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Blaise Pascal

Blaise Pascal
Full name Blaise Pascal
Born June 19, 1623(1623-06-19)
Died August 19, 1662 (aged 39)
Era 17th-century philosophy
Region Western Philosophy
School Continental Philosophy, precursor to existentialism
Main interests Theology, Mathematics
Notable ideas Pascal's Wager, Pascal's triangle, Pascal's law

Blaise Pascal (French pronunciation: [blɛz paskal]), (June 19, 1623, Clermont-Ferrand – August 19, 1662, Paris) was a French mathematician, physicist, and Catholic philosopher. He was a child prodigy who was educated by his father, a civil servant. 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 in defense of the scientific method.

Pascal was a mathematician of the first order. He 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 later corresponded with Pierre de Fermat on probability theory, strongly influencing the development of modern economics and social science. Following Galileo and Torricelli, in 1646 he refuted Aristotle's followers who insisted that nature abhors a vacuum. His results caused many disputes before being accepted.

In 1646, he and his sister Jacqueline identified with the religious movement within Catholicism known by its detractors as Jansenism.[1] His father died in 1651. Following a mystical experience in late 1654, he had his "second conversion", 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, the former set in the conflict between Jansenists and Jesuits. In this year, he also wrote an important treatise on the arithmetic of triangles. Between 1658 and 1659 he wrote on the cycloid and its use in calculating the volume of solids.

Pascal had poor health especially after his eighteenth year and his death came just two months after his 39th birthday.[2]

Contents

Early life and education

Pascal lost his mother, Antoinette Begon, at the age of three.[3] 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,[4] 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. 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; perhaps more importantly, he was allowed to sit in as a silent on-looker at the gatherings of some of the greatest mathematicians and scientists in Europe—such as Roberval, Desargues, Mydorge, Gassendi, and Descartes—in the monastic cell of Père Mersenne.

Particularly of interest to Pascal was a work of Desargues on conic sections. Following Desargues' thinking, the sixteen-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, when shown the manuscript, refused to believe that the composition was not by the elder Pascal. When assured by Mersenne that it was, indeed, the product of the son 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 sixteen-year-old child."[5]

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.[6] 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 Year War, defaulted on the government's bonds. Suddenly Étienne Pascal's worth had dropped from nearly 66,000 livres to less than 7,300.

An early Pascaline on display at the Musée des Arts et Métiers, Paris

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 neighbor 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, Pascal, not yet nineteen, constructed a mechanical calculator capable of addition and subtraction, called Pascal's calculator or the Pascaline. The Musée des Arts et Métiers in Paris and the Zwinger museum in Dresden, Germany, exhibit two of his original mechanical calculators. Though these machines are early forerunners to computer engineering, the calculator failed to be a great commercial success. Because it was extraordinarily expensive the Pascaline became little more than a toy, and status symbol, for the very rich both in France and throughout Europe. However, Pascal continued to make improvements to his design through the next decade and built fifty machines in total.

Contributions to mathematics

Pascal's triangle. Each number is the sum of the two directly above it. The triangle demonstrates many mathematical properties in addition to showing binomial coefficients.

Pascal continued to influence mathematics throughout his life. His Traité du triangle arithmétique ("Treatise on the Arithmetical Triangle") of 1653 described a convenient tabular presentation for binomial coefficients, now called Pascal's triangle. The triangle can also be represented:

0 1 2 3 4 5 6
0 1 1 1 1 1 1 1
1 1 2 3 4 5 6
2 1 3 6 10 15
3 1 4 10 20
4 1 5 15
5 1 6
6 1

He defines the numbers in the triangle by recursion: Call the number in the (m+1)st row and (n+1)st 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 for m = 1, 2, 3... and n = 1, 2, 3... The generator t00 = 1. Pascal concludes with the proof,

t_{mn} = \frac{(m+n)(m+n-1)...(m+1)}{n(n-1)...1}.\

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' formulation of the infinitesimal calculus.[7]

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 John Wallis, Christiaan Huygens, Christopher Wren, and others; Pascal, under the pseudonym Amos Dettonville, 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 Mind"), originally written as a preface to a geometry textbook for one of the famous "Petites-Ecoles de Port-Royal" ("Little Schools of 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 of such a 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

