Pascal studying the cycloid, by Augustin Pajou, 1785.

Gallery of Blaise Pascal

1836

Portrait of Blaise Pascal, French mathematician and writer. Illustration from "Le Plutarque Francais" by Edmond Mennechet, 1836 (colour engraving).

Gallery of Blaise Pascal

1923

Rue Beaubourg, Paris, France

French mathemetician and physicist, at work in his home on the Rue Beaubourg, Paris, in 1652. Published in June 1923. Illustration by Rene Lelong.

Gallery of Blaise Pascal

1961

Painting of Blaise Pascal made by François II Quesnel for Gérard Edelinck in 1691.

Gallery of Blaise Pascal

Anonymous portrait of Blaise Pascal.

Gallery of Blaise Pascal

Portrait of Blaise Pascal, French mathematician, physicist, philosopher and theologian. Painting by Philippe de Champaigne.

Gallery of Blaise Pascal

Pascal and Desargues share to Descartes their experiments on the weight of the air: the young mathematician Blaise Pascal and Girard Desargues discussing his theory of atmospheric pressure with Rene Descartes in the Place des Vosges (Place Royale) during its construction between 1605 and 1612 in Paris. Marouflaged canvas by Francois Flameng, 19th century. La Sorbonne, Paris.

Pascal and Desargues share to Descartes their experiments on the weight of the air: the young mathematician Blaise Pascal and Girard Desargues discussing his theory of atmospheric pressure with Rene Descartes in the Place des Vosges (Place Royale) during its construction between 1605 and 1612 in Paris. Marouflaged canvas by Francois Flameng, 19th century. La Sorbonne, Paris.

Connections

mentor: Marin Mersenne

Acquaintance: René Descartes

Friend: Antoine Arnauld

Portrait of Antoine Arnauld, dit le Grand Arnauld (1612-1697). Photo (C) RMN-Grand Palais (musée de Port-Royal des Champs) / Gérard Blot.

Blaise Pascal was a French mathematician, physicist, religious philosopher, and master of prose. He laid the foundation for the modern theory of probabilities, formulated what came to be known as Pascal’s principle of pressure, and propagated a religious doctrine that taught the experience of God through the heart rather than through reason.

Background

Blaise Pascal was born on June 9, 1623, in Clermont-Ferrand, Auvergne, France. He was the third of Étienne Pascal's children and his only son. Pascal's mother, Antoinette Begon, died when he was only three years old. In 1632 the Pascal family, Étienne and his four children left Clermont and settled in Paris. Pascal's father had an interest in science and mathematics, was a local judge and member of the Noblesse de Robe.

Education

Blaise Pascal's father had unorthodox educational views and decided to teach his son himself. Étienne Pascal decided that Pascal was not to study mathematics before the age of 15 and all mathematics texts were removed from their house. Pascal, however, his curiosity raised by this, started to work on geometry himself at the age of 12. He discovered that the sum of the angles of a triangle are two right angles and, when his father found out, he relented and allowed Pascal a copy of Euclid.

At the age of 14, Blaise Pascal started to accompany his father to Mersenne's meetings. Mersenne belonged to the religious order of the Minims, and his cell in Paris was a frequent meeting place for Gassendi, Roberval, Carcavi, Auzout, Mydorge, Mylon, Desargues and others. Soon, certainly by the time he was 15, Blaise came to admire the work of Desargues. At the age of sixteen, Pascal presented a single piece of paper to one of Mersenne's meetings in June 1639. It contained a number of projective geometry theorems, including Pascal's mystic hexagon.

Career

In December 1639 the Blaise Pascal family left Paris to live in Rouen where Étienne had been appointed as a tax collector for Upper Normandy. Shortly after settling in Rouen, Blaise had his first work, Essay on Conic Sections published in February 1640.

Pascal invented the first digital calculator to help his father with his work collecting taxes. He worked on it for three years between 1642 and 1645. The device, called the Pascaline, resembled a mechanical calculator of the 1940s. This, almost certainly, makes Pascal the second person to invent a mechanical calculator for Schickard had manufactured one in 1624.

There were problems faced by Pascal in the design of the calculator which were due to the design of the French currency at that time. There were 20 sols in a livre and 12 deniers in a sol. The system remained in France until 1799 but in Britain, a system with similar multiples lasted until 1971. Pascal had to solve much harder technical problems to work with this division of the livre into 240 than he would have had if the division had been 100. However, production of the machines started in 1642 and by 1652 fifty prototypes had been produced, but few machines were sold, and the manufacture of Pascal's arithmetical calculator ceased in that year.

From about 1646 Pascal began a series of experiments on atmospheric pressure. By 1647 he had proved to his satisfaction that a vacuum existed. Descartes visited Pascal on 23 September. His visit only lasted two days and the two argued about the vacuum which Descartes did not believe in. In October 1647 Pascal wrote New Experiments Concerning Vacuums which led to disputes with a number of scientists who, like Descartes, did not believe in a vacuum.

