Étienne Pascal's worth had dropped from nearly 66,000 livres to less than 7,300. Like so many others, Étienne was eventually forced to flee Paris because of his opposition to the fiscal policies of Cardinal Richelieu, leaving his three children in the care of his neighbour Madame Sainctot, a great beauty with an infamous past who kept one of the most glittering and intellectual salons in all France. It was only when Jacqueline performed well in a children's play with Richelieu in attendance that Étienne was pardoned. In time, Étienne was back in good graces with the cardinal and in 1639 had been appointed the king's commissioner of taxes in the city of Rouen—a city whose tax records, thanks to uprisings, were in utter chaos. Pascaline In 1642, in an effort to ease his father's endless, exhausting calculations, and recalculations, of taxes owed and paid (into which work the young Pascal had been recruited), Pascal, not yet 19, constructed a mechanical calculator capable of addition and subtraction, called Pascal's calculator or the Pascal Blaise Pascal (/pæˈskæl/ pask-AL, also UK: /-ˈskɑːl, ˈpæskəl, -skæl/ -AHL, PASK-əl, -al, US: /pɑːˈskɑːl/ pah-SKAHL;[3][4][5][6][7] French: [blɛz paskal]; 19 June 1623 – 19 August 1662) was a French mathematician, physicist, inventor, philosopher, writer and Catholic theologian. He was a child prodigy who was educated by his father, a tax collector in Rouen. Pascal's earliest mathematical work was on the conics sections; he wrote a significant treatise on the subject of projective geometry at the age of 16. He later corresponded with Pierre de Fermat on probability theory, strongly influencing the development of modern economics and social science. In 1642, while still a teenager, he started some pioneering work on calculating machines (called Pascal's calculators and later Pascalines), establishing him as one of the first two inventors of the mechanical calculator. He was a child prodigy who was educated by his father, a tax collector in Rouen. Pascal's earliest mathematical work was on the conics sections; he wrote a significant treatise on the subject of projective geometry at the age of 16. He later corresponded with Pierre de Fermat on probability theory, strongly influencing the development of modern economics and social science. In 1642, while still a teenager, he started some pioneering work on calculating machines (called Pascal's calculators and later Pascalines), establishing him as one of the first two inventors of the mechanical calculator.[8][9]
He also worked in the natural and applied sciences, where he made important contributions to the study of fluids, and clarified the concepts of pressure and vacuum by generalising the work of Evangelista Torricelli. Following Galileo Galilei and Torricelli, in 1647, he rebutted Aristotle's followers who insisted that nature abhors a vacuum. Pascal's results caused many disputes before being accepted. Pascal also wrote in defense of the scientific method.
In 1646, he and his sister Jacqueline identified with the religious movement within Catholicism known by its detractors as Jansenism.[10] Following a religious experience in late 1654, he began writing influential works on philosophy and theology. His two most famous works date from this period: the Lettres provinciales and the Pensées, the former set in the conflict between Jansenists and Jesuits. The latter contains Pascal's Wager, known in the original as the Discourse on the Machine, a probabilistic argument for God's existence. In that year, he also wrote an important treatise on the arithmetical triangle. Between 1658 and 1659, he wrote on the cycloid and its use in calculating the volume of solids.
Throughout his life, Pascal was in frail health, especially after the age of 18; he died just two months after his 39th birthday.[11]
Pascal was born in Clermont-Ferrand, which is in France's Auvergne region, by the Massif Central. He lost his mother, Antoinette Begon, at the age of three.[12] His father, Étienne Pascal (1588–1651), who also had an interest in science and mathematics, was a local judge and member of the "Noblesse de Robe". Pascal had two sisters, the younger Jacqueline and the elder Gilberte.