Portrait of Pascal

Pascal's work in the fields of the study 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. 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. This was based on the Aristotelian notion that creation was a thing of substance, whether visible or invisible; and this substance was forever in motion. Furthermore, "Everything that is in motion must be moved by something," Aristotle declared.[8] Therefore, to the Aristotelian trained scientists of Pascal's time, a vacuum was an impossibility. How so? As proof it was pointed out:

  • Light passed through the so-called "vacuum" in the glass tube.
  • Aristotle wrote how everything moved, and must be moved by something.
  • Therefore, since there had to be an invisible "something" to move the light through the glass tube, there was no vacuum in the tube. Not in the glass tube or anywhere else. Vacuums—the absence of any and everything—were simply an impossibility.

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.

On September 19, 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:

"The weather was chancy last Saturday...[but] around five o'clock that morning...the Puy-de-Dôme was visible...so I decided to give it a try. Several important people of the city of Clermont had asked me to let them know when I would make the ascent...I was delighted to have them with me in this great work... "...at eight o'clock we met in the gardens of the Minim Fathers, which has the lowest elevation in town....First I poured sixteen pounds of quicksilver...into a vessel...then took several glass tubes...each four feet long and hermetically sealed at one end and opened at the other...then placed them in the vessel [of quicksilver]...I found the quick silver stood at 26" and 3½ lines above the quicksilver in the vessel...I repeated the experiment two more times while standing in the same spot...[they] produced the same result each time... "I attached one of the tubes to the vessel and marked the height of the quicksilver and...asked Father Chastin, one of the Minim Brothers...to watch if any changes should occur through the day...Taking the other tube and a portion of the quick silver...I walked to the top of Puy-de-Dôme, about 500 fathoms higher than the monastery, where upon experiment...found that the quicksilver reached a height of only 23" and 2 lines...I repeated the experiment five times with care...each at different points on the summit...found the same height of quicksilver...in each case..."[9]

Pascal replicated the experiment in Paris by carrying a barometer up to the top of the bell tower at the church of Saint-Jacques-de-la-Boucherie, a height of about fifty meters. The mercury dropped two lines. These, and other lesser experiments carried out by Pascal, were hailed throughout Europe as 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 other prominent scientists, including Descartes.

Pascal introduced a primitive form of roulette and the roulette wheel in the 17th century in his search for a perpetual motion machine.[10]

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, Pensées #72

Religious conversion

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 circulate 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.[11]

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

In the winter of 1646, Pascal's 58 year-old father broke his hip when he slipped and fell on an icy street of Rouen; given the man's age and the state of medicine in the 17th century, a broken hip could be a very serious condition, perhaps even fatal. Rouen was home to two of the finest doctors in France: Monsieur Doctor Deslandes and Monsieur Doctor de La Bouteillerie. The elder Pascal "would not let anyone other than these men attend him...It was a good choice, for the old man survived and was able to walk again..."[12] But treatment and rehabilitation took three months, during which time La Bouteillerie and Deslandes had become household guests.

Both men were followers of Jean Guillebert, proponent of a splinter group from the main body of Catholic teaching known as Jansenism. This still fairly small sect was making surprising inroads into the French Catholic community at that time. It espoused rigorous Augustinism. Blaise spoke with the doctors frequently, and upon his successful treatment of Étienne, borrowed works by Jansenist authors from them. In this period, Pascal experienced a sort of "first conversion" and began to write on theological subjects in the course of the following year.

Pascal fell away from this initial religious engagement and experienced a few years of what some biographers have called his "worldly period" (1648–54). His father died in 1651 and left his inheritance to Pascal and Jacqueline, of which Pascal acted as her conservator. Jacqueline announced that she would soon become a postulant in the Jansenist convent of Port-Royal. Pascal was deeply affected and very sad, not because of her choice, but because of his chronic poor health; he too needed her.

