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Blaise Pascal

Blaise Pascal (, ,  ;     ; 19 June 1623 – 19 August 1662) was a French mathematician, physicist, inventor, philosopher, and Catholic writer.

Pascal was a child prodigy who was educated by his father, a tax collector in Rouen. His earliest mathematical work was on projective geometry; he wrote a significant treatise on the subject of conic sections at the age of 16. He later corresponded with Pierre de Fermat on probability theory, strongly influencing the development of modern economics and social science. In 1642, he started some pioneering work on calculating machines (called Pascal's calculators and later Pascalines), establishing him as one of the first two inventors of the mechanical calculator.

Like his contemporary René Descartes, Pascal was also a pioneer in the natural and applied sciences. Pascal wrote in defense of the scientific method and produced several controversial results. He made important contributions to the study of fluids, and clarified the concepts of pressure and vacuum by generalising the work of Evangelista Torricelli. Following Torricelli and Galileo Galilei, he rebutted the likes of Aristotle and Descartes who insisted that nature abhors a vacuum in 1647.

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. The latter contains Pascal's wager, known in the original as the Discourse on the Machine, a fideistic probabilistic argument for God's existence. 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.

Early life and education

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, also an amateur mathematician, was a local judge and member of the "Noblesse de Robe". Pascal had two sisters, the younger Jacqueline and the elder Gilberte.

Move to Paris
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 a key member of the family. Étienne, who never remarried, decided that he alone would educate his children.

The young Pascal showed an extraordinary intellectual ability, with an amazing aptitude for mathematics and science. Etienne had tried to keep his son from learning mathematics; but by the age of 12, Pascal had rediscovered, on his own, using charcoal on a tile floor, Euclid’s first thirty-two geometric propositions, and was thus given a copy of Euclid's Elements.

Essay on Conics
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 René 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."

Leaving Paris
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 Cardinal 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 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.

Pascaline
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. He built 20 finished machines over the following 10 years.

Probability
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, 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 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.

Treatise on the Arithmetical Triangle
Pascal's Traité du triangle arithmétique, written in 1654 but published posthumously in 1665, described a convenient tabular presentation for binomial coefficients which he called the arithmetical triangle, but is now called Pascal's triangle. The triangle can also be represented: He defined 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 concluded with the proof,
 * $$t_{mn} = \frac{(m+n)(m+n-1)\cdots(m+1)}{n(n-1)\cdots 1}.$$

In the same treatise, Pascal gave an explicit statement of the principle of mathematical induction. 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.

That same year, Pascal had a religious experience, and mostly gave up work in mathematics.

Cycloid
In 1658, Pascal, while suffering from a toothache, began considering several problems concerning the cycloid. His toothache disappeared, and he took this as a heavenly sign to proceed 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.

Physics

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 SI unit of pressure and 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.

Fluid dynamics
His work in the fields 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.

Vacuum
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 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.

First atmospheric pressure vs. altitude experiment
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, 4790 ft 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 $3 1/2$ 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. He found with both experiments that an ascent of 7 fathoms lowers the mercury by half a line. Note: Pascal used pouce and ligne for "inch" and "line", and toise for "fathom".

In a reply to Étienne Noël, who believed in the plenum, 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 follow from it; instead, if it leads to something contrary to a single one of the phenomena, that suffices to establish its falsity."

Blaise Pascal Chairs are given to outstanding international scientists to conduct their research in the Ile de France region.

Religious conversion
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 let anyone other than these men attend him...It was a good choice, for the old man survived and was able to walk again..." However 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.

Memorial
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 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.

Literature
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 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 midst 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.

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 follow 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."

Philosophy
Pascal is arguably best known as a philosopher, considered by some the second greatest French mind behind 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.

In terms of God, Descartes and Pascal disagreed. Pascal wrote that "I cannot forgive Descartes. In all his philosophy he would have been quite willing to dispense with God, but he couldn't avoid letting him put the world in motion; afterwards he didn't need God anymore". He opposed the rationalism of people like Descartes as applied to the existence of a God, preferring faith as "reason can decide nothing here". For Pascal the nature of God was such that such proofs cannot reveal God. Humans "are in darkness and estranged from God" because "he has hidden Himself from their knowledge".

