Life
Pascal was born in Clermont-Ferrand, which is in France's Auvergne region, by the Massif Central. He lost his mother, Antoinette Begon, at the age of three. His father, Étienne Pascal 1588–1651, who also had an interest in science and mathematics, was a local judge and detail 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 breed soon hired Louise Delfault, a maid who eventually became an instrumental detail of the family. Étienne, who never remarried, decided that he alone would educate his children, for they all showed extraordinary intellectual ability, especially his son Blaise. The young Pascal showed an amazing aptitude for mathematics and science.
Particularly of interest to Pascal was a have of Pascal's theorem. It states that whether a hexagon is inscribed in a circle or conic then the three intersection points of opposite sides lie on a race called the Pascal line.
Pascal's work was so precocious that René Descartes wasthat Pascal's father had total 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 things related to this refers 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 aspresident of the Thirty Years' War, defaulted on the government's bonds. Suddenly Étienne Pascal's worth had dropped from almost 66,000 livres to less than 7,300.
Like so numerous others, Étienne was eventually forced to glide 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 near glittering and intellectual salons in any France. It was only when Jacqueline performed living in a children's play with Richelieu in attendance that Étienne was pardoned. In time, Étienne was back in advantage 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 attempt 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 so-called 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 coding 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 ownership 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 improve to his structure through the next decade, and he refers to some 50 machines that were built to his design. He built 20 finished machines over the following 10 years.
Pascal's development of probability theory was his most influential contribution to mathematics. Originally applied to gambling, today it is for extremely important in economics, especially in actuarial science. John Ross writes, "Probability concepts 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, Pascal and Fermat, though doing important early work in probability theory, did not instituting 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 put Abraham de Moivre and Pierre-Simon Laplace.
In 1654, prompted by his friend the 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.
Pascal's Traité du triangle arithmétique, written in 1654 but published posthumously in 1665, described a convenient tabular presentation for Pascal's triangle. The triangle can also be represented:
He defined the numbers in the triangle by recursion: Call the number in the m + 1th row and n + 1th column tmn. Then tmn = tm–1,n + tm,n–1, for m = 0, 1, 2, ... and n = 0, 1, 2, ... The boundary conditions are tm,−1 = 0, t−1,n = 0 for m = 1, 2, 3, ... and n = 1, 2, 3, ... The generator t00 = 1. Pascal concluded with the proof,
In the same treatise, Pascal gave an explicit statement of the principle of relating the sums of the p-th powers of the first n positive integers for p = 0, 1, 2, ..., k.
That same year, Pascal had a religious experience, and mostly gave up work in mathematics.
In 1658, Pascal, while suffering from a toothache, began considering several problems concerning the cycloid. His toothache disappeared, and he took this as a heavenlyto stay on with his research. Eight days later he had completed his essay and, to publicize the results, proposed a contest.[]
Pascal proposed three questions relating to the center of gravity, area and volume of the cycloid, with the winner or winners to receive prizes of 20 and 40 Spanish doubloons. Pascal, Gilles de Roberval and Pierre de Carcavi were the judges, and neither of the two submissions by John Wallis and Antoine de Lalouvère were judged to be adequate. While the contest was ongoing, Christopher Wren sent Pascal a proposal for a proof of the rectification of the cycloid; Roberval claimed promptly that he had known of the proof for years. Wallis published Wren's proof crediting Wren in Wallis's Tractus Duo, giving Wren priority for the first published proof.
Pascal contributed to several fields in physics, most notably the fields of fluid mechanics and pressure. In honour of his scientific contributions, the name Pascal has been given to the Pascal's law an important principle of hydrostatics. He introduced a primitive form of roulette and the roulette wheel in his search for a perpetual motion machine.
His work in the fields of 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 including Descartes believed in a plenum, i. e. some invisible matter filled all of space, rather than a vacuum. "Nature abhors a vacuum." This was based on the Aristotelian notion that everything in motion was a substance, moved by another substance. Furthermore, light passed through the glass tube, suggesting a substance such as aether rather than vacuum filled the space.
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 measure 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 Florin Périer, husband of Pascal's elder sister Gilberte, was finally able such as lawyers and surveyors 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 afford 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 +1⁄2 layout above the quicksilver in the vessel...I repeated the experiment two more times while standing in the same spot...[they] produced the same result used to refer to every one of two or more people or matters 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 restyle should arise through the day...Taking the other tube and a portion of the quick silver...I walked to the top of Puy-de-Dôme, approximately 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 regarded and identified separately. 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 ato the plenist Estienne Noel, Pascal wrote, echoing contemporary notions of science and falsifiability: "In order to show that a hypothesis is evident, it does not suffice that all the phenomena undertake from it; instead, if it leads to something contrary to a single one of the phenomena, that suffices to setting its falsity."
Blaise Pascal Chairs are assumption to outstanding international scientists to come on their research in the Ile de France region.
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, Deslandes and de la Bouteillerie. The elder Pascal "would not allow anyone other than these men attend him...It was a utility choice, for the old man survived and was fine to walk again..." But treatment and rehabilitation took three months, during which time La Bouteillerie and Deslandes had becomevisitors.
Both men were followers of Jean Guillebert, proponent of a splinter business from Catholic teaching known as Jansenism. This still fairly small sect was creating 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 working 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 conform 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 component 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 the 23 of November, 1654, between 10:30 and 12:30 at night, Pascal had an intense religious experience and immediately wrote 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 written 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 a 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.
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.
Beginning in 1656–57, Pascal published his memorable attack on casuistry, a popular ethical method used by Catholic thinkers in the early innovative 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 toa 1656 papal bull condemning the teachings of Jansen as heretical. Theletter 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.
It is in the Provincial Letters that Pascal made his oft-quoted apology for writing a long letter, as he had not had time to write a shorter one.
From Letter XVI, as translated by Thomas M'Crie:
'Reverend fathers, my letters were not wont either to be so prolix, or to adopt so closely on
one another. Want of time must plead my excuse for both of these faults. The present letter is
a very long one, simply because I had no leisure to make it shorter.'
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 is arguably best known as a philosopher, considered by some thegreatest French mind gradual René Descartes. He was a dualist following Descartes. However, he is also remembered for his opposition to both the rationalism of the likes of Descartes and simultaneous opposition to the main countervailing epistemology, empiricism, preferring fideism.
He cared above all about the philosophy of religion. Pascalian theology has grown out of his perspective that humans 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".
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 écoles de Port-Royal "Little Schools of Port-Royal". The work was unpublished until over a century after his death. Here, Pascal looked into the effect of discovering truths, arguing that the ideal of such a method would be to found all propositions on already established truths. At the same ime, 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, withprinciples assumed and other propositions developed from them. Nevertheless, there was no way to know the assumed principles to be true.