"Suddenly there was war in the Pascal household. Blaise pleaded with Jacqueline not to leave, but she was adamant. He commanded her to stay, but that didn't work, either. At the heart of this was...Blaise's fear of abandonment...if Jacqueline entered Port-Royal, she would have to leave her inheritance behind...[but] nothing would change her mind."[13]

By the end of October in 1651, a truce had been reached between brother and sister. In return for a healthy annual stipend, Jacqueline signed over her part of the inheritance to her brother. Gilberte had already been given her inheritance in the form of a dowry. In early January, Jacqueline left for Port-Royal. On that day, according to Gilberte concerning her brother, "He retired very sadly to his rooms without seeing Jacqueline, who was waiting in the little parlor..."[14] In early June of 1653, after what must have seemed like endless badgering from Jacqueline, Pascal formally signed over the whole of his sister's inheritance to Port-Royal, which, to him, "had begun to smell like a cult."[15] With two-thirds of his father's estate now gone, the 29 year old Pascal was now consigned to genteel poverty.

For a while, Pascal pursued the life of a bachelor. He showed strong interest in one woman while in Auvergne. He referred to her as the "Sappho of the countryside."[16] During this time, Pascal wrote Discours sur les passions de l'amour ("Conversation about the Passions of Love") and apparently contemplated marriage — which he was later to describe as "the lowest of the conditions of life permitted to a Christian."[17] Jacqueline reproached him for his frivolity and prayed for his reform.[18] During visits to his sister at Port-Royal in 1654, he displayed contempt for affairs of the world but was not drawn to God.[19]

Brush with death

In October 1654, Pascal is said to have been involved in an accident at the Neuilly-sur-Seine 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. On 23 November 1654, between 10:30 and 12:30 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.[20] This piece is now known as the Memorial. The story of the carriage accident as having led to the experience described in the Memorial is disputed by some scholars.[21] 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 travelled 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, and in particular Antonio Escobar). Pascal denounced casuistry as the mere use of complex reasoning to justify moral laxity and all sorts of sins. 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, in the midsts of the formulary controversy, 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.

Wide praise has been given to the Provincial Letters. Voltaire called the Letters "the best-written book that has yet appeared in France."[22] 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.[23]

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 pro and anti Jansenists 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."[24] His beliefs renewed, he set his mind to write his final, unfinished testament, the Pensées.

The Pensées

Pascal's most influential theological work, referred to posthumously as the Pensées ("Thoughts"), was not completed before his death. It was to have been a sustained and coherent examination and defense of the Christian faith, with the original title Apologie de la religion Chrétienne ("Defense of the Christian Religion"). What was found upon sifting through his personal items after his death were numerous scraps of paper with isolated thoughts, grouped in a tentative, but telling, order. The first version of the detached notes appeared in print as a book in 1670 titled Pensées de M. Pascal sur la religion, et sur quelques autres sujets ("Thoughts of M. Pascal on religion, and on some other subjects") and soon thereafter became a classic. One of the Apologie's main strategies was to use the contradictory philosophies of skepticism and stoicism, personalized by Montaigne on one hand, and Epictetus on the other, in order to bring the unbeliever to such despair and confusion that he would embrace God. This strategy was deemed quite hazardous by Pierre Nicole, Antoine Arnauld and other friends and scholars of Port-Royal, who were concerned that these fragmentary "thoughts" might lead to skepticism rather than to piety. Henceforth, they concealed the skeptical pieces and modified some of the rest, lest King or Church should take offense[25] for at that time the persecution of Port-Royal had ceased, and the editors were not interested in a renewal of controversy. Not until the nineteenth century were the Pensées published in their full and authentic text.

Pascal's Pensées is widely considered to be a masterpiece, and a landmark in French prose. When commenting on one particular section (Thought #72), Sainte-Beuve praised it as the finest pages in the French language.[26] Will Durant, in his 11-volume, comprehensive The Story of Civilization series, hailed it as "the most eloquent book in French prose."[27] In Pensées, Pascal surveys several philosophical paradoxes: infinity and nothing, faith and reason, soul and matter, death and life, meaning and vanity—seemingly arriving at no definitive conclusions besides humility, ignorance, and grace. Rolling these into one he develops Pascal's Wager.

Last works and death

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 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."[28]

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.[29]

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 poor health was never precisely determined, though speculation focuses on tuberculosis, stomach cancer, or a combination of the two.[30] The headaches which afflicted Pascal are generally attributed to his brain lesion.

Legacy

In honor 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."[31] 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.