In 1631, five years after the death of his wife,[2] Étienne Pascal moved with his children to Paris. The newly arrived family soon hired Louise Delfault, a maid who eventually became an instrumental member of the family. Étienne, who never remarried, decided that he alone would educate his children, for they all showed extraordinary intellectual ability, particularly his son Blaise. The young Pascal showed an amazing aptitude for mathematics and science.
Particularly of interest to Pascal was a work of Desargues on conic sections. Following Desargues' thinking, the 16-year-old Pascal produced, as a means of proof, a short treatise on what was called the "Mystic Hexagram", "Essai pour les coniques" ("Essay on Conics") and sent it—his first serious work of mathematics—to Père Mersenne in Paris; it is known still today as Pascal's theorem. It states that if a hexagon is inscribed in a circle (or conic) then the three intersection points of opposite sides lie on a line (called the Pascal line).
Pascal's work was so precocious that Descartes was convinced that Pascal's father had written it. When assured by Mersenne that it was, indeed, the product of the son and not the father, Descartes dismissed it with a sniff: "I do not find it strange that he has offered demonstrations about conics more appropriate than those of the ancients," adding, "but other matters related to this subject can be proposed that would scarcely occur to a 16-year-old child."[13]
In France at that time offices and positions could be—and were—bought and sold. In 1631, Étienne sold his position as second president of the Cour des Aides for 65,665 livres.[14] The money was invested in a government bond which provided, if not a lavish, then certainly a comfortable income which allowed the Pascal family to move to, and enjoy, Paris. But in 1638 Richelieu, desperate for money to carry on the Thirty Years' War, defaulted on the government's bonds. Suddenly Étienne Pascal's worth had dropped from nearly 66,000 livres to less than 7,300.
Like so many others, Étienne was eventually forced to flee Paris because of his opposition to the fiscal policies of Cardinal Richelieu, leaving his three children in the care of his neighbour Madame Sainctot, a great beauty with an infamous past who kept one of the most glittering and intellectual salons in all France. It was only when Jacqueline performed well in a children's play with Richelieu in attendance that Étienne was pardoned. In time, Étienne was back in good graces with the cardinal and in 1639 had been appointed the king's commissioner of taxes in the city of Rouen—a city whose tax records, thanks to uprisings, were in utter chaos.
In 1642, in an effort to ease his father's endless, exhausting calculations, and recalculations, of taxes owed and paid (into which work the young Pascal had been recruited), Pascal, not yet 19, constructed a mechanical calculator capable of addition and subtraction, called Pascal's calculator or the Pascaline. Of the eight Pascalines known to have survived, four are held by the Musée des Arts et Métiers in Paris and one more by the Zwinger museum in Dresden, Germany, exhibit two of his original mechanical calculators.[15]
Although these machines are pioneering forerunners to a further 400 years of development of mechanical methods of calculation, and in a In 1631, five years after the death of his wife,[2] Étienne Pascal moved with his children to Paris. The newly arrived family soon hired Louise Delfault, a maid who eventually became an instrumental member of the family. Étienne, who never remarried, decided that he alone would educate his children, for they all showed extraordinary intellectual ability, particularly his son Blaise. The young Pascal showed an amazing aptitude for mathematics and science.
Particularly of interest to Pascal was a work of Desargues on conic sections. Following Desargues' thinking, the 16-year-old Pascal produced, as a means of proof, a short treatise on what was called the "Mystic Hexagram", "Essai pour les coniques" ("Essay on Conics") and sent it—his first serious work of mathematics—to Père Mersenne in Paris; it is known still today as Pascal's theorem. It states that if a hexagon is inscribed in a circle (or conic) then the three intersection points of opposite sides lie on a line (called the Pascal line).
