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Blaise Pascal

2007 Schools Wikipedia Selection. Related subjects: Mathematicians

                    Blaise Pascal
                    Blaise Pascal
         Born June 19, 1623
              Clermont-Ferrand, France
      Died    August 19, 1662
              Paris, France
   Occupation mathematician, physicist, philosopher

   Blaise Pascal (pronounced [blez pɑskɑl]), ( June 19, 1623 – August 19,
   1662) was a French mathematician, physicist, and religious philosopher.
   He was a child prodigy who was educated by his father. Pascal's
   earliest work was in the natural and applied sciences where he made
   important contributions to the construction of mechanical calculators,
   the study of fluids, and clarified the concepts of pressure and vacuum
   by generalizing the work of Evangelista Torricelli. Pascal also wrote
   powerfully in defense of the scientific method.

   He was a mathematician of the first order. Pascal helped create two
   major new areas of research. He wrote a significant treatise on the
   subject of projective geometry at the age of sixteen and corresponded
   with Pierre de Fermat from 1654 and later on probability theory,
   strongly influencing the development of modern economics and social
   science.

   Following a mystical experience in late 1654, he abandoned his
   scientific work and devoted himself to philosophy and theology. His two
   most famous works date from this period: the Lettres provinciales and
   the Pensées. However, he had suffered from ill-health throughout his
   life and his new interests were ended by his early death two months
   after his 39th birthday.

Early life and education

   Born in Clermont-Ferrand, in the Auvergne region of France, Blaise
   Pascal lost his mother, Antoinette Begon, at the age of three. His
   father, Étienne Pascal (1588–1651), was a local judge and member of the
   petite noblesse, who also had an interest in science and mathematics.
   Blaise Pascal was brother to Jacqueline Pascal and two other sisters,
   only one of whom, Gilberte, survived past childhood.

   In 1631, Étienne moved with his children to Paris. Étienne decided that
   he would educate his son who showed extraordinary intellectual ability.
   Young Pascal showed immediate aptitude for mathematics and science,
   perhaps inspired by his father's regular conversations with Paris'
   leading geometricians, including Roberval, Mersenne, Desargues,
   Mydorge, Gassendi, and Descartes. At the age of eleven, he composed a
   short treatise on the sounds of vibrating bodies and Étienne responded
   by forbidding his son to further pursue mathematics until the age of
   fifteen so as not to harm his study of Latin and Greek. One day,
   however, Étienne found Blaise (now twelve) writing an independent proof
   that the sum of the angles of a triangle is equal to two right angles
   with a piece of coal on a wall. From then on, the boy was allowed to
   study Euclid.

   Particularly of interest to Pascal was the work of Desargues. Following
   Desargues's thinking, at age sixteen Pascal produced a treatise on
   conic sections, Essai pour les coniques ("Essay on Conics"). Most of it
   has been lost, but an important original result has lasted, now known
   as Pascal's theorem. Pascal's work was so precocious that Descartes,
   when shown the manuscript, refused to believe that the composition was
   not by his father.

   In 1638, Étienne's opposition to the fiscal policies of Cardinal
   Richelieu eventually forced the family to flee Paris. It was only when
   Jacqueline performed well in a children's play with Richelieu in
   attendance that Étienne was pardoned. By 1639, the family had moved to
   Rouen where Étienne became a tax collector.

   At age eighteen, Pascal constructed a mechanical calculator capable of
   addition and subtraction, called Pascal's calculator or the Pascaline,
   to help his father with this work. The Zwinger museum, in Dresden,
   Germany, exhibits one of his original mechanical calculators. Though
   these machines are early forerunners to computer engineering, the
   calculator failed to be a great commercial success. Pascal continued to
   make improvements to his design through the next decade and built fifty
   machines in total.