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".

Philosophy of 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 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 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.

Pensées
"Man is only a reed, the weakest in nature, but he is a thinking reed."
 * Blaise Pascal, Pensées No. 200

Pascal's most influential theological work, referred to posthumously as the Pensées ("Thoughts") 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".

The Pensées 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 Pyrrhonism 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.

Last works and death

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. Pascal also designated the operation principles which were later used to plan public transportation: The carriages had a fixed route, fixed price, and left even if there were no passengers. It is widely considered that the idea of public transportation was well ahead of time. The lines were not commercially successful, and the last one closed by 1675.

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 affected Pascal are generally attributed to his brain lesion.

Legacy

One of the Universities of Clermont-Ferrand, France – Université Blaise Pascal – is named after him. Établissement scolaire français Blaise-Pascal in Lubumbashi, Democratic Republic of the Congo is named after Pascal.

The 1969 Eric Rohmer film My Night at Maud's is based on the work of Pascal. 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 chameleon in the film Tangled is named for Pascal.

A programming language is named for Pascal. In 2014, Nvidia announced its new Pascal microarchitecture, which is named for Pascal. The first graphics cards featuring Pascal were released in 2016.

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 are at war with and acts as a parental figure for other machines trying to adapt to their newly-found individuality.

The otter in the Animal Crossing series is named for Pascal.

Minor planet 4500 Pascal is named in his honor.

Pope Paul VI, in encyclical Populorum progressio, issued in 1967, quotes Pascal's Pensées: "True humanism points the way toward God and acknowledges the task to which we are called, the task which offers us the real meaning of human life. Man is not the ultimate measure of man. Man becomes truly man only by passing beyond himself. In the words of Pascal: 'Man infinitely surpasses man."

In 2023, Pope Francis released an apostolic letter, Sublimitas et miseria hominis, dedicated to Blaise Pascal, in commemoration of the fourth centenary of his birth.

Works

 * "Essai pour les coniques" [Essay on conics] (1639)
 * Experiences nouvelles touchant le vide [New experiments with the vacuum] (1647)
 * Récit de la grande expérience de l'équilibre des liqueurs [Account of the great experiment on equilibrium in liquids] (1648)
 * Traité du triangle arithmétique [Treatise on the arithmetical triangle] (written c. 1654; publ. 1665)
 * Lettres provinciales [The provincial letters] (1656–57)
 * De l'Esprit géométrique [On the geometrical spirit] (1657 or 1658)
 * Écrit sur la signature du formulaire (1661)
 * Pensées [Thoughts] (incomplete at death; publ. 1670)
 * "Discourse on the Passion of Love"
 * "On the Conversion of the Sinner"

title: Blaise Pascal


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Brittonic languages

The Brittonic languages (also Brythonic or British Celtic; ieithoedd Brythonaidd/Prydeinig; yethow brythonek/predennek; and yezhoù predenek) form one of the two branches of the Insular Celtic language family; the other is Goidelic. It comprises the extant languages Breton, Cornish, and Welsh. The name Brythonic was derived by Welsh Celticist John Rhys from the Welsh word Brython, meaning Ancient Britons as opposed to an Anglo-Saxon or Gael.

The Brittonic languages derive from the Common Brittonic language, spoken throughout Great Britain during the Iron Age and Roman period. In the 5th and 6th centuries emigrating Britons also took Brittonic speech to the continent, most significantly in Brittany and Britonia. During the next few centuries, in much of Britain the language was replaced by Old English and Scottish Gaelic, with the remaining Common Brittonic language splitting into regional dialects, eventually evolving into Welsh, Cornish, Breton, Cumbric, and probably Pictish. Welsh and Breton continue to be spoken as native languages, while a revival in Cornish has led to an increase in speakers of that language. Cumbric and Pictish are extinct, having been replaced by Goidelic and Anglic speech. The Isle of Man and Orkney may also have originally spoken a Brittonic language, but this was later supplanted by Goidelic on the Isle of Man and Norse on Orkney. There is also a community of Brittonic language speakers in Y Wladfa (the Welsh settlement in Patagonia).