Pascal's work was so precocious that Descartes was convinced that Pascal's fa Pascal's work was so precocious that Descartes was convinced that Pascal's father had written it. When assured by Mersenne that it was, indeed, the product of the son and not the father, Descartes dismissed it with a sniff: "I do not find it strange that he has offered demonstrations about conics more appropriate than those of the ancients," adding, "but other matters related to this subject can be proposed that would scarcely occur to a 16-year-old child."[13]
In France at that time offices and positions could be—and were—bought and sold. In 1631, Étienne sold his position as second president of the Cour des Aides for 65,665 livres.[14] The money was invested in a government bond which provided, if not a lavish, then certainly a comfortable income which allowed the Pascal family to move to, and enjoy, Paris. But in 1638 Richelieu, desperate for money to carry on the Thirty Years' War, defaulted on the government's bonds. Suddenly Étienne Pascal's worth had dropped from nearly 66,000 livres to less than 7,300.
Like so many others, Étienne was eventually forced to flee Paris because Like so many others, Étienne was eventually forced to flee Paris because of his opposition to the fiscal policies of Cardinal Richelieu, leaving his three children in the care of his neighbour Madame Sainctot, a great beauty with an infamous past who kept one of the most glittering and intellectual salons in all France. It was only when Jacqueline performed well in a children's play with Richelieu in attendance that Étienne was pardoned. In time, Étienne was back in good graces with the cardinal and in 1639 had been appointed the king's commissioner of taxes in the city of Rouen—a city whose tax records, thanks to uprisings, were in utter chaos.
In 1642, in an effort to ease his father's endless, exhausting calculations, and recalculations, of taxes owed and paid (into which work the young Pascal had been recruited), Pascal, not yet 19, constructed a mechanical calculator capable of addition and subtraction, called Pascal's calculator or the Pascaline. Of the eight Pascalines known to have survived, four are held by the Musée des Arts et Métiers in Paris and one more by the Zwinger museum in Dresden, Germany, exhibit two of his original mechanical calculators.[15]
Although these machines are pioneering forerunners to a further 400 years of development of mechanical methods of calculation, and in a sense to the later field of computer engineering, the calculator failed to be a great commercial success. Partly because it was still quite cumbersome to use in practice, but probably primarily because it was extraordinarily expensive, the Pascaline became little more than a toy, and a status symbol, for the very rich both in France and elsewhere in Europe. Pascal continued to make improvements to his design through the next decade, and he refers to some 50 machines that were built to his design.[16] he built 20 finished machines over the following 10 years[17]
Pascal continued to influence mathematics throughout his life. The Although these machines are pioneering forerunners to a further 400 years of development of mechanical methods of calculation, and in a sense to the later field of computer engineering, the calculator failed to be a great commercial success. Partly because it was still quite cumbersome to use in practice, but probably primarily because it was extraordinarily expensive, the Pascaline became little more than a toy, and a status symbol, for the very rich both in France and elsewhere in Europe. Pascal continued to make improvements to his design through the next decade, and he refers to some 50 machines that were built to his design.[16] he built 20 finished machines over the following 10 years[17]
Pascal continued to influence mathematics throughout his life. The University of Waterloo, Ontario, Canada, holds an annual math contest named in Pascal's honour.[18]
Pascal's development of probability theory was his most influential contribution to mathematics. Originally applied to gambling, today it is extremely important in economics, especially in actuarial science. John Ross writes, "Probability theory and the discoveries following it changed the way we regard uncertainty, risk, decision-making, and an individual's and society's ability to influence the course of future events."[19] However, Pascal and Fermat, though doing important early work in probability theory, did not develop the field very far. Christiaan Huygens, learning of the subject from the correspondence of Pascal and Fermat, wrote the first book on the subject. Later figures who continued the development of the theory include Abraham de Moivre and Pierre-Simon Laplace.