Contributions to mathematics

   Portrait of Blaise Pascal
   Enlarge
   Portrait of Blaise Pascal

   In addition to the childhood marvels previously mentioned, Pascal
   continued to influence mathematics throughout his life. In 1653, Pascal
   wrote his Traité du triangle arithmétique ("Treatment of the
   Arithmetical Triangle") in which he described a convenient tabular
   presentation for binomial coefficients, now called Pascal's triangle. (
   Yang Hui, a Chinese mathematician of the Qin dynasty, had independently
   worked out a concept similar to Pascal's triangle four centuries
   earlier.)

   In 1654, prompted by a friend interested in gambling problems, he
   corresponded with Fermat on the subject, and from that collaboration
   was born the mathematical theory of probabilities. The friend was the
   Chevalier de Méré, and 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's formulation of
   the infinitesimal calculus.

   After a religious experience in 1654, Pascal mostly gave up work in
   mathematics. However, after a sleepless night in 1658, he anonymously
   offered a prize for the quadrature of a cycloid. Solutions were offered
   by Wallis, Huygens, Wren, and others; Pascal, under a pseudonym,
   published his own solution. Controversy and heated argument followed
   after Pascal announced himself the winner.

Philosophy of mathematics

   Pascal's major contribution to the philosophy of mathematics came with
   his De l'Esprit géométrique ("On the Geometrical Spirit"), originally
   written as a preface to a geometry textbook for one of the famous
   "Little Schools of Port-Royal" (Les Petites-Ecoles de Port-Royal). The
   work was unpublished until over a century after his death. Here, Pascal
   looked into the issue of discovering truths, arguing that the ideal
   such method would be to found all propositions on already established
   truths. At the same time, however, he claimed this was impossible
   because such established truths would require other truths to back them
   up—first principles, therefore, cannot be reached. Based on this,
   Pascal argued that the procedure used in geometry was as perfect as
   possible, with certain principles assumed and other propositions
   developed from them. Nevertheless, there was no way to know the assumed
   principles to be true.

   Pascal also used De l'Esprit géométrique to develop a theory of
   definition. He distinguished between definitions which are conventional
   labels defined by the writer and definitions which are within the
   language and understood by everyone because they naturally designate
   their referent. The second type would be characteristic of the
   philosophy of essentialism. Pascal claimed that only definitions of the
   first type were important to science and mathematics, arguing that
   those fields should adopt the philosophy of formalism as formulated by
   Descartes.

   In De l'Art de persuader ("On the Art of Persuasion"), Pascal looked
   deeper into geometry's axiomatic method, specifically the question of
   how people come to be convinced of the axioms upon which later
   conclusions are based. Pascal agreed with Montaigne that achieving
   certainty in these axioms and conclusions through human methods is
   impossible. He asserted that these principles can only be grasped
   through intuition, and that this fact underscored the necessity for
   submission to God in searching out truths.

Contributions to the physical sciences

   Pascal's work in the fields of the study of fluids ( 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. By 1646, Pascal had learned of
   Evangelista Torricelli's experimentation with barometers. Having
   replicated an experiment which 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 contended that,
   rather than a vacuum, some invisible matter was present.

   Following more experimentation in this vein, in 1647 Pascal produced
   Experiences nouvelles touchant le vide ("New Experiments with the
   Vacuum"), which detailed basic rules describing to what degree various
   liquids could be supported by air pressure. It also provided reasons
   why it was indeed a vacuum above the column of liquid in a barometer
   tube.

   In 1648, Pascal continued his experiments by having his brother-in-law
   carry a barometer to a higher elevation, confirming that the level of
   mercury would change, a result which Pascal replicated by carrying a
   barometer up and down a church tower in Paris. The experiment was
   hailed throughout Europe as finally establishing the principle and
   value of the barometer.

   In the face of criticism that some invisible matter must exist in
   Pascal's empty space, Pascal, in his reply to Estienne Noel, gave one
   of the seventeenth century's major statements on the scientific method:
   "In order to show that a hypothesis is evident, it does not suffice
   that all the phenomena follow from it; instead, if it leads to
   something contrary to a single one of the phenomena, that suffices to
   establish its falsity." His insistence on the existence of the vacuum
   also led to conflict with a number of other prominent scientists,
   including Descartes.