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)

Miscellaneous

  • In France, prestigious annual awards, Blaise Pascal Chairs are given to outstanding international scientists to conduct their research in the Ile de France region.[32]
  • The University of Waterloo, Ontario, Canada, holds an annual math contest named in his honour. The Pascal Contest is open to any student from around the world, who is fifteen years or under and is in grade nine or lower.[33]
  • Roberto Rossellini directed a filmed biopic (entitled Blaise Pascal) which originally aired on Italian television in 1971.
  • Pascal was a subject for the first edition of the 1984 BBC Two documentary, "The Sea of Faith", presented by Don Cupitt (see Sea of Faith: Television series).

See also

Notes

  1. ^ "Blaise Pascal". Catholic Encyclopedia. http://www.newadvent.org/cathen/11511a.htm. Retrieved 2009-02-23. 
  2. ^ Hald, Anders A History of Probability and Statistics and Its Applications before 1750, (Wiley Publications, 1990) pp.44
  3. ^ Devlin, p. 20.
  4. ^ O'Connor, J.J.; Robertson, E.F. (August 2006). "Étienne Pascal". University of St. Andrews, Scotland. http://www-history.mcs.st-andrews.ac.uk/Biographies/Pascal_Etienne.html. Retrieved 5 February 2010. 
  5. ^ The Story of Civilization: Volume 8, "The Age of Louis XIV" by Will & Ariel Durant; chapter II, subsection 4.1 p.56)
  6. ^ Connor, James A., Pascal's Wager(HarperCollins, NY, 2006) p.42
  7. ^ "The Mathematical Leibniz". Math.rutgers.edu. http://www.math.rutgers.edu/courses/436/Honors02/leibniz.html. Retrieved 2009-08-16. 
  8. ^ Aristotle,Physics,VII,1.
  9. ^ Périer to Pascal, September 1647,Œuves completes de Pascal, 2:682.
  10. ^ 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."
  11. ^ Sainte-Beuve, Port-Royal, I, 89.
  12. ^ Connor, James A. Pascal's Wager (HarperCollins, 2006)p.70
  13. ^ Miel p.122
  14. ^ Jacqueline Pascal, "Memoir" p. 87
  15. ^ Miel p.124
  16. ^ Pascal, Pensées, Havet ed. Introd., p. civ.
  17. ^ Mesnard, Pascal, 57.
  18. ^ The Story of Civilization: Volume 8, "The Age of Louis XIV" by Will & Ariel Durant, p.58)
  19. ^ Encyclopedia of Philosophy, 52.
  20. ^ Oeuvres complètes, 618.
  21. ^ MathPages, http://www.mathpages.com/. . .
  22. ^ Voltaire, Age of Louis XIV 424, 358.
  23. ^ Voltaire, Age of Louis XIV 359.
  24. ^ Sainte-Beuve, Port-Royal, III, 173f.; Beard, Charles, Port-Royal, I 84.
  25. ^ Pascal, Pensées, Introduction, p. xxviii; Mesnard, Pascal, 137–138.
  26. ^ Sainte-Beuve, Seventeenth Century, 174.
  27. ^ The Story of Civilization: Volume 8, "The Age of Louis XIV" by Will & Ariel Durant, chapter II, Subsection 4.4 (pg. 66)
  28. ^ Muir, 104.
  29. ^ Muir, 104.
  30. ^ Muir, 103.
  31. ^ "Pascal's legacy". Nature.com. 2004-10-01. http://www.nature.com/embor/journal/v5/n1s/full/7400229.html. Retrieved 2009-08-16. 
  32. ^ "Chaires Blaise Pascal". Chaires Blaise Pascal. http://www.chaires-blaise-pascal.org/uk/index.html. Retrieved 2009-08-16. 
  33. ^ "CEMC - Pascal, Cayley and Fermat - Mathematics Contests - University of Waterloo". Cemc.uwaterloo.ca. 2008-06-23. http://www.cemc.uwaterloo.ca/contests/pcf.html. Retrieved 2009-08-16. 