In 1654, prompted by his friend the Chevalier de Méré, he corresponded with Pierre de Fermat on the subject of gambling problems, and from that collaboration was born the mathematical theory of probabilities.[20] The specific problem was that of two players who want to finish a game early and, given the current circumstances of the game, want to divide the stakes fairly, based on the chance each has of winning the game from that point. From this discussion, the notion of expected value was introduced. Pascal later (in the Pensées) used a probabilistic argument, Pascal's wager, to justify belief in God and a virtuous life. The work done by Fermat and Pascal into the calculus of probabilities laid important groundwork for Leibniz' formulation of the calculus.[21]
Pascal's Traité du triangle arithmétique ("Treatise on the Arithmetical Triangle") of 1654 described a convenient tabular presentation for binomial coefficients, now called Pascal's triangle. The triangle can also be represented:
In 1658, Pascal, while suffering from a toothache, began considering several problems concerning the cycloid. His toothache disappeared, and he took this as a heavenly sign to proceed with his research. Eight days later he had completed his essay and, to publicize the results, proposed a contest.
Pascal proposed three questions relating to the center of gravity, area and volume of the cycloid, with the winner or winners to receive prizes of 20 and 40 Spanish doubloons. Pascal, Gilles de Roberval and Pierre de Carcavi were the judges, and neither of the two submissions (by John Wallis and Antoine de Lalouvère) were judged to be adequate.[23] While the contest was ongoing, Christopher Wren sent Pascal a proposal for a proof of the rectification of the cycloid; Roberval claimed promptly that he had known of the proof for years. Wallis published Wren's proof (crediting Wren) in Wallis's Tractus Duo, giving Wren priority for the first published proof.
Pascal contributed to several fields in physics, most notably the fields of fluid mechanics and pressure. In honour of his scientific contributions, the name Pascal has been given to the SI unit of pressure and Pascal's law (an important principle of hydrostatics). He introduced a primitive form of roulette and the roulette wheel in his search for a perpetual motion machine.[24]
His work in the fields of hydrodynamics and hydrostatics centered on the principles of hydraulic fluids. His inventions include the hydraulic press (using hydraulic pressure to multiply force) and the syringe. He proved that hydrostatic pressure depends not on the weight of the fluid but on the elevation difference. He demonstrated this principle by attaching a thin tube to a barrel full of water and filling the tube with water up to the level of the third floor of a building. This caused the barrel to leak, in what became known as < His work in the fields of hydrodynamics and hydrostatics centered on the principles of hydraulic fluids. His inventions include the hydraulic press (using hydraulic pressure to multiply force) and the syringe. He proved that hydrostatic pressure depends not on the weight of the fluid but on the elevation difference. He demonstrated this principle by attaching a thin tube to a barrel full of water and filling the tube with water up to the level of the third floor of a building. This caused the barrel to leak, in what became known as Pascal's barrel experiment.
By 1647, Pasc By 1647, Pascal had learned of Evangelista Torricelli's experimentation with barometers. Having replicated an experiment that involved placing a tube filled with mercury upside down in a bowl of mercury, Pascal questioned what force kept some mercury in the tube and what filled the space above the mercury in the tube. At the time, most scientists including Descartes believed in a plenum, i. e. some invisible matter filled all of space, rather than a vacuum. "Nature abhors a vacuum." This was based on the Aristotelian notion that everything in motion was a substance, moved by another substance.[25] Furthermore, light passed through the glass tube, suggesting a substance such as aether rather than vacuum filled the space.
The Torricellian vacuum found that air pressure is equal to the weight of 30 inches of mercury. If air has a finite weight, Earth's atmosphere must have a maximum height. Pascal reasoned that if true, air pressure on a high mountain must be less than at a lower altitude. He lived near the Puy de Dôme mountain, 4,790 feet (1,460 m) tall, but his health was poor so could not climb it.[26] On 19 September 1648, after many months of Pascal's friendly but insistent prodding, Florin Périer, husband of Pascal's elder sister Gilberte, was finally able to carry out the fact-finding mission vital to Pascal's theory. The account, written by Périer, reads:
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Pascal's identity relating the sums of the p-th powers of the first n positive integers for p = 0, 1, 2, ..., k.
Pascal proposed three questions relating to the