In August 1648 Pascal observed that the pressure of the atmosphere decreases with height and deduced that a vacuum existed above the atmosphere.

Étienne Pascal died in September 1651 and following this Pascal wrote to one of his sisters giving a deeply Christian meaning to death in general and his father's death in particular. His ideas here were to form the basis for his later philosophical work Pensées.

From May 1653 Pascal worked on mathematics and physics writing Treatise on the Equilibrium of Liquids (1653) in which he explains Pascal's law of pressure.

Although Pascal was not the first to study the Pascal triangle, his work on the topic in Treatise on the Arithmetical Triangle was the most important on this topic and, through the work of Wallis, Pascal's work on the binomial coefficients was to lead Newton to his discovery of the general binomial theorem for fractional and negative powers.

Pascal worked on conic sections and produced important theorems in projective geometry. In The Generation of Conic Sections (mostly completed by March 1648 but worked on again in 1653 and 1654) Pascal considered conics generated by central projection of a circle. This was meant to be the first part of a treatise on conics which Pascal never completed. The work is now lost but Leibniz and Tschirnhaus made notes from it and it is through these notes that a fairly complete picture of the work is now possible.

In correspondence with Fermat, he laid the foundation for the theory of probability. This correspondence consisted of five letters and occurred in the summer of 1654. They considered the dice problem, already studied by Cardan, and the problem of points also considered by Cardan and, around the same time, Pacioli and Tartaglia. The dice problem asks how many times one must throw a pair of dice before one expects a double six while the problem of points asks how to divide the stakes if a game of dice is incomplete. They solved the problem of points for a two-player game but did not develop powerful enough mathematical methods to solve it for three or more players.

Pascal's last work was on the cycloid, the curve traced by a point on the circumference of a rolling circle. In 1658 Pascal started to think about mathematical problems again as he lay awake at night unable to sleep for pain. He applied Cavalieri's calculus of indivisibles to the problem of the area of any segment of the cycloid and the centre of gravity of any segment. He also solved the problems of the volume and surface area of the solid of revolution formed by rotating the cycloid about the x-axis.

Pascal published a challenge offering two prizes for solutions to these problems to Wren, Laloubère, Leibniz, Huygens, Wallis, Fermat and several other mathematicians. Wallis and Laloubère entered the competition but Laloubère's solution was wrong and Wallis was also not successful. Sluze, Ricci, Huygens, Wren, and Fermat all communicated their discoveries to Pascal without entering the competition. Wren had been working on Pascal's challenge, and he in turn challenged Pascal, Fermat and Roberval to find the arc length, the length of the arch, of the cycloid.

Pascal published his own solutions to his challenge problems in the Letters to Carcavi. After that time on he took little interest in science and spent his last years giving to the poor and going from church to church in Paris attending one religious service after another.

Events of 1646 were very significant for the young Pascal. In that year his father injured his leg and had to recuperate in his house. He was looked after by two young brothers from a religious movement just outside Rouen. They had a profound effect on the young Pascal, and he became deeply religious. Sometime around 1654 he nearly lost his life in an accident. The horses pulling his carriage bolted and the carriage was left hanging over a bridge above the river Seine. Although he was rescued without any physical injury, it does appear that he was much affected psychologically. Not long after he underwent another religious experience, on 23 November 1654, and he pledged his life to Christianity.

After this time Pascal made visits to the Jansenist monastery Port-Royal des Champs about 30 km south-west of Paris. He began to publish anonymous works on religious topics, eighteen Provincial Letters being published during 1656 and early 1657. These were written in defense of his friend Antoine Arnauld, an opponent of the Jesuits and a defender of Jansenism, who was on trial before the faculty of theology in Paris for his controversial religious works.

Pascal's most famous work in philosophy is Pensées, a collection of personal thoughts on human suffering and faith in God which he began in late 1656 and continued to work on during 1657 and 1658. This work contains 'Pascal's wager' which claims to prove that belief in God is rational with the following argument: "If God does not exist, one will lose nothing by believing in him, while if he does exist, one will lose everything by not believing."

Politics

Despite its minor status, the "Discourses on the Great" is nevertheless of interest since it is the only work of Pascal’s that attempts to formulate something like a social or political philosophy. The work (which is addressed to a young man of high degree) begins with a parable about a castaway on an island whom the inhabitants (owing to his close physical resemblance) mistake for their long-lost king. Such, Pascal argues, is the condition of those born to nobility or wealth within society: it is only by coincidence or lucky accident and by the power of custom and convention, not by nature, that they have their status. From this, it follows that persons of rank are obligated to conduct themselves with due humility and must never allow themselves to treat those on society’s lower rungs with insolence or disrespect. Pascal concludes the Discourses by reminding his young learner of his true condition and enjoins him to rule and lead with beneficence.

