Blaise Pascal (/pæˈskæl, pɑːˈskɑːl/; French: [blɛz paskal]; 19 June 1623 – 19 August 1662) was a French mathematician, physicist, inventor, writer and Catholic theologian. He was a child prodigy who was educated by his father, a tax collector in Rouen. Pascal's earliest work was in the natural and applied sciences where he made important contributions to the study of fluids, and clarified the concepts of pressure and vacuum by generalising the work of Evangelista Torricelli. Pascal also wrote in defence of the scientific method.
In 1642, while still a teenager, he started some pioneering work on calculating machines. After three years of effort and 50 prototypes, he built 20 finished machines (called Pascal's calculators and later Pascalines) over the following 10 years, establishing him as one of the first two inventors of the mechanical calculator.
Pascal was an important mathematician, helping create two major new areas of research: he wrote a significant treatise on the subject of projective geometry at the age of 16, and later corresponded with Pierre de Fermat on probability theory, strongly influencing the development of modern economics and social science. Following Galileo Galilei and Torricelli, in 1647, he rebutted Aristotle's followers who insisted that nature abhors a vacuum. Pascal's results caused many disputes before being accepted.
In 1646, he and his sister Jacqueline identified with the religious movement within Catholicism known by its detractors as Jansenism. Following a religious experience in late 1654, he began writing influential works on philosophy and theology. His two most famous works date from this period: the Lettres provinciales and the Pensées, the former set in the conflict between Jansenists and Jesuits. In that year, he also wrote an important treatise on the arithmetical triangle. Between 1658 and 1659, he wrote on the cycloid and its use in calculating the volume of solids.
Throughout his life, Pascal was in frail health, especially after the age of 18; he died just two months after his 39th birthday.
Painting of Blaise Pascal made by François II Quesnel for Gérard Edelinck in 1691
|Born||19 June 1623|
|Died||19 August 1662 (aged 39)|
Pascal was born in Clermont-Ferrand, which is in France's Auvergne region. He lost his mother, Antoinette Begon, at the age of three. 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, Étienne Pascal moved with his children to Paris. The newly arrived family soon hired Louise Delfault, a maid who eventually became an instrumental member of the family. Étienne, who never remarried, decided that he alone would educate his children, for they all showed extraordinary intellectual ability, particularly his son Blaise. The young Pascal showed an amazing aptitude for mathematics and science.
Particularly of interest to Pascal was a work of Desargues on conic sections. Following Desargues' thinking, the 16-year-old Pascal produced, as a means of proof, a short treatise on what was called the "Mystic Hexagram", Essai pour les coniques ("Essay on Conics") and sent it—his first serious work of mathematics—to Père Mersenne in Paris; it is known still today as Pascal's theorem. It states that if a hexagon is inscribed in a circle (or conic) then the three intersection points of opposite sides lie on a line (called the Pascal line).
Pascal's work was so precocious that Descartes was convinced that Pascal's father had written it. When assured by Mersenne that it was, indeed, the product of the son and not the father, Descartes dismissed it with a sniff: "I do not find it strange that he has offered demonstrations about conics more appropriate than those of the ancients," adding, "but other matters related to this subject can be proposed that would scarcely occur to a 16-year-old child."
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. The money was invested in a government bond which provided, if not a lavish, then certainly a comfortable income which allowed the Pascal family to move to, and enjoy, Paris. But in 1638 Richelieu, desperate for money to carry on the Thirty Years' War, defaulted on the government's bonds. Suddenly Étienne Pascal's worth had dropped from nearly 66,000 livres to less than 7,300.
Like so many others, Étienne was eventually forced to flee Paris because of his opposition to the fiscal policies of Cardinal Richelieu, leaving his three children in the care of his neighbour Madame Sainctot, a great beauty with an infamous past who kept one of the most glittering and intellectual salons in all France. It was only when Jacqueline performed well in a children's play with Richelieu in attendance that Étienne was pardoned. In time, Étienne was back in good graces with the cardinal and in 1639 had been appointed the king's commissioner of taxes in the city of Rouen—a city whose tax records, thanks to uprisings, were in utter chaos.
