Blaise Pascal (19June 162319August 1662) was a French mathematician, physicist, inventor, philosopher, and Catholic writer.
Pascal was a child prodigy who was educated by his father Étienne Pascal, a tax collector in Rouen. His earliest mathematical work was on projective geometry; he wrote a significant treatise on the subject of conic sections 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, 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.See Schickard versus Pascal: An Empty Debate? and
Like his contemporary René Descartes, Pascal was also a pioneer in the natural and applied sciences. Pascal wrote in defence of the scientific method and produced several controversial results. He made important contributions to the study of fluids, and clarified the concepts of pressure and vacuum by generalising the work of Evangelista Torricelli. The SI unit for pressure is named for Pascal. Following Torricelli and Galileo Galilei, in 1647, he rebutted the likes of Aristotle and Descartes who insisted that nature abhors a vacuum.
He is also credited as the inventor of modern public transportation, having established the carrosses à cinq sols, the first modern public transport service, shortly before his death in 1662.
In 1646, he and his sister Jacqueline identified with the religious movement within Catholicism known by its detractors as Jansenism. 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 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 fideistic probabilistic argument for why one should believe in God. 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. Following several years of illness, Pascal died in Paris at the age of 39.
Early life and education
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. His father, Étienne Pascal, also an amateur mathematician, was a local judge and member of the "Noblesse de Robe". Pascal had two sisters, the younger Jacqueline and the elder Gilberte.
Move to Paris In 1631, five years after the death of his wife, Étienne Pascal moved with his children to Paris. The newly arrived family soon hired Louise Delfault, a maid who eventually became a key member of the family. Étienne, who never remarried, decided that he alone would educate his children.
The young Pascal showed an extraordinary intellectual ability, with an amazing aptitude for mathematics and science. Etienne had tried to keep his son from learning mathematics; but by the age of 12, Pascal had rediscovered, on his own, using charcoal on a tile floor, Euclid’s first thirty-two geometric propositions, and was thus given a copy of Euclid's Elements.Cole, J. R. (1995). Pascal : the man and his two loves. United Kingdom: NYU Press. p. 40
Essay on Conics 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 René 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 replied: "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."The Story of Civilization: Volume 8, "The Age of Louis XIV" by Will & Ariel Durant; chapter II, subsection 4.1 p. 56
Leaving Paris 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.Connor, James A., Pascal's wager: the man who played dice with God (HarperCollins, NY, 2006) p. 42 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 Cardinal 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 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 of 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 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, which exhibit two of his original mechanical calculators.A complete list of known Pascalines and also a review of contemporary replicas can be found at Surviving Pascalines and Replica Pascalines at http://things-that-count.net
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. He also presented the first mechanical calculator to Christina, Queen of Sweden in 1652. 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.(fr) La Machine d'arithmétique, Blaise Pascal , Wikisource He built 20 finished machines over the following 10 years.
Mathematics Probability In 1654, prompted by his friend the Chevalier de Méré, Pascal corresponded with Pierre de Fermat on the subject of gambling problems, and from that collaboration was born the mathematical theory of probability. 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. The notion of expected value evolved from this discussion. 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." Pascal, in the Pensées, used a probabilistic argument, Pascal's wager, to justify belief in God and a virtuous life. 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. The work done by Fermat and Pascal on the calculus of probabilities laid important groundwork for Leibniz's formulation of the calculus.
Treatise on the Arithmetical Triangle
Pascal's Traité du triangle arithmétique, written in 1654 but published posthumously in 1665, described a convenient tabular presentation for binomial coefficients which he called the arithmetical triangle, but is now called Pascal's triangle. The triangle can also be represented: 01234560 1 1 1 11111 1 2 3 4 5 6 21 3 6 10 15 3 14 10 20 4 15 15 5 16 6 1
He defined the numbers in the triangle by recursion: Call the number in the (m + 1)th row and (n + 1)th column tmn. Then tmn = tm−1,n + tm,n−1, for m = 0, 1, 2, ... and n = 0, 1, 2, ... The boundary conditions are tm,−1 = 0, t−1,n = 0 for m = 1, 2, 3, ... and n = 1, 2, 3, ... The generator t00 = 1. Pascal concluded with the proof,
In the same treatise, Pascal gave an explicit statement of the principle of mathematical induction. In 1654, he proved Pascal's identity relating the sums of the p-th powers of the first n positive integers for p = 0, 1, 2, ..., k.
That same year, Pascal had a religious experience, and he mostly gave up work in mathematics.
Cycloid
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 centre 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. 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.
Physics
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.MIT, "Inventor of the Week Archive: Pascal : Mechanical Calculator", May 2003. "Pascal worked on many versions of the devices, leading to his attempt to create a perpetual motion machine. He has been credited with introducing the roulette machine, which was a by-product of these experiments." Blaise Pascal Chairs are given to outstanding international scientists to conduct their research in the Ile de France region.
Fluid dynamics