Name
The names "Brittonic" and "Brythonic" are scholarly conventions referring to the Celtic languages of Britain and to the ancestral language they originated from, designated Common Brittonic, in contrast to the Goidelic languages originating in Ireland. Both were created in the 19th century to avoid the ambiguity of earlier terms such as "British" and "Cymric". "Brythonic" was coined in 1879 by the Celticist John Rhys from the Welsh word Brython. "Brittonic", derived from "Briton" and also earlier spelled "Britonic" and "Britonnic", emerged later in the 19th century. "Brittonic" became more prominent through the 20th century, and was used in Kenneth H. Jackson's highly influential 1953 work on the topic, Language and History in Early Britain. Jackson noted by that time that "Brythonic" had become a dated term: "of late there has been an increasing tendency to use Brittonic instead." Today, "Brittonic" often replaces "Brythonic" in the literature. Rudolf Thurneysen used "Britannic" in his influential A Grammar of Old Irish, although this never became popular among subsequent scholars.

Comparable historical terms include the Medieval Latin lingua Britannica and sermo Britannicus and the Welsh Brythoneg. Some writers use "British" for the language and its descendants, although, due to the risk of confusion, others avoid it or use it only in a restricted sense. Jackson, and later John T. Koch, use "British" only for the early phase of the Common Brittonic language.

Before Jackson's work, "Brittonic" and "Brythonic" were often used for all the P-Celtic languages, including not just the varieties in Britain but those Continental Celtic languages that similarly experienced the evolution of the Proto-Celtic language element to. However, subsequent writers have tended to follow Jackson's scheme, rendering this use obsolete.

The name "Britain" itself comes from Britannia~Brittania, via Old French Bretaigne and Middle English Breteyne, possibly influenced by Old English Bryten[lond], probably also from Latin Brittania, ultimately an adaptation of the native word for the island, Pritanī.

An early written reference to the British Isles may derive from the works of the Greek explorer Pytheas of Massalia; later Greek writers such as Diodorus of Sicily and Strabo who quote Pytheas' use of variants such as πρεττανική (Prettanikē), "The Britannic [land, island]", and νησοι βρεττανιαι (nēsoi brettaniai), "Britannic islands", with Pretani being a Celtic word that might mean 'painted ones' or 'tattooed folk', referring to body decoration.

Evidence
Knowledge of the Brittonic languages comes from a variety of sources. The early language's information is obtained from coins, inscriptions, and comments by classical writers as well as place names and personal names recorded by them. For later languages, there is information from medieval writers and modern native speakers, together with place names. The names recorded in the Roman period are given in Rivet and Smith.

Characteristics
The Brittonic branch is also referred to as P-Celtic because linguistic reconstruction of the Brittonic reflex of the Proto-Indo-European phoneme * is p as opposed to Goidelic k. Such nomenclature usually implies acceptance of the P-Celtic and Q-Celtic hypothesis rather than the Insular Celtic hypothesis because the term includes certain Continental Celtic languages as well. (For a discussion, see Celtic languages.)