In 1642, in an effort to ease his father's endless, exhausting calculations, and recalculations, of taxes owed and paid (into which work the young Pascal had been recruited), Pascal, not yet 19, constructed a mechanical calculator capable of addition and subtraction, called Pascal's calculator or the Pascaline. Of the eight Pascalines known to have survived, four are held by the Musée des Arts et Métiers in Paris and one more by the Zwinger museum in Dresden, Germany, exhibit two of his original mechanical calculators. Although these machines are pioneering forerunners to a further 400 years of development of mechanical methods of calculation, and in a sense to the later field of computer engineering, the calculator failed to be a great commercial success. Partly because it was still quite cumbersome to use in practice, but probably primarily because it was extraordinarily expensive, the Pascaline became little more than a toy, and a status symbol, for the very rich both in France and elsewhere in Europe. Pascal continued to make improvements to his design through the next decade, and he refers to some 50 machines that were built to his design.
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:
He defines the numbers in the triangle by recursion: Call the number in the (m + 1)th row and (n + 1)th column tmn. Then tmn = tm–1,n + tm,n–1, for m = 0, 1, 2, ... and n = 0, 1, 2, ... The boundary conditions are tm,−1 = 0, t−1,n = 0 for m = 1, 2, 3, ... and n = 1, 2, 3, ... The generator t00 = 1. Pascal concludes with the proof,
In 1654, prompted by his friend the Chevalier de Méré, he corresponded with Pierre de Fermat on the subject of gambling problems, and from that collaboration was born the mathematical theory of probabilities. The specific problem was that of two players who want to finish a game early and, given the current circumstances of the game, want to divide the stakes fairly, based on the chance each has of winning the game from that point. From this discussion, the notion of expected value was introduced. Pascal later (in the Pensées) used a probabilistic argument, Pascal's Wager, to justify belief in God and a virtuous life. The work done by Fermat and Pascal into the calculus of probabilities laid important groundwork for Leibniz' formulation of the calculus.
After a religious experience in 1654, Pascal mostly gave up work in mathematics.
Pascal's major contribution to the philosophy of mathematics came with his De l'Esprit géométrique ("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 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 be grasped only through intuition, and that this fact underscored the necessity for submission to God in searching out truths.
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. 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. Therefore, to the Aristotelian trained scientists of Pascal's time, a vacuum was an impossibility. How so? As proof it was pointed out:
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 Récit de la grande expérience de l'équilibre 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 Dôme mountain, 4,790 feet (1,460 m) tall, but his health was poor so could not climb it. On 19 September 1648, after many months of Pascal's friendly but insistent prodding, Florin Périer, husband of Pascal's elder sister Gilberte, was finally able to carry out the fact-finding mission vital to Pascal's theory. The account, written by Périer, reads:
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 16 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 31⁄2 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...
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 50 metres. The mercury dropped two lines.
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 17th century's major statements on the scientific method, which is a striking anticipation of the idea popularised by Karl Popper that scientific theories are characterised by their falsifiability: "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.
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.
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..." 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" (1648–54). 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.
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.
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..." In 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." 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.
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. 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. 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.
Beginning in 1656–57, 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 there—purity of language, nobility of thought, solidity in reasoning, finesse in raillery, and throughout an agrément not to be found anywhere else."
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"). The first version of the numerous scraps of paper found after his death appeared in print as a book in 1669 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.
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. Will Durant hailed the Pensées as "the most eloquent book in French prose".
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 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."
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, the carrosses à 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-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 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.
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.
In France, prestigious annual awards, Blaise Pascal Chairs are given to outstanding international scientists to conduct their research in the Ile de France region. One of the Universities of Clermont-Ferrand, France – Université Blaise Pascal – is named after him. The University of Waterloo, Ontario, Canada, holds an annual math contest named in his honour.
Pascalian theology has grown out of his perspective that we are, according to Wood, "born into a duplicitous world that shapes us into duplicitous subjects and so we find it easy to reject God continually and deceive ourselves about our own sinfulness".
Roberto Rossellini directed a filmed biopic, Blaise Pascal, which originally aired on Italian television in 1971. Pascal was a subject of the first edition of the 1984 BBC Two documentary, Sea of Faith, presented by Don Cupitt.
The 2017 game Nier: Automata has multiple characters named after famous philosophers; one of these is a sentient pacifistic machine named Pascal, who serves as a major supporting character. Pascal creates a village for machines to live peacefully with the androids they're at war with and acts as a parental figure for other machines trying to adapt to their newly-found individuality.
