Blaise Pascal

Blaise Pascal (June 19, 1623 – August 19, 1662) was a French mathematician, physicist, and religious philosopher. Pascal's important contributions to the natural and applied sciences include the construction of mechanical calculators, the study of fluids, and clarification of concepts such as pressure and vacuum. Pascal also did groundwork in projective geometry and in probability theory, which has had major ramifications in economics and the social sciences.

Most of these contributions were made early in his life, as following a mystical experience in 1654, he fell away from mathematics and physics and devoted himself to reflection and writing about philosophy and theology. This period was characterized by the composition of his two most famous works, the Lettres provinciales and the Pensées. Pascal suffered from ill-health throughout his life and died two months after his 39th birthday.

Family and early life

Born in Clermont, in the Auvergne region of France, Blaise Pascal lost his mother, Antoinette Begon, at the age of three. His father, Étienne Pascal (1588 – 1651), was a local judge and member of the petit noblesse, who also had an interest in science and mathematics. Blaise Pascal was the brother of Jacqueline Pascal and two other sisters, only one of whom, Gilberte, survived past childhood.

In 1631, Étienne moved with his children to Paris. Étienne decided that he himself would educate his son, who showed extraordinary mental and intellectual abilities. Initially, Étienne declared that his son would not study mathematics until the age of fifteen, so that he could focus on the study of Latin and Greek without distraction. At the age of twelve, however, Blaise Pascal discovered independently Euclid's proposition that the sum of the angles of a triangle is equal to two right angles. In response to this, his father granted him a copy of Euclid's Elements.

In 1638, Étienne's opposition to fiscal relations of Cardinal Richelieu caused the family to flee Paris. It was only when Jacqueline performed well in a children's play performed in front of Richelieu that Étienne was pardoned. By 1639, the family had moved to Rouen where Étienne became a tax collector.

At age eighteen Pascal constructed a mechanical calculator, called Pascal's calculator or the Pascaline, capable of addition and subtraction to help his father with this work (the Zwinger museum, in Dresden, Germany, exhibits one of his original mechanical calculators). The calculator failed to be a great commercial success, though Pascal continued to make improvements to his design through the next decade and built a total of fifty machines.

Contributions to mathematics

When Pascal was just fourteen, a group of Paris's leading geometricians, including Roberval, Mersenne, Desargues, and Mydorge, admitted him to their weekly meetings, which Pascal's father already attended. Particularly of interest to Pascal was the work of Desargues. Following in the footsteps of some of Desargues's thinking, at age sixteen Pascal produced a treatise on conic sections, Essai pour les coniques ("Essay on Conics"), which included an important original result described by Pascal as the "mystic hexagon" and now known as Pascal's theorem.

In 1653 Pascal wrote his Traité du triangle arithmétique in which he described a convenient tabular presentation for binomial coefficients, the "arithmetical triangle", now called Pascal's triangle. It should be noted, however, that Yang Hui, a Chinese mathematician in the Qin dynasty, had worked out a concept similar to Pascal's triangle four centuries earlier.

In 1654, prompted by a friend interested in gambling problems, he corresponded with Fermat on the subject, and from that collaboration was born the mathematical theory of probabilities. The friend was the Chevalier de Méré, and the specific problem was that of two players who want to finish a game early and, given the current circumstances of the game, want to divide the stakes fairly, based on the chance each has of winning the game from that point. 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's formulation of the infinitesimal calculus.

After a religious experience in 1654, Pascal mostly gave up work in mathematics. However, one sleepless night in 1658 produced a significant inquiry into the properties of the cycloid.

Philosophy of mathematics

Pascal's major contribution to the philosophy of mathematics came with his De l'Esprit géométrique ("On the Geometrical Spirit"), originally written as a preface to a geometry textbook. The work was unpublished until over a century after his death. Here Pascal looked into the issue of discovering truths, arguing that the ideal such 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 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.