Adult life, religion, philosophy, and literature

     For after all what is man in nature? A nothing in relation to
     infinity, all in relation to nothing, a central point between
     nothing and all and infinitely far from understanding either. The
     ends of things and their beginnings are impregnably concealed from
     him in an impenetrable secret. He is equally incapable of seeing the
     nothingness out of which he was drawn and the infinite in which he
     is engulfed. -Blaise Pascal

Religious conversion

   Pascal studying the cycloid, by Augustin Pajou, 1785, Louvre
   Enlarge
   Pascal studying the cycloid, by Augustin Pajou, 1785, Louvre

   Biographically, we can say that two basic influences led him to his
   conversion: sickness and Jansenism. From as early as his eighteenth
   year, Pascal suffered from a nervous ailment that left him hardly a day
   without pain. In 1647, a paralytic attack so disabled him that he could
   not move without crutches. His head ached, his bowels burned, his legs
   and feet were continually cold, and required wearisome aids to
   circulation of the blood; he wore stockings steeped in brandy to warm
   his feet. Partly to get better medical treatment, he moved to Paris
   with his sister Jacqueline. His health improved, but his nervous system
   had been permanently damaged. Henceforth, he was subject to deepening
   hypochondria, which affected his character and his philosophy. He
   became irritable, subject to fits of proud and imperious anger, and
   seldom smiled.

   In 1645, Pascal's father was wounded in the thigh and was consequently
   looked after by a Jansenist physician. Blaise spoke with the doctor
   frequently, and upon his successful treatment of Étienne, borrowed
   works by Jansenist authors through him. In this period, Pascal
   experienced a sort of "first conversion" and began in the course of the
   following year to write on theological subjects.

   Pascal fell away from this initial religious engagement and experienced
   a few years of what he called a "worldly period" (1648–54). His father
   died in 1651, and Pascal gained control over both his inheritance as
   well as his sister Jacqueline's. In that same year, Jacqueline moved to
   become a nun at Port-Royal despite her brother's opposition. When the
   time came for her to make her ultimate vows, he refused to return to
   her enough of her inheritance to pay her dowry as a bride of Christ.
   Without the money, she would attain a less desirable position in the
   convent hierarchy. Eventually, however, Pascal relented on this point.

   With his sister's affairs settled, Pascal found himself both rich and
   free. He took a sumptuously furnished home, staffed it with many
   servants, and drove about Paris in a coach behind four or six horses.
   His leisure was spent in the company of wits, women, and gamblers (as
   evidenced by his work on probability). For an exciting while, he
   pursued in Auvergne a lady of beauty and learning, whom he referred to
   as the " Sappho of the countryside." Around this time, Pascal wrote
   Discours sur les passions de l'amour ("Conversation about the Passions
   of Love"), and apparently he contemplated marriage—which he was later
   to describe as "the lowest of the conditions of life permitted to a
   Christian."

   Jacqueline reproached him for his frivolity and prayed for his reform.
   During visits to his sister at Port-Royal in 1654, he displayed
   contempt for affairs of the world but was not drawn to God.

Brush with death

   On November 23, 1654, he was involved in an accident at the Neuilly
   bridge where the horses plunged over the parapet and the carriage
   nearly followed them. Fortunately, the reins broke and the coach hung
   halfway over the edge. Pascal and his friends emerged unscathed, but
   the sensitive philosopher, terrified by the nearness of death, fainted
   away and remained unconscious for some time. Upon recovering fifteen
   days later, between ten thirty and twelve thirty at night, Pascal had
   an intense religious vision and immediately recorded the experience in
   a brief note to himself which began: "Fire. God of Abraham, God of
   Isaac, God of Jacob, not of the philosophers and the scholars…" and
   concluded by quoting Psalm 119:16: "I will not forget thy word. Amen."
   He seems to have carefully sewn this document into his coat and always
   transferred it when he changed clothes; a servant discovered it only by
   chance after his death. During his lifetime, Pascal was often
   mistakenly thought to be a libertine, and was later dismissed as an
   individual who had only made a deathbed conversion.