The Blaise Pascal Chair, (Chaires Internationales de Recherche Blaise Pascal, France), established in 1996 by the Government of the Île-de-France Region for internationally acclaimed foreign scientists in all disciplines. A scientific committee annually selects the most outstanding candidates from all over the world. Since its inception a number of famous scientists were the
Blaise Pascal Chair laureates: Gérard Debreu (UC Berkeley, 1983 Nobel Prize in Economics), Ahmed Zewail (Caltech, 1999 Nobel Prize in Chemistry),
Igor Mel'čuk (University of Montreal, the world leading researcher in linguistics),
George Smoot (LBL, 2006 Nobel Prize in experimental Astrophysics),
Robert Langlands (UBC, 1996 Wolf Prize, one of the most
influential mathematicians of the 20th
century), outstanding theoretical physicists Gabriele Veneziano (CERN/College de France),
Alexander Zamolodchikov (Rutgers), and others.Blaise Pascal University
Blaise Pascal University (French: Université Blaise-Pascal), also known as Université Blaise Pascal, Clermont-Ferrand II or just Clermont-Ferrand II, is a public university with its main campus on 53 acres (210,000 m2) in Clermont-Ferrand, France, with satellite locations in other parts of the region of Auvergne, including Vichy, Moulins, Montluçon, and Aubière.On 1 January 2017, the university became part of the University Clermont Auvergne.European Academy of Sciences
The European Academy of Sciences (EurASc) (Latin: Academia Scientiarum Europaea) is an international non-profit organization aiming to promote excellence in science and technology. Based in Brussels, Belgium, it has about 600 members, including 65 Nobel Prize and Fields Medal winners, from 45 countries. It was established on 17 December 2003.
Since 2004, the academy has published multidisciplinary annals, e-newsletters for science and technology, and since 2009 various books. Its first general assemblies and ceremonies of awards were organized in Brussels and since 2009 each year in another country (2009: Università di Bologna, Italy; 2010: Academy of Athens, Greece; 2011: Università di Milano, Italy; 2012: Université de Liège, Belgium; 2013: L.C.C de Toulouse, France; 2014: Casa do Infante, Porto, Portugal; 2015: Le Quartz Centre de Congrès Brest, France; 2016: Palais des Académies in Brussels, Belgium; 2017: Lisbon Academy of Sciences, Lisbon, Portugal; 2018: Bielefeld, Center for Interdisciplinary Research, Germany. Since 2012 the academy has also organized an annual symposium called The Future of Sciences in the 21st Century.Fideism
Fideism () is an epistemological theory which maintains that faith is independent of reason, or that reason and faith are hostile to each other and faith is superior at arriving at particular truths (see natural theology). The word fideism comes from fides, the Latin word for faith, and literally means "faith-ism".Theologians and philosophers have responded in various ways to the place of faith and reason in determining the truth of metaphysical ideas, morality, and religious beliefs. A fideist is one who argues for fideism. Historically, fideism is most commonly ascribed to four philosophers: Blaise Pascal, Søren Kierkegaard, William James, and Ludwig Wittgenstein; with fideism being a label applied in a negative sense by their opponents, but which is not always supported by their own ideas and works or followers. There are a number of different forms of fideism.Hydraulics
Hydraulics (from Greek: Υδραυλική) is a technology and applied science using engineering, chemistry, and other sciences involving the mechanical properties and use of liquids. At a very basic level, hydraulics is the liquid counterpart of pneumatics, which concerns gases. Fluid mechanics provides the theoretical foundation for hydraulics, which focuses on the applied engineering using the properties of fluids. In its fluid power applications, hydraulics is used for the generation, control, and transmission of power by the use of pressurized liquids. Hydraulic topics range through some parts of science and most of engineering modules, and cover concepts such as pipe flow, dam design, fluidics and fluid control circuitry. The principles of hydraulics are in use naturally in the human body within the vascular system and erectile tissue.
Free surface hydraulics is the branch of hydraulics dealing with free surface flow, such as occurring in rivers, canals, lakes, estuaries and seas. Its sub-field open-channel flow studies the flow in open channels.
The word "hydraulics" originates from the Greek word ὑδραυλικός (hydraulikos) which in turn originates from ὕδωρ (hydor, Greek for water) and αὐλός (aulos, meaning pipe).Jacqueline Pascal
Jacqueline Pascal (4 October 1625 – 4 October 1661), sister of Blaise Pascal, was born at Clermont-Ferrand, Auvergne, France.