In De l'Art de persuader, 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's answer was that these principles can only be grasped through intuition, and that this fact underscored the necessity in searching out truths for submission to God.

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.

Contributions to the physical sciences

Pascal's notable contributions to the fields of the study of fluids (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. In honor of his scientific contributions, the name Pascal has been given to an SI unit of pressure and to a programming language, and the name Pascal's law to an important principle of hydrostatics.

The vacuum

By 1646 Pascal had learned of Evangelista Torricelli's experimentation with barometers. Having replicated an experiment which involved placing a tube filled with mercury upside down in a bowl of mercury, Pascal questioned what force kept some mercury in the tube and what filled the space above the mercury in the tube. At the time, most scientists contended that some invisible matter was present there – not a vacuum.

Following more experimentation in this vein, in 1647 Pascal produced Experiences nouvelles touchant le vide, 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.

In 1648 Pascal continued his experiments by having his brother-in-law carry a barometer to higher elevation, confirming that the level of mercury would change, a result which Pascal replicated by carrying a barometer up and down a church tower in Paris.

In the face of criticism that some invisible matter existed in Pascal's empty space, Pascal delivered in reply to Estienne Noel one of the seventeenth century's major statements on the scientific method: "In order to show that a hypothesis is evident, it does not suffice that all the phenomena follow from it; instead, if it leads to something contrary to a single one of the phenomena, that suffices to establish its falsity." His insistence on the existence of the vacuum also led to conflict with a number of other prominent scientists, including Descartes.

Later life, religious conversion and death

In 1646, Pascal's father was wounded in the thigh. He was looked after by two brothers. Blaise Pascal spoke with the brothers frequently, and they lent him works by French Jansenist authors. In this period, Pascal experienced a sort of "first conversion" and began in the course of the following year to write on theological subjects.

Pascal fell away from this initial religious engagement and experienced the early 1650s as a "worldly period." His father died in 1651, and Pascal gained control over both his inheritance and that of his sister Jacqueline. In the same Jacqueline moved to become a nun at Port-Royal following the Jansenist movement. Pascal opposed this. When it came time for her ultimate vows, he refused to return to her enough of her inheritance to pay her dowry as a bride of Christ; without money she would attain a less desirable position in the convent hierarchy. Eventually, however, he relented on this point. ^[1]

Pascal spent the next three years in the company of friends who were gamblers and womanizers (as evidenced by his work on probability). During visits to his sister at Port-Royal in 1654, he displayed contempt for affairs of the world but was not drawn to God. ^[2]

Pascal's religious commitment revitalized

In late 1654 he was involved in an accident at the Neuilly bridge where the horses plunged over the parapet but the carriage survived. [3] Fifteen days later, on November 23, 1654, between ten thirty and twelve thirty 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 concluded by quoting Psalms 118:16: "I will not forget thy word. Amen." He seems carefully to have sewn this document into his coat and always transferred it when he changed clothes; a servant discovered it only by chance after his death.^[4] During his lifetime, Pascal was often mistakenly thought to be a libertine, and was later dismissed as an individual who had only a deathbed conversion.

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 traveled between Port-Royal and Paris. 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."

The Provincial Letters

Beginning in 1656, Pascal devoted himself to a memorable attack on casuistry, a popular ethical method used by Catholic thinkers in the early modern period (especially the Jesuits). Pascal denounced casuistry as the mere use of complex reasoning to justify moral laxity. His writings on this subject, a defense of the Jansenist Antoine Arnauld who had been condemned by the Faculté de Théologie at the Sorbonne, appeared as the Lettres provinciales, or "Provincial Letters," an 18-letter series published between 1656 and 1657 under the pseudonym Louis de Montalte. This work incensed Louis XIV, who ordered in 1660 that the book be shredded and burnt. In 1661, the Jansenist school at Port-Royal was condemned and closed down; those involved in it had to sign a 1656 papal bull condemning the teachings of Jansen as heretical.