Other major characteristics include: Initial s-: Lenition: Voiceless spirants: Nasal assimilation:
 * The retention of the Proto-Celtic sequences am and an, which mostly result from the Proto-Indo-European syllabic nasals.
 * Celtic (written u in Latin texts and ou in Greek) became gw- in initial position, -w- internally, whereas in Gaelic it is f- in initial position and disappears internally:
 * Proto-Celtic windos 'white, fair' became Welsh gwyn (masculine), gwen (feminine), Cornish gwynn, Breton gwenn. Contrast Irish fionn 'fair'.
 * Proto-Celtic wassos 'servant, young man' became Welsh, Cornish, and Breton gwas. Contrast Middle Irish foss.
 * Initial s- followed by a vowel was changed to h-:
 * Welsh hen 'old', hir 'long', hafal 'similar'
 * Cornish hen 'ancient', hir 'long', haval 'similar'
 * Breton hen 'ancient', hir 'long', hañval 'similar'
 * Contrast Irish sean 'old', síor 'long', samhail 'similarity'
 * Initial s- was lost before, and :
 * slemon became Welsh llyfn, Cornish leven and Breton levn 'smooth'. Contrast Irish sleamhain 'smooth, slimy'
 * smeru became Welsh mêr, Cornish mer, and Breton mel 'marrow'. Contrast Irish sméar
 * The initial clusters sp-, sr-, sw- became f-, fr-, chw-:
 * sɸera became Welsh ffêr 'ankle', Cornish fer 'shank, lower leg' and Breton fer 'ankle'. Contrast Old Irish seir 'heel, ankle'
 * srogna 'nostril' became Welsh ffroen, Cornish frig and Breton froen. Contrast Irish srón
 * swīs 'you' (plural) became Welsh chwi, Cornish hwy and Breton c'hwi. Contrast Old Irish síi
 * Voiceless plosives become voiced plosives in intervocalic position.
 * d, g , b
 * Contrast Irish th, ch, ph
 * Voiced plosives,  (later  or , then lost in Welsh and Cornish; remained as  in Breton), , and  became soft spirants in an intervocalic position and before liquids:
 * Welsh dd, f
 * Cornish dh, v
 * Breton z, c'h , v
 * Contrast Irish dh, gh, bh, mh
 * Geminated voiceless plosives transformed into spirants; (pp),  (cc),  (tt) became  (later ),  (ch/c'h),  (th/zh) before a vowel or liquid:
 * cippus > Breton kef, Cornish kyf, Welsh cyff, 'tree trunk'
 * cattos > Breton kazh, Cornish kath, Welsh cath, 'cat' vs. Irish cat
 * bucca > Breton boc'h, Cornish bogh, Welsh boch, 'cheek'
 * Voiceless stops become spirants after liquids:
 * artos 'bear' > Welsh/Cornish arth, Breton arzh, compare Old Irish art
 * Voiced stops were assimilated to a preceding nasal:
 * Brittonic retains original nasals before -t and -k, whereas Goidelic alters -nt to -d, and -nk to -g:
 * Breton kant 'hundred' vs. Irish céad; Breton Ankou '[personification of] Death', Irish éag 'die'

Classification
The family tree of the Brittonic languages is as follows:

 * Common Brittonic
 * Western Brittonic
 * Cumbric
 * Welsh
 * Southwestern Brittonic
 * Cornish
 * Breton

Brittonic languages in use today are Welsh, Cornish and Breton. Welsh and Breton have been spoken continuously since they formed. For all practical purposes Cornish died out during the 18th or 19th century, but a revival movement has more recently created small numbers of new speakers. Also notable are the extinct language Cumbric, and possibly the extinct Pictish. One view, advanced in the 1950s and based on apparently unintelligible ogham inscriptions, was that the Picts may have also used a non-Indo-European language. This view, while attracting broad popular appeal, has virtually no following in contemporary linguistic scholarship.

History and origins
The modern Brittonic languages are generally considered to all derive from a common ancestral language termed Brittonic, British, Common Brittonic, Old Brittonic or Proto-Brittonic, which is thought to have developed from Proto-Celtic or early Insular Celtic by the 6th century BC.

A major archaeogenetics study uncovered a migration into southern Britain in the middle to late Bronze Age, during the 500-year period 1,300–800 BC. The newcomers were genetically most similar to ancient individuals from Gaul. During 1,000–875 BC, their genetic markers swiftly spread through southern Britain, but not northern Britain. The authors describe this as a "plausible vector for the spread of early Celtic languages into Britain". There was much less inward migration during the Iron Age, so it is likely that Celtic reached Britain before then. Barry Cunliffe suggests that a Goidelic branch of Celtic may already have been spoken in Britain, but that this middle Bronze Age migration would have introduced the Brittonic branch.