References

  • Adamson, Donald. Blaise Pascal: Mathematician, Physicist, and Thinker about God (1995)
  • Adamson, Donald. "Pascal’s Views on Mathematics and the Divine," Mathematics and the Divine: A Historical Study (eds. T. Koetsier and L. Bergmans. Amsterdam: Elsevier 2005), pp. 407-21.
  • Broome, J.H. Pascal. (London: E. Arnold, 1965). ISBN 0-7131-5021-1
  • Davidson, Hugh M. Blaise Pascal. (Boston: Twayne Publishers), 1983.
  • Devlin, Keith, The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern, Basic Books; 1 edition (September 22, 2008), ISBN 978-0465009107.
  • Farrell, John. "Pascal and Power". Chapter seven of Paranoia and Modernity: Cervantes to Rousseau (Cornell UP, 2006).
  • Goldmann, Lucien, The hidden God; a study of tragic vision in the Pensees of Pascal and the tragedies of Racine (original ed. 1955, Trans. Philip Thody. London: Routledge, 1964.
  • Jordan, Jeff. Pascal’s Wager: Pragmatic Arguments and Belief in God. (Oxford: Clarendon Press, 2006).
  • Mackie, John Leslie. The Miracle of Theism: Arguments for and against the Existence of God. (Oxford: Oxford University Press, 1982).
  • Miel, Jan. Pascal and Theology. (Baltimore: John Hopkins University Press, 1969).
  • Muir, Jane. Of Men and Numbers. (New York: Dover Publications, Inc, 1996). ISBN 0-486-28973-7
  • Encyclopedia of Philosophy, 1967 edition, s.v. "Pascal, Blaise."
  • Pascal, Blaise. Oeuvres complètes. (Paris: Seuil, 1960).
  • Pascal, Blaise. Oeuvres complètes. Jean Mesnard, ed. 4 vols have appeared. (Paris: Desclée-Brouwer, 1964-0
  • Saka, Paul. “Pascal’s Wager and the Many Gods Objection,” Religious Studies, 2001, pp.321-41.
  • Tobin, Paul. "The Rejection of Pascal’s Wager: A Skeptic’s Guide to the Bible and the Historical Jesus". authorsonline.co.uk, 2009.

External links


Quotes

Up to date as of January 14, 2010

From Wikiquote

To make light of philosophy is to be a true philosopher.

Blaise Pascal (19 June 162319 August 1662) was a French mathematician, physicist and theologian

Contents

Sourced

Our reason is always disappointed by the inconstancy of appearances.
If we look at our work immediately after completing it, we are still too involved; if too long afterwards, we cannot pick up the thread again.
  • People almost invariably arrive at their beliefs not on the basis of proof but on the basis of what they find attractive.
    • The Art of Persuasion
  • Entre nous, et l'enfer ou le ciel, il n'y a que la vie entre deux, qui est la chose du monde la plus fragile.
    • Discours sur les passions de l'amour
    • Between us, and Hell or Heaven, there is only life between the two, which is the most fragile thing in the world.
    • Variant translation: Between us and heaven or hell there is only life, which is the frailest thing in the world.
  • Je n'ai fait celle-ci plus longue que parce que je n'ai pas eu le loisir de la faire plus courte.
    • I would have written a shorter letter, but I did not have the time.
    • Source: Provincial Letters: Letter XVI (English Translation)
    • Literally: I made this [letter] very long, because I did not have the leisure to make it shorter.
    • Such statements have also been attributed to Mark Twain, T.S. Eliot, Cicero, and others besides.
  • L'homme n'est ni ange ni bête, et le malheur veut que qui veut faire l'ange fait la bête.
    • Laf. 678
  • It is not permitted to the most equitable of men to be a judge in his own cause.
    • Pensées (1670) Chapter 4, I
  • For as old age is that period of life most remote from infancy, who does not see that old age in this universal man ought not to be sought in the times nearest his birth, but in those most remote from it?
    • Preface to the Treatise on Vacuum
  • Habit is a second nature and it destroys the first.
    • Pensées (1670) No. 376