Aside from their religious influence, the Lettres provinciales 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 Jean-Jacques Rousseau. The first few letters promote major principles of Jansenist teaching, for instance the dogmas of "proximate power" (Letter I) and "sufficient grace" (Letter II), and explain why they are not heretical. The later letters find Pascal more on the defensive – pressure on the Port Royal Jansenists to renounce their teachings was constantly growing through this time – and contain the assault on casuistry. Letter XIV contains the famous quote, "I would have written a shorter letter, but I did not have the time."

The Pensées

Pascal's most influential theological work, the Pensées, was unfinished by his death. It was to have been a sustained and coherent examination of and defense of the Christian faith, with the original title Apologie de la religion Chrétienne ("Apology of the Christian Religion"). A version of the detached notes for that book appeared in print in 1670 (the Port-Royal edition) and soon became a classic. Several attempts have been made to arrange the notes systematically; notable editions include those of Brunschvicg, Lafuma, and (most recently) Sellier. (See, also, the monumental edition of his Oeuvres complètes (1964–1991), which is known as the Tercententary Edition and was realized by Jean Mesnard; this edition reviews the dating, history, and critical bibliography of each of Pascal's texts.) It remains unclear, however, precisely what structure Pascal intended.

In the Pensées, Pascal continues themes developed in De l'Art de persuader by asserting that the acquisition of knowledge must be a religious experience, because reason alone cannot lead to certainty from basic principles that are open to question. Only through divine revelation can we gain certainty. In terms of philosophy, the Pensées were an attack against skepticism. Pascal also attempted to assert that Christianity is the true religion, referencing history, miracles, and the realization of prophecy. Ultimately, however, he found that the evidence, though not unbelievable, was not totally convincing. Pascal took this to mean that reasoning alone could not lead one to faith; God's grace was also necessary.

Last works and death

In 1659 Pascal, whose health had never been good, fell seriously ill. Despite an autopsy being performed after his death, the cause of his continual poor health was never determined, though speculation focuses on tuberculosis, stomach cancer, or a combination of the two.^[5]

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, exhorting the Jansenists not to give in. Later that year, his sister Jacqueline died, which convinced Pascal to cease his polemics on Jansenism. Pascal's last major achievement, returning to his mechanical genius, was inaugurating perhaps the first bus line, moving passengers within Paris in a carriage with many seats.

In 1662, Pascal's illness became more violent. Aware that he had little chance to survive, he sought a move to the hospital for incurable diseases, but his doctors declared that he was to unstable to be carried. In Paris on August 18, 1662, Pascal went into convulsions and received extreme unction. He died the next morning, his last words being "May God never abandon me," and was buried in the cemetery of Saint-Étienne-du-Mont.^[6]

Works

Essai pour les coniques (1639)
Experiences nouvelles touchant le vide (1647)
Traité du triangle arithmétique (1653)
Lettres provinciales (1656-7)
De l'Esprit géométrique (1657 or 1658)
Écrit sur la signature du formulaire (1661)
Pensées (incomplete at death)

References

Broome, JH. Pascal. ISBN 0713150211
Muir, Jane. Of Men and Numbers. New York: Dover Publications, Inc, 1996. ISBN 0486289737
Encyclopedia of Philosophy, 1967 edition, s.v. "Pascal, Blaise."
Pascal, Blaise. Oeuvres complètes. Paris: Seuil, 1963.

Notes

^ Muir, 93.
^ Encyclopedia of Philosophy, 52.
^ Oeuvres complètes, 618.
^ Muir, 103.
^ Muir, 104.

External links

O'Connor, John J.; Robertson, Edmund F., "Blaise Pascal", MacTutor History of Mathematics Archive, University of St Andrews
Etext of Pascal's Pensées (English, in various formats)
Etext of Pascal's Lettres Provinciales (English)
Etext of a number of Pascal's minor works (English translation) including, among others, De l'Esprit géométrique and De l'Art de persuader.