Like her brother she was a prodigy, composing verses when only eight years old, and a five-act comedy at eleven. In 1646, the influence of her brother converted her to Jansenism. Then in 1652, she took the veil, and entered Port-Royal Abbey, Paris, despite the strong opposition of her brother, and subsequently was largely instrumental in the latter's own final conversion. She vehemently opposed the attempt to compel the assent of the nuns to the Papal bulls condemning Jansenism, but was at last compelled to yield. This blow, however, hastened her death, which occurred at Paris on 4 October 1661, the same day she turned 36.Lettres provinciales
The Lettres provinciales (Provincial letters) are a series of eighteen letters written by French philosopher and theologian Blaise Pascal under the pseudonym Louis de Montalte. Written in the midst of the formulary controversy between the Jansenists and the Jesuits, they are a defense of the Jansenist Antoine Arnauld from Port-Royal-des-Champs, a friend of Pascal who in 1656 was condemned by the Faculté de Théologie at the Sorbonne in Paris for views that were claimed to be heretical. The First letter is dated January 23, 1656 and the Eighteenth March 24, 1657. A fragmentary Nineteenth letter is frequently included with the other eighteen.
In these letters, Pascal humorously attacked casuistry, a rhetorical method often used by Jesuit theologians, and accused Jesuits of moral laxity. Being quickly forced underground while writing the Provincial Letters, Pascal pretended they were reports from a Parisian to a friend in the provinces, on the moral and theological issues then exciting the intellectual and religious circles in the capital. In the letters, Pascal's tone combines the fervor of a convert with the wit and polish of a man of the world. Their style meant that, quite apart from their religious influence, the Provincial Letters were popular as a literary work. Adding to that popularity was Pascal's use of humor, mockery, and satire in his arguments. The letters also influenced the prose of later French writers like Voltaire and Jean-Jacques Rousseau. Brilliantly written by Pascal, the Provincial Letters would not have been possible without the work of theologians from Port-Royal; indeed, most of the arguments Pascal deployed were already to be found in Arnauld's Théologie morale des Jésuites, something which led the Jesuit Nicolas Caussin to reply to Pascal's perceived libel. Pascal's main source on Jesuit casuistry was Antonio Escobar's Summula casuum conscientiae (1627), several propositions of which would be later condemned by Pope Innocent XI.
Paradoxically, the Provincial Letters were both a success and a defeat: a defeat, on the political and theological level, and a success on the moral level. The final letter from Pascal, in 1657, had defied the Pope himself, provoking Alexander VII to condemn the letters. But that didn't stop most of educated France from reading them. Moreover, even Pope Alexander, while publicly opposing them, nonetheless was persuaded by Pascal's arguments. Just a few years later (1665–66, and then 1679), Alexander condemned "laxity" in the church and ordered a revision of casuistical texts.Lycée Blaise Pascal
Lycée Blaise Pascal or Lycée Français Blaise Pascal (LFBP) may refer to:
Lycée Français Blaise Pascal Abidjan - Abidjan, Ivory Coast
Lycée Blaise Pascal de Libreville - Libreville, Gabon
The high school division of the École Pascal (FR) in Paris
Lycée Blaise-Pascal (Orsay)
Lycée Blaise-Pascal (Charbonnières-les-Bains)
Lycée Blaise-Pascal (Châteauroux)
Lycée Blaise-Pascal (FR) (Clermont-Ferrand)
Lycée Blaise-Pascal (Colmar)
Lycée Blaise-Pascal (Brie-Comte-Robert)
Lycée Blaise-Pascal (Rouen)
Lycée Blaise-Pascal (Longuenesse)Lycée Blaise Pascal de Libreville
Lycée Blaise Pascal de Libreville is a French international school in Libreville, Gabon. It includes collège (junior high school) and lycée (senior high school) levels.The school is named after the 17th-century French scholar Blaise Pascal.Lycée Français Blaise Pascal Abidjan
Lycée Français Blaise Pascal (LFBP) is a French international school in Abidjan, Ivory Coast. It includes the Ecole Jacques Prévert, the collège-lycée (junior and senior high school) and a scientific post-secondary preparatory school for French Grandes Écoles.Pascal's calculator
Pascal's calculator (also known as the arithmetic machine or Pascaline) is a mechanical calculator invented by Blaise Pascal in the early 17th century. Pascal was led to develop a calculator by the laborious arithmetical calculations required by his father's work as supervisor of taxes in Rouen. He designed the machine to add and subtract two numbers directly and to perform multiplication and division through repeated addition or subtraction.
Pascal's calculator was especially successful in the design of its carry mechanism, which adds 1 to 9 on one dial, and when it changes from 9 to 0, carries 1 to the next dial. His innovation made each digit independent of the state of the others, which enabled multiple carries to rapidly cascade from one digit to another regardless of the machine's capacity. Pascal was also the first to shrink and adapt for his purpose a lantern gear, used in turret clocks and water wheels, which could resist the strength of any operator input with very little added friction.