Pensées

The heart has its reasons, which reason does not know. We feel it in a thousand things.
  • 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. (72)
  • An advocate who has been well paid in advance will find the cause he is pleading all the more just. (82)
  • A trifle consoles us because a trifle upsets us.
  • All men naturally hate one another; there could not be four friends in the world. (101)
  • Tout notre raisonnement se réduit à céder au sentiment. (274)
    • All our reasoning boils down to yielding to sentiment.
  • Anyone who found the secret of rejoicing when things go well without being annoyed when they go badly would have found the point. (181)
  • Bless yourself with holy water, have Masses said, and so on; by a simple and natural process this will make you believe, and will dull you — will quiet your proudly critical intellect. (233)
  • Caesar was too old, it seems to me, to go off and amuse himself conquering the world. Such a pastime was all right for Augustus and Alexander; they were young men, not easily held in check, but Caesar ought to have been more mature. (132)
  • Curiosité n'est que vanité. Le plus souvent, on ne veut savoir que pour en parler. (152)
    • Curiosity is nothing more than vanity. More often than not we only seek knowledge to show it off.
  • Epictetus goes much further when he asks: Why do we not lose our temper if someone tells us that we have a headache, while we do lose it if someone says there is anything wrong with our arguments or our choice? (80)
  • Equality of possessions is no doubt right, but, as men could not make might obey right, they have made right obey might. (299)
  • Peu d'amitiés subsisteraient, si chacun savait ce que son ami dit de lui lorsqu'il n'y est pas. (100)
    • Few friendships would remain, if each knew what his friend said of him when he wasn't there.
  • For knowledge of the first principles, like space, time, motion, number, is as solid as any derived through reason, and it is on such knowledge, coming from the heart and instinct, that reason has to depend and base all its arguments. (282)
  • Go to confession and communion; you will find it a relief and a strengthening. (82)
  • Dieu est une sphère infinie, dont le centre est partout et la circonférence nulle part. (72)
    • God is an infinite sphere whose center is everywhere and circumference is nowhere.
  • How hollow is the heart of man, and how full of excrement! (143)
  • I cannot imagine a man without thought; he would be a stone or an animal. (339)
  • S'il se vante, je l'abaisse,
    S'il s'abaisse, je le vante;
    Et le contredis toujours,
    Jusqu'à ce qu'il comprenne
    Qu'il est un monstre incompréhensible.
    (420)
    • Translation: If [Man] exalt himself, I humble him,
      If he humble himself, I exalt him;
      And [I] always contradict him,
      Until he understands
      That he is an incomprehensible monster.
  • If our condition were truly happy we should not need to divert ourselves from thinking about it. (170)
  • If we look at our work immediately after completing it, we are still too involved; if too long afterwards, we cannot pick up the thread again. (381)
  • Imagination cannot make fools wise, but it makes them happy, as against reason, which only makes its friends wretched: one covers them with glory, the other with shame. (82)
  • It is a funny sort of justice whose limits are marked by a river; true on this side of the Pyrenees, false on the other. (294)
  • Il n'est pas certain que tout soit incertain. (387)
    • It is not certain that everything is uncertain.
  • It is not in space that I must seek my human dignity, but in the ordering of my thought. It will do me no good to own land. Through space the universe grasps me and swallows me up like a speck; through thought I grasp it. (348)
  • Il n'est pas honteux pour l'homme de succomber sous la douleur et il est honteux de succomber sous le plaisir. (160)
    • It is not shameful for a man to succumb to pain and it is shameful to succumb to pleasure.
  • Justice is as much a matter of fashion as charm is. (309)
  • Knowledge of physical science will not console me for ignorance of morality in time of affliction, but knowledge of morality will always console me for ignorance of physical science. (67)
  • Make religion attractive, make good men wish it were true, and then show that it is. Worthy of reverence because it really understands human nature. Attractive because it promises true good. (187)
  • L'homme n'est qu'un roseau, le plus faible de la nature; mais c'est un roseau pensant. (Pascal, Pensées, ed.Ch.M des Granges, Garnier, Paris, 1964, no.347 p.162)
    • Man is only a reed, the weakest of nature, but he is a thinking reed.
  • Man is only a disguise, a liar, a hypocrite, both to himself and to others. (377)
  • Man is so made that if he is told often enough that he is a fool he believes it. (535)
  • Men spend their time chasing a ball or a hare; it is the very sport of kings. (141)
  • Nothing is so conformable to reason as to disavow reason. (272)
  • Nothing is surer than that the people will be weak. (330)
  • One must have deeper motives and judge everything accordingly, but go on talking like an ordinary person.
  • One must know oneself. If this does not serve to discover truth, it at least serves as a rule of life, and there is nothing better. (66)
  • Notre raison est toujours déçue par l'inconstance des apparences. (83)
    • Our reason is always disappointed by the inconsistency of appearances.
  • All these examples of wretchedness prove his greatness. It is the wretchedness of a great lord, the wretchedness of a dispossessed king. (425)
  • Qu’est-ce donc que nous crie cette avidité et cette impuissance, sinon qu’il y a eu autrefois en l’homme un véritable bonheur dont il ne lui reste maintenant que la marque et la trace toute vide, qu’il essaye inutilement de remplir de tout ce qui l’environne, en cherchant dans les choses absentes le secours qu’il n’obtient pas des présentes, et que les unes et les autres sont incapables de lui donner, parce que ce gouffre infini ne peut être rempli que par un objet infini et immuable, c'est-à-dire que par Dieu même. (425)