   His belief and religious commitment revitalized, Pascal visited the
   older of two convents at Port-Royal for a two-week retreat in January
   1655. For the next four years, he regularly traveled between Port-Royal
   and Paris. It was at this point immediately after his conversion when
   he began writing his first major literary work on religion, the
   Provincial Letters.

The Provincial Letters

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   Beginning in 1656, Pascal published his memorable attack on casuistry,
   a popular ethical method used by Catholic thinkers in the early modern
   period (especially the Jesuits). Pascal denounced casuistry as the mere
   use of complex reasoning to justify moral laxity. His method of framing
   his arguments was clever: the Provincial Letters pretended to be the
   report of a Parisian to a friend in the provinces on the moral and
   theological issues then exciting the intellectual and religious circles
   in the capital. Pascal, combining the fervor of a convert with the wit
   and polish of a man of the world, reached a new level of style in
   French prose. The 18-letter series was published between 1656 and 1657
   under the pseudonym Louis de Montalte and incensed Louis XIV. The king
   ordered that the book be shredded and burnt in 1660. In 1661, the
   Jansenist school at Port-Royal was condemned and closed down; those
   involved with the school had to sign a 1656 papal bull condemning the
   teachings of Jansen as heretical. The final letter from Pascal, in
   1657, had defied the Pope himself, provoking Alexander VII to condemn
   the letters. But that didn't stop all of educated France from reading
   them. Even Pope Alexander, while publicly opposing them, nonetheless
   was persuaded by Pascal's arguments. He condemned "laxism" in the
   church and ordered a revision of casuistical texts just a few years
   later (1665–66).

   Aside from their religious influence, the Provincial Letters were
   popular as a literary work. Pascal's use of humor, mockery, and vicious
   satire in his arguments made the letters ripe for public consumption,
   and influenced the prose of later French writers like Voltaire and
   Jean-Jacques Rousseau. The first few letters promote major principles
   of Jansenist teaching, such as the dogmas of "proximate power" (Letter
   I) and "sufficient grace" (Letter II), and explain why they are not
   heretical. The later letters find Pascal more on the defensive—pressure
   on the Port Royal Jansenists to renounce their teachings was constantly
   growing through this time—and contain the assault on casuistry. Letter
   XVI contains the unique apology, "I would have written a shorter
   letter, but I did not have the time."

   Wide praise has been given to the Provincial Letters. Voltaire called
   the Letters "the best-written book that has yet appeared in France."
   And when Bossuet was asked what book he would rather have written had
   he not written his own, he answered, the Provincial Letters of Pascal.

Miracle

   When Pascal was back in Paris just after overseeing the publication of
   the last Letter, his religion was reinforced by the close association
   to an apparent miracle in the chapel of the Port-Royal nunnery. His
   10-year-old niece, Marguerite Périer, was suffering from a painful
   fistula lacrymalis that exuded noisome pus through her eyes and nose—an
   affliction the doctors pronounced hopeless. Then, on March 24, 1657, a
   believer presented to Port-Royal what he and others claimed to be a
   thorn from the crown that had tortured Christ. The nuns, in solemn
   ceremony and singing psalms, placed the thorn on their altar. Each in
   turn kissed the relic, and one of them, seeing Marguerite among the
   worshipers, took the thorn and with it touched the girl's sore. That
   evening, we are told, Marguerite expressed surprise that her eye no
   longer pained her; her mother was astonished to find no sign of the
   fistula; a physician, summoned, reported that the discharge and
   swelling had disappeared. He, not the nuns, spread word of what he
   termed a miraculous cure. Seven other physicians who had had previous
   knowledge of Marguerite's fistula signed a statement that in their
   judgment a miracle had taken place. The diocesan officials
   investigated, came to the same conclusion, and authorized a Te Deum
   Mass in Port-Royal. Crowds of believers came to see and kiss the thorn;
   all of Catholic Paris acclaimed a miracle. Later, both Jansenists and
   Catholics used this well-documented miracle to their defense. In 1728,
   Pope Benedict XIII referred to the case as proving that the age of
   miracles had not passed.

