SUPPORT THE WORK

GetWiki

Blaise Pascal

ARTICLE SUBJECTS
news  →
unix  →
wiki  →
ARTICLE TYPES
feed  →
help  →
wiki  →
ARTICLE ORIGINS
Blaise Pascal
[ temporary import ]
- the content below is remote from Wikipedia
- it has been imported raw for GetWiki
{{pp-move-indef}}{{pp-semi-indef}}{{short description|French mathematician, physicist, inventor, writer, and Christian philosopher}}{{Use dmy dates|date=December 2013}}

factoids

Contributions to mathematics

File:PascalTriangleAnimated2.gif|thumb|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 coefficientsbinomial coefficientsPascal continued to influence mathematics throughout his life. His TraitÃ© du triangle arithmÃ©tique ("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:{| class="wikitable"! style="width:20px;" |! style="width:20px;"|0! style="width:20px;"|1! style="width:20px;"|2! style="width:20px;"|3! style="width:20px;"|4! style="width:20px;"|5! style="width:20px;"|60 >|11 >|2 >|3 >|4 >|5 >|6 >|He defines the numbers in the triangle by recursion: Call the number in the (m + 1)th row and (n + 1)th column t'mn. Then t'mn = t'mâ€“1,n + t'm,nâ€“1, for m = 0, 1, 2, ... and n = 0, 1, 2, ... The boundary conditions are tm,âˆ’1 = 0, tâˆ’1,n = 0 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)cdots(m+1)}{n(n-1)cdots 1}.
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.JOURNAL, Kieren MacMillan, Jonathan Sondow, Proofs of power sum and binomial coefficient congruences via Pascal's identity, American Mathematical Monthly, 2011, 118, 6, 549â€“551, 10.4169/amer.math.monthly.118.06.549, 1011.0076, In 1654, prompted by his friend the Chevalier de MÃ©rÃ©, he corresponded with Pierre de Fermat on the subject of gambling problems, and from that collaboration was born the mathematical theory of probabilities.{{sfn|Devlin|p=24}} 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 PensÃ©es) 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.WEB,weblink The Mathematical Leibniz, Math.rutgers.edu, 16 August 2009, After a religious experience in 1654, Pascal mostly gave up work in mathematics.

Philosophy of mathematics

Pascal's major contribution to the philosophy of mathematics came with his De l'Esprit gÃ©omÃ©trique ("Of the Geometrical Spirit"), 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 upâ€”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 gÃ©omÃ©trique 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 be grasped only through intuition, and that this fact underscored the necessity for submission to God in searching out truths.

Contributions to the physical sciences

File:Pascal's Barrel.png|thumb|An illustration of the (apocryphal) Pascal's barrelPascal's barrelPascal'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. 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, 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 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 that this substance was forever in motion. Furthermore, "Everything that is in motion must be moved by something," Aristotle declared.Aristotle, Physics, VII, 1. 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 â€“ the absence of any and everything â€“ 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. This work was followed by RÃ©cit de la grande expÃ©rience de l'Ã©quilibre des liqueurs ("Account of the great experiment on equilibrium in liquids") published in 1648.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 DÃ´me mountain, {{convert|4790|ft}} tall, but his health was poor so could not climb it.MAGAZINE
, Ley
, Willy
,
,
,
,
,
, June 1966
, The Re-Designed Solar System
, Galaxy Science Fiction
, 94â€“106
,
, On 19 September 1648, after many months of Pascal's friendly but insistent prodding, Florin PÃ©rier, 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 PÃ©rier, reads:
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...

Adult life, religion, philosophy, and literature

{{Catholic philosophy}}

Religious conversion

File:Pascal Pajou Louvre RF2981.jpg|thumb|left|upright|Pascal studying the cycloid, by Augustin Pajou, 1785, LouvreLouvreIn 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..."Connor, James A., Pascal's wager: the man who played dice with God (HarperCollins, NY, 2006) {{isbn|0-06-076691-3}} p. 70 But treatment and rehabilitation took three months, during which time La Bouteillerie and Deslandes had become regular visitors.Both men were followers of Jean Guillebert, proponent of a splinter group from 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 after their successful treatment of his father, borrowed from them works by Jansenist authors. 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" (1648â€“54). His father died in 1651 and left his inheritance to Pascal and his sister Jacqueline, for whom Pascal acted as 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 needed her just as she had needed him.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..."Jacqueline Pascal, "Memoir" p. 87In early June 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."Miel, Jan. Pascal and Theology. (Baltimore: Johns Hopkins University Press, 1969), p. 124 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. During visits to his sister at Port-Royal in 1654, he displayed contempt for affairs of the world but was not drawn to God.Richard H. Popkin, Paul Edwards (ed.), Encyclopedia of Philosophy, 1967 edition, s.v. "Pascal, Blaise.", vol. 6, p. 52â€“55, New York: Macmillan

Brush with death

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.Pascal, Blaise. Oeuvres complÃ¨tes. (Paris: Seuil, 1960), p. 618 This piece is now known as the Memorial. The story of the carriage accident{{clarify|date=July 2012}} as having led to the experience described in the Memorial is disputed by some scholars.MathPages, Hold Your Horses. For the sources on which the hypothesis of a link between a carriage accident and Pascal's second conversion is based, and for a sage weighing of the evidence for and against, see Henri Gouhier, Blaise Pascal: Commentaires, Vrin, 1984, pp. 379ff.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

{{French literature sidebar}}Beginning in 1656â€“57, 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. 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 Alexander VII himself. Even Pope Alexander, while publicly opposing them, nonetheless was persuaded by Pascal's arguments.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.Charles Perrault wrote of the Letters: "Everything is thereâ€”purity of language, nobility of thought, solidity in reasoning, finesse in raillery, and throughout an agrÃ©ment not to be found anywhere else."Charles Perrault, ParallÃ¨le des Anciens et des Modernes (Paris, 1693), Vol. I, p. 296.