    • What does this craving, and this helplessness, proclaim but that there was once in man a true happiness, of which all that now remains is the empty print and trace? This he tries in vain to fill with everything around him, seeking in things that are not there the help he cannot find in those that are, though none can help, since this infinite abyss can be filled only with an infinite and immutable object, in other words by God himself.
  • Différence entre J.-C. et Mahomet. Mahomet non prédit, J.-C. prédit. Mahomet en tuant, J.-C. en faisant tuer les siens. Mahomet en défendant de lire, les apôtres en ordonnant de lire. Enfin cela est si contraire que si Mahomet a pris la voie de réussir humainement, J.-C. a pris celle de périr humainement et qu'au lieu de conclure que puisque Mahomet a réussi, J.-C. a bien pu réussir, il faut dire que puisque Mahomet a réussi, J.-C. devait périr.
    • The difference between Jesus Christ and Mahomet. — Mahomet was not foretold; Jesus Christ was foretold.
      Mahomet slew; Jesus Christ caused His own to be slain.
      Mahomet forbade reading; the Apostles ordered reading.
      In fact the two are so opposed, that if Mahomet took the way to succeed from a worldly point of view, Jesus Christ, from the same point of view, took the way to perish. And instead of concluding that, since Mahomet succeeded, Jesus Christ might well have succeeded, we ought to say that since Mahomet succeeded, Jesus Christ should have failed.
    • (598)
  • Put the world's greatest philosopher on a plank that is wider than need be; if there is a precipe below, although his reason may convince him that he is safe, his imagination will prevail.
  • Le silence est la plus grande persécution; jamais les saints ne se sont tus. (919)
    • Silence is the greatest persecution; never do the saints keep themselves silent.
  • That something so obvious as the vanity of the world should be so little recognized that people find it odd and surprising to be told that it is foolish to seek greatness; that is most remarkable.
  • The eternal silence of these infinite spaces terrifies me.
  • The grandeur of man is great in that he knows himself to be miserable.
  • Le coeur a ses raisons, que la raison ne connaît point. On le sent en mille choses. C'est le cœur qui sent Dieu, et non la raison. Voilà ce que c'est que la foi parfaite, Dieu sensible au cœur.
    • The heart has its reasons, which reason does not know. We feel it in a thousand things. It is the heart which experiences God, and not the reason. This, then, is faith: God felt by the heart, not by the reason.
  • Le nez de Cléopâtre, s'il eût été plus court, toute la face de la terre aurait changé.
    • The nose of Cleopatra, if it had been shorter, would have changed all the face of the earth.
  • The two principles of truth, reason and senses, are not only both not genuine, but are engaged in mutual deception. The senses deceive reason through false appearances, and the senses are disturbed by passions, which produce false impressions.
  • The wisest reason takes as her own principles those which the imagination of man has everywhere rashly introduced.
  • There no doubt exist natural laws, but once this fine reason of ours was corrupted, it corrupted everything.
  • Thinking too little about things or thinking too much both make us obstinate and fanatical.
  • This is what I see, and what troubles me. I look on all sides, and everywhere I see nothing but obscurity. Nature offers me nothing that is not a matter of doubt and disquiet.
  • Those who are clever in imagination are far more pleased with themselves than prudent men could reasonably be.
  • Thought constitutes the greatness of man.
  • Se moquer de la philosophie, c'est vraiment philosopher (4)
    • To make light of philosophy is to be a true philosopher.
  • La vraie morale se moque de la morale.
    • True morality makes fun of morality.
  • We understand nothing of the works of God unless we take it as a principle that He wishes to blind some and to enlighten others.
  • We would never travel on the sea if we had no hope of telling about it later... We lose our lives with joy provided people talk about it... Even philosophers wish for admirers.
  • What a Chimera is man! What a novelty, a monster, a chaos, a contradiction, a prodigy! Judge of all things, an imbecile worm of the earth; depository of truth, and sewer of error and doubt; the glory and refuse of the universe.
  • What amazes me the most is to see that everyone is not amazed at his own weakness.
  • What must I do? I see nothing but obscurities on every side. Shall I believe I am nothing? Shall I believe I am God?
  • What part of us feels pleasure? Is it our hand, our arm, our flesh, or our blood? It must obviously be something immaterial.
  • Who dispenses reputation? Who makes us respect and rever persons, works, laws, the great? Who but this faculty of imagination? All the riches of the earth are inadequate without its approval.
  • Qui sait si cette autre moitié de la vie où nous pensons veiller n'est pas un autre sommeil un peu différent du premier.
    • Who knows if this other half of life where we think we're awake is not another sleep a little different from the first.
  • Why are you killing me for your own benefit? I am unarmed.' 'Why, do you not live on the other side of the water? My friend, if you lived on this side, I should be a murderer, but since you live on the other side, I am a brave man and it is right.'
    • Variant: "Why do you kill me? What! do you not live on the other side of the water? If you lived on this side, my friend, I should be an assassin, and it would be unjust to slay you in this manner. But since you live on the other side, I am a hero, and it is just." (293)
  • Wisdom leads us back to childhood.
    • Variant: Wisdom sends us to childhood. Nisi efficiamini sicut parvuli. (271)
  • You must wager; it is not optional... Let us weigh the gain and the loss in wagering that God exists... If you gain, you gain all; if you lose, you lose nothing. Wager, then, without hesitation, that He exists.