   Pascal made himself an armorial emblem of an eye surrounded by a crown
   of thorns, with the inscription Scio cui credidi—"I know whom I have
   believed." His beliefs renewed, he set his mind to write his final,
   and, alas, unfinished testament, the Pensées.

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Last works and death

   Pascal's epitaph in Saint-Étienne-du-Mont, where he was buried
   Enlarge
   Pascal's epitaph in Saint-Étienne-du-Mont, where he was buried

   T. S. Eliot described him during this phase of his life as "a man of
   the world among ascetics, and an ascetic among men of the world."
   Pascal's ascetic lifestyle derived from a belief that it was natural
   and necessary for man to suffer. In 1659, Pascal, whose health had
   never been good, fell seriously ill. During his last years, he
   frequently tried to reject the ministrations of his doctors, saying,
   "Sickness is the natural state of Christians."

   Louis XIV suppressed the Jansenist movement at Port-Royal in 1661. In
   response, Pascal wrote one of his final works, Écrit sur la signature
   du formulaire ("Writ on the Signing of the Form"), exhorting the
   Jansenists not to give in. Later that year, his sister Jacqueline died,
   which convinced Pascal to cease his polemics on Jansenism. Pascal's
   last major achievement, returning to his mechanical genius, was
   inaugurating perhaps the first bus line, moving passengers within Paris
   in a carriage with many seats.

   In 1662, Pascal's illness became more violent. Aware that his health
   was fading quickly, he sought a move to the hospital for incurable
   diseases, but his doctors declared that he was too unstable to be
   carried. In Paris on August 18, 1662, Pascal went into convulsions and
   received extreme unction. He died the next morning, his last words
   being "May God never abandon me," and was buried in the cemetery of
   Saint-Étienne-du-Mont.

   An autopsy performed after his death revealed grave problems with his
   stomach and other organs of his abdomen, along with damage to his
   brain. Despite the autopsy, the cause of his continual poor health was
   never precisely determined, though speculation focuses on tuberculosis,
   stomach cancer, or a combination of the two. The headaches which
   afflicted Pascal are generally attributed to his brain lesion.

Legacy

   In honour of his scientific contributions, the name Pascal has been
   given to the SI unit of pressure, to a programming language, and
   Pascal's law (an important principle of hydrostatics), and as mentioned
   above, Pascal's triangle and Pascal's wager still bear his name.

   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." However, it should be noted that 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 literature, Pascal is regarded as one of the most important authors
   of the French Classical Period and is read today as one of the greatest
   masters of French prose. His use of satire and wit influenced later
   polemicists. The content of his literary work is best remembered for
   its strong opposition to the rationalism of René Descartes and
   simultaneous assertion that the main countervailing philosophy,
   empiricism, was also insufficient for determining major truths.

Other

   In Canada, there is an annual math contest named in his honour. The
   Pascal Contest is open to any student in Canada who is 14 years or
   under and is in grade 9 or lower.

   A discussion of Pascal figures prominently in the movie My Night At
   Maud's by the French director Éric Rohmer.

   Roberto Rossellini directed a filmed biopic (entitled Blaise Pascal)
   which originally aired on Italian television in 1971. Pierre Arditi
   starred as Pascal.

Works

     * Essai pour les coniques (1639)
     * Experiences nouvelles touchant le vide (1647)
     * Traité du triangle arithmétique (1653)
     * Lettres provinciales (1656–57)
     * De l'Esprit géométrique (1657 or 1658)
     * Écrit sur la signature du formulaire (1661)
     * Pensées (incomplete at death)

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