Brittonic languages were probably spoken before the Roman invasion throughout most of Great Britain, though the Isle of Man later had a Goidelic language, Manx. During the period of the Roman occupation of what is now England and Wales (AD 43 to c. 410), Common Brittonic borrowed a large stock of Latin words, both for concepts unfamiliar in the pre-urban society of Celtic Britain such as urbanization and new tactics of warfare, as well as for rather more mundane words which displaced native terms (most notably, the word for 'fish' in all the Brittonic languages derives from the Latin piscis rather than the native ēskos – which may survive, however, in the Welsh name of the River Usk, Wysg). Approximately 800 of these Latin loan-words have survived in the three modern Brittonic languages. Pictish may have resisted Latin influence to a greater extent than the other Brittonic languages.

It is probable that at the start of the Post-Roman period, Common Brittonic was differentiated into at least two major dialect groups – Southwestern and Western. (Additional dialects have also been posited, but have left little or no evidence, such as an Eastern Brittonic spoken in what is now the East of England.) Between the end of the Roman occupation and the mid-6th century, the two dialects began to diverge into recognizably separate varieties, the Western into Cumbric and Welsh, and the Southwestern into Cornish and its closely related sister language Breton, which was carried to continental Armorica. Jackson showed that a few of the dialect distinctions between West and Southwest Brittonic go back a long way. New divergencies began around AD 500 but other changes that were shared occurred in the 6th century. Other common changes occurred in the 7th century onward and are possibly due to inherent tendencies. Thus the concept of a Common Brittonic language ends by AD 600. Substantial numbers of Britons certainly remained in the expanding area controlled by Anglo-Saxons, but over the fifth and sixth centuries they mostly adopted the Old English language and culture.

Decline
The Brittonic languages spoken in what are now Scotland, the Isle of Man, and England began to be displaced in the 5th century through the settlement of Irish-speaking Gaels and Germanic peoples. Henry of Huntingdon wrote c. 1129 that Pictish was "no longer spoken".

The displacement of the languages of Brittonic descent was probably complete in all of Britain except Cornwall, Wales, and the English counties bordering these areas such as Devon, by the 11th century. Western Herefordshire continued to speak Welsh until the late nineteenth century, and isolated pockets of Shropshire speak Welsh today.

Sound changes
The regular consonantal sound changes from Proto-Celtic to Welsh, Cornish, and Breton are summarised in the following table. Where the graphemes have a different value from the corresponding IPA symbols, the IPA equivalent is indicated between slashes. V represents a vowel; C represents a consonant.

Place names and river names
The principal legacy left behind in those territories from which the Brittonic languages were displaced is that of toponyms (place names) and hydronyms (names of rivers and other bodies of water). There are many Brittonic place names in lowland Scotland and in the parts of England where it is agreed that substantial Brittonic speakers remained (Brittonic names, apart from those of the former Romano-British towns, are scarce over most of England). Names derived (sometimes indirectly) from Brittonic include London, Penicuik, Perth, Aberdeen, York, Dorchester, Dover, and Colchester. Brittonic elements found in England include bre- and bal- for 'hill', while some such as co[o]mb[e] (from cwm) for 'small deep valley' and tor for 'hill, rocky headland' are examples of Brittonic words that were borrowed into English. Others reflect the presence of Britons such as Dumbarton – from the Scottish Gaelic Dùn Breatainn meaning 'Fort of the Britons', and Walton meaning (in Anglo-Saxon) a tun 'settlement' where the Wealh 'Britons' still lived.

The number of Celtic river names in England generally increases from east to west, a map showing these being given by Jackson. These include Avon, Chew, Frome, Axe, Brue and Exe, but also river names containing the elements der-/dar-/dur- and -went e.g. Derwent, Darwen, Deer, Adur, Dour, Darent, and Went. These names exhibit multiple different Celtic roots. One is *dubri- 'water' (Breton dour, Cumbric dowr, Welsh dŵr), also found in the place-name Dover (attested in the Roman period as Dubrīs); this is the source of rivers named Dour. Another is deru̯o- 'oak' or 'true' (Bret. derv, Cumb. derow, W. derw), coupled with two agent suffixes, -ent and -iū; this is the origin of Derwent, Darent, and Darwen (attested in the Roman period as Deru̯entiō). The final root to be examined is went/uent. In Roman Britain, there were three tribal capitals named U̯entā (modern Winchester, Caerwent, and Caistor St Edmunds), whose meaning was 'place, town'.