Pascal's most influential theological work, referred to posthumously as the PensÃ©es ("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 ChrÃ©tienne ("Defense of the Christian Religion"). The first version of the numerous scraps of paper found after his death appeared in print as a book in 1669 titled PensÃ©es 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.Pascal's PensÃ©es 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.Sainte-Beuve, Seventeenth Century {{isbn|1-113-16675-4}} p. 174 (2009 reprint). Will Durant hailed the PensÃ©es as "the most eloquent book in French prose".The Story of Civilization: Volume 8, "The Age of Louis XIV" by Will & Ariel Durant, chapter II, Subsection 4.4, p. 66 {{isbn|1-56731-019-2}}

Last works and death

File:Epitaph Blaise Pascal Saint-Etienne.jpg|thumb|Pascal's epitaph in Saint-Ã‰tienne-du-MontSaint-Ã‰tienne-du-MontT. 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 a person 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."Muir, Jane. Of Men and Numbers. (New York: Dover Publications, Inc, 1996). {{isbn|0-486-28973-7}}, p. 104.Louis XIV suppressed the Jansenist movement at Port-Royal in 1661. In response, Pascal wrote one of his final works, Ã‰crit 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, the carrosses Ã  cinq sols, moving passengers within Paris in a carriage with many seats.In 1662, Pascal's illness became more violent, and his emotional condition had severely worsened since his sister's death. 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 18 August 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-Ã‰tienne-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 poor health was never precisely determined, though speculation focuses on tuberculosis, stomach cancer, or a combination of the two.Muir, Jane. Of Men and Numbers. (New York: Dover Publications, Inc, 1996). {{isbn|0-486-28973-7}}, p. 103. The headaches which afflicted Pascal are generally attributed to his brain lesion.

Works

• Essai pour les coniques [Essay on conics] (1639)
• Experiences nouvelles touchant le vide [New experiments with the vacuum] (1647)
• RÃ©cit de la grande expÃ©rience de l'Ã©quilibre des liqueurs [Account of the great experiment on equilibrium in liquids] (1648)
• Lettres provinciales [The provincial letters] (1656â€“57)
• Ã‰crit sur la signature du formulaire (1661)
• TraitÃ© du triangle arithmÃ©tique (Treatise on arithmetical triangle) (written c. 1654;David Pengelley - "Pascal's Treatise on the Arithmetical Triangle" publ. 1665)
• PensÃ©es [Thoughts] (incomplete at death; publ. 1670)

References

{{Reflist|30em}}

• Adamson, Donald. Blaise Pascal: Mathematician, Physicist, and Thinker about God (1995) {{isbn|0-333-55036-6}}
• 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. 407â€“21.
• Broome, J.H. Pascal. (London: E. Arnold, 1965). {{isbn|0-7131-5021-1}}
• Davidson, Hugh M. Blaise Pascal. (Boston: Twayne Publishers), 1983.
• BOOK, Devlin, Keith, Keith Devlin, 2008, The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern, New York, Basic Books, 978-0-465-00910-7, {{sfnRef, Devlin, }}
• 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).
• Groothuis, Douglas. On Pascal. (Belmont: Wadsworth, 2002). {{isbn|978-0534583910}}
• Jordan, Jeff. Pascal's Wager: Pragmatic Arguments and Belief in God. (Oxford: Clarendon Press, 2006).
• Landkildehus, SÃ¸ren. "Kierkegaard and Pascal as kindred spirits in the Fight against Christendom" in Kierkegaard and the Renaissance and Modern Traditions (ed. Jon Stewart. Farnham: Ashgate Publishing, 2009).
• Mackie, John Leslie. The Miracle of Theism: Arguments for and against the Existence of God. (Oxford: Oxford University Press, 1982).
• Pugh, Anthony R. The Composition of Pascal's Apologia, (University of Toronto Press, 1984).
• JOURNAL, Saka, Paul, 2001, Pascal's Wager and the Many Gods Objection, Religious Studies, 37, 3, 321â€“41, 10.1017/S0034412501005686,
• BOOK, Stephen, Leslie, Leslie Stephen, Studies of a Biographer, 2, Duckworth and Co., London, 241â€“284, s:,
• Tobin, Paul. "The Rejection of Pascal's Wager: A Skeptic's Guide to the Bible and the Historical Jesus". authorsonline.co.uk, 2009.
• Yves Morvan, Pascal Ã  Mirefleurs ? Les dessins de la maison de Domat, Impr. Blandin, 1985. (FRBNF40378895)

{{Blaise Pascal}}{{Navboxes|title = Articles related to Blaise Pascal|list ={{Age of Enlightenment}}{{Catholicism|collapsed}}{{History of the Catholic Church|collapsed}}{{History of Catholic theology|collapsed}}{{philosophy of religion}}}}{{Scientists whose names are used as SI units}}{{Authority control}}

- content above as imported from Wikipedia
- "Blaise Pascal" does not exist on GetWiki (yet)
- time: 4:31am EDT - Thu, Apr 25 2019
[ this remote article is provided by Wikipedia ]
LATEST EDITS [ see all ]
GETWIKI 09 MAY 2016
GETWIKI 18 OCT 2015
M.R.M. Parrott
Biographies
GETWIKI 20 AUG 2014
GETWIKI 19 AUG 2014
GETWIKI 18 AUG 2014
Wikinfo
Culture
CONNECT