Pascal designed the machine in 1642, and after 50 prototypes, he presented it to the public in 1645, dedicating it to Pierre Séguier, then chancellor of France. Pascal built around twenty more machines during the next decade, many of which improved on his original design. In 1649, King Louis XIV of France gave Pascal a royal privilege (similar to a patent), which gave him the exclusive right to design and manufacture calculating machines in France. Nine Pascal calculators presently exist; most are on display in European museums.
Many later calculators either were directly inspired by, or shaped by the same historical influences which led to, Pascal's invention. Gottfried Leibniz invented his Leibniz wheels after 1671, after trying to add an automatic multiplication feature to the Pascaline. In 1820, Thomas de Colmar designed his arithmometer, the first mechanical calculator strong enough and reliable enough to be used daily in an office environment. It is not clear whether he ever saw Leibniz's device, but he either re-invented it or utilised Leibniz's invention of the step drum.Pascal's law
Pascal's law (also Pascal's principle or the principle of transmission of fluid-pressure) is a principle in fluid mechanics that states that pressure at a point has infinite direction, and thus a pressure change at any point in a confined incompressible fluid is transmitted throughout the fluid such that the same change occurs everywhere. The law was established by French mathematician Blaise Pascal in 1647–48.Pascal's theorem
In projective geometry, Pascal's theorem (also known as the hexagrammum mysticum theorem) states that if six arbitrary points are chosen on a conic (which may be an ellipse, parabola or hyperbola in an appropriate affine plane) and joined by line segments in any order to form a hexagon, then the three pairs of opposite sides of the hexagon (extended if necessary) meet at three points which lie on a straight line, called the Pascal line of the hexagon. It is named after Blaise Pascal.
The theorem is also valid in the Euclidean plane, but the statement needs to be adjusted to deal with the special cases when opposite sides are parallel.Pascal's wager
Pascal's wager is an argument in philosophy presented by the seventeenth-century French philosopher, mathematician and physicist, Blaise Pascal (1623–1662). It posits that humans bet with their lives that God either exists or does not.
Pascal argues that a rational person should live as though God exists and seek to believe in God. If God does not actually exist, such a person will have only a finite loss (some pleasures, luxury, etc.), whereas he stands to receive infinite gains (as represented by eternity in Heaven) and avoid infinite losses (eternity in Hell).Pascal's Wager was based on the idea of the Christian God, though similar arguments have occurred in other religious traditions. The original wager was set out in section 233 of Pascal's posthumously published Pensées ("Thoughts"). These previously unpublished notes were assembled to form an incomplete treatise on Christian apologetics.
Historically, Pascal's wager was groundbreaking because it charted new territory in probability theory, marked the first formal use of decision theory, and anticipated future philosophies such as existentialism, pragmatism and voluntarism.Pascal (unit)
The pascal (symbol: Pa) is the SI derived unit of pressure used to quantify internal pressure, stress, Young's modulus and ultimate tensile strength. It is defined as one newton per square metre. It is named after the French polymath Blaise Pascal.
Common multiple units of the pascal are the hectopascal (1 hPa = 100 Pa) which is equal to one millibar, and the kilopascal (1 kPa = 1000 Pa) which is equal to one centibar.
The unit of measurement called standard atmosphere (atm) is defined as 101325 Pa. Meteorological reports in the United States typically state atmospheric pressure in millibars. In Canada these reports are given in kilopascals.Pensées
The Pensées ("Thoughts") is a collection of fragments on theology and philosophy written by 17th-century philosopher and mathematician Blaise Pascal. Pascal's religious conversion led him into a life of asceticism, and the Pensées was in many ways his life's work. The Pensées represented Pascal's defense of the Christian religion. The concept of "Pascal's Wager" stems from a portion of this work.University of Clermont Auvergne
University Clermont Auvergne (French: Université Clermont Auvergne) is a public university with its main campus in Clermont-Ferrand, France. It was created with the merger of Blaise Pascal University and the University of Auvergne on 1 January 2017.
The Université Clermont Auvergne comprises 22 components, divided into Training and Research Units (UFR, formerly faculties), Schools and Institutes (IUT).Étienne Pascal
Étienne Pascal (Clermont, 2 May 1588 – Paris, 24 September 1651) was a French chief tax officer and the father of Blaise Pascal.
Scientists whose names are used as units
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