Unsourced

  • Men never do evil so completely and cheerfully as when they do it from religious conviction.
  • If God does not exist, one will lose nothing by believing in him, while if he does exist, one will lose everything by not believing.
  • In every man's heart there is an emptiness that only God can fill with his son Jesus Christ.
  • Justice without force is powerless; force without justice is tyrannical.
  • Ne pouvant fortifier la justice, on a justifié la force.
    • Not being able to fortify justice, they justified force.
  • Ce qui fait qu'on va si loin dans l'amour, c'est que l'on ne songe pas que l'on aura besoin d'autre chose que ce que l'on aime.
    • That which makes us go so far for love is that we never think that we might have need of anything besides that which we love.
  • C'est une maladie naturelle à l'homme de croire qu'il possède la vérité.
    • It is man's natural sickness to believe that he possesses the Truth.
  • Les hommes se gouvernent plus par caprice que par raison.
    • Man governs himself more by capriciousness (impulse) than reason
  • Penser fait la grandeur de l'homme.
    • Thinking makes man great.
  • Puisqu'on ne peut être universel en sachant tout ce qui se peut savoir sur tout, il faut savoir peu de tout.
    • Since one cannot be universal by knowing everything that can be known about everything, it is necessary to know a little about everything.
  • Jurisdiction is given not for the sake of the judge, but for that of the litigant.
    • Possibly translated from Pensées, Section XIV, 879
  • The last thing one knows in constructing a work is what to put first.
  • Clarity of mind means clarity of passion, too; this is why the great and clear mind loves ardently and sees distinctly what it loves.

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Simple English

[[File:|thumb|Painting of Blaise Pascal]] Blaise Pascal (1623 - 1662) was a French mathematician whose mother died when he was 3 years old. His father's name was Étienne. He had two sisters, Jaqueline and Gilberte. Pascal was completely educated by his father. Pascal was considered a child prodigy. Though best known for his works in math, including the creation of Pascal's Triangle, which is named after him, and developments in the field of probability, Pascal was also a scientist. He wrote in support of the scientific method and also contributed to physics. Later he wrote two books about Christianity.

Pascal was born in Clermont, France and died in Paris, France at 39. He died from a malignant stomach ulcer.








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