Brittonicisms in English
Some, including J. R. R. Tolkien, have argued that Celtic has acted as a substrate to English for both the lexicon and syntax. It is generally accepted that Brittonic effects on English are lexically few, aside from toponyms, consisting of a small number of domestic and geographical words, which "may" include bin, brock, carr, comb, crag and tor. Another legacy may be the sheep-counting system yan tan tethera in the north, in the traditionally Celtic areas of England such as Cumbria. Several words of Cornish origin are still in use in English as mining-related terms, including costean, gunnies, and vug.

Those who argue against the theory of a more significant Brittonic influence than is widely accepted point out that many toponyms have no semantic continuation from the Brittonic language. A notable example is Avon which comes from the Celtic term for river abona or the Welsh term for river, afon, but was used by the English as a personal name. Likewise the River Ouse, Yorkshire, contains the Celtic word usa which merely means 'water' and the name of the river Trent simply comes from the Welsh word for a 'trespasser' (figuratively suggesting 'overflowing river').

Scholars supporting a Brittonic substrate in English argue that the use of periphrastic constructions (using auxiliary verbs such as do and be in the continuous/progressive) of the English verb, which is more widespread than in the other Germanic languages, is traceable to Brittonic influence. Others, however, find this unlikely since many of these forms are only attested in the later Middle English period; these scholars claim a native English development rather than Celtic influence. Ian G. Roberts postulates Northern Germanic influence, despite such constructions not existing in Norse. Literary Welsh has the simple present Caraf = 'I love' and the present stative (al. continuous/progressive) Yr wyf yn caru = 'I am loving', where the Brittonic syntax is partly mirrored in English. (However, English I am loving comes from older I am a-loving, from still older ich am on luvende 'I am in the process of loving'). In the Germanic sister languages of English, there is only one form, for example Ich liebe in German, though in colloquial usage in some German dialects, a progressive aspect form has evolved which is formally similar to those found in Celtic languages, and somewhat less similar to the Modern English form, e.g. 'I am working' is Ich bin am Arbeiten, literally: 'I am on the working'. The same structure is also found in modern Dutch (Ik ben aan het werk), alongside other structures (e.g. Ik zit te werken, lit. 'I sit to working'). These parallel developments suggest that the English progressive is not necessarily due to Celtic influence; moreover, the native English development of the structure can be traced over 1000 years and more of English literature.

Some researchers (Filppula, et al., 2001) argue that other elements of English syntax reflect Brittonic influences. For instance, in English tag questions, the form of the tag depends on the verb form in the main statement (aren't I?, isn't he?, won't we?, etc.). The German nicht wahr? and the French n'est-ce pas?, by contrast, are fixed forms which can be used with almost any main statement. It has been claimed that the English system has been borrowed from Brittonic, since Welsh tag questions vary in almost exactly the same way.

Brittonic effect on the Goidelic languages
Far more notable, but less well known, are Brittonic influences on Scottish Gaelic, though Scottish and Irish Gaelic, with their wider range of preposition-based periphrastic constructions, suggest that such constructions descend from their common Celtic heritage. Scottish Gaelic contains several P-Celtic loanwords, but, as there is a far greater overlap in terms of Celtic vocabulary than with English, it is not always possible to disentangle P- and Q-Celtic words. However, some common words such as monadh = Welsh mynydd, Cumbric monidh are particularly evident.

The Brittonic influence on Scots Gaelic is often indicated by considering Irish language usage, which is not likely to have been influenced so much by Brittonic. In particular, the word srath (anglicised as "strath") is a native Goidelic word, but its usage appears to have been modified by the Welsh cognate ystrad whose meaning is slightly different. The effect on Irish has been the loan from British of many Latin-derived words. This has been associated with the Christianisation of Ireland from Britain.

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title: Brittonic languages