Simply stated, the political philosophy expressed in the Discourses is noblesse oblige. Pascal acknowledges that the origins of human inequality are of two kinds, natural and institutional. The former arise from relative abilities or deficiencies of mind or body. For instance, A has better eyesight than B; X is taller and stronger than Y). Institutional inequalities, unless they are sanctioned by divine law, are entirely conventional and sometimes even arbitrary and can be rescinded or overturned. That, as far as a social theory is concerned, is about as far as Pascal goes in the Discourses. Since his primary purpose is to offer moral instruction to a young nobleman, he doesn’t address topics like property, the social contract, divine right theory, which was a view recently and avidly affirmed by Louis XIV, or the ethics of revolt. From scattered comments in the Pensées, it is known that he was politically conservative and despised violence. Apparently his experience during the Fronde led him to believe that even oppressive order is better than anarchy and that there is no worse social evil than civil war.

Views

Of the many great natural philosophers of the 17th century - a group that includes both theoreticians and experimentalists and such illustrious names as Galileo, Descartes, Bacon, Boyle, Huygens, and Gassendi - Pascal arguably was the one who came closest to articulating a coherent, comprehensive, durable philosophy of science consistent with and comparable to the standard view that prevails today, except that he came up short. As Desmond M. Clarke has argued, Pascal was torn between his love of geometric proof and pure logical demonstration on the one hand and his skeptical, pragmatic instincts in favor of down-to-earth experimentalism and empiricism on the other. As a result, he seemed trapped in a kind of philosophical limbo. Similarly, although he seemed to recognize that the knowledge of the natural world is only probable and can never be certain, a part of him nevertheless remained enthralled by the “will-o-the-wisp” or "Holy Grail" of absolute certainty.

In most other respects, Pascal’s outlook is ahead of its time and admirable in its self-restraint and in its awareness of its own limitations. Unlike Bacon, he makes room for hypothesis and even imaginative insight and conjecture (l’esprit de finesse) and also allows a deductive component like Descartes (l’esprit géométrique). He acknowledges that all hypotheses must be tested and confirmed by rigorous experiments, and even if he didn’t actually carry out his experiments exactly as described, he nevertheless accepts the necessity of such testing. Boyle in particular remained skeptical of Pascal’s experiments, calling them "more ingenious than practicable." He especially marveled at the availability of 40-ft. Torricelli tubes and of brass fittings engineered to nearly microscopic precision. Attempting to reproduce one of Pascal’s hydrostatic tests involving a fly in a chamber of water, Boyle attests that "upon tryal with a strong flie" the creature "presently drowned."

Pascal fully understood that once a hypothesis is tested and confirmed, the problem of determining the true cause of the phenomenon still remains and becomes itself a matter for further conjecture. For example, take his prediction, experimentally confirmed, that the level of mercury in a Torricelli tube will decline as altitude increases. Pascal claimed that this phenomenon was due to the weight of air, though he knew that other factors might also explain the same effect. Indeed, for all he knew, an invisible emanation from the god Mercury may have influenced his results. (Ironically, the famous Puy-de-Dôme experiment had been performed near an ancient temple to that deity). As Pascal observed to Father Noël, fanciful explanations for phenomena are as easy to imagine as they are impossible to disprove.

In his correspondence with Noël, Pascal at one point suggests that it is fatal for one’s hypothesis if an experimental test fails to confirm a predicted outcome. However, as he himself and his fellow experimentalists certainly knew, there can be nearly as many reasons why an expected result does not occur, such as defective apparatus, lack of proper controls, measurement errors, extraordinary test circumstances, etc, as there are explanations for a result that occurs as expected. Apparently, in his haste to champion the new science of experimentalism against its critics, both Cartesian and Scholastic, Pascal wanted to at least be able to say that if experiments cannot conclusively prove a given hypothesis, then they may at least be able to disprove it. If this was his intention, he was anticipating by nearly three centuries Karl Popper’s theory of empirical falsification and opposed to (and seemingly fearful at the prospect of) any view similar to Willard Van Orman Quine’s theory of confirmation holism, according to which all scientific claims are at best only probable and there is no such thing as a decisive experiment.

Pascal has been plausibly labeled an empiricist, a foundationalist, even a positivist and a skeptic. The confusion is understandable and is due largely to the fact that his epistemological views are complex and seem in certain respects equivocal or inconsistent. For example, he accepts the rule of authority in some areas of knowledge, such as ancient history, while opposing and even forbidding it in others, especially physical science. He also recognizes three different types or sources of knowledge related to his so-called "three orders": body/sense; mind/reason; heart/will or instinct, each with its own domain or area of applicability, level of certainty, and tests of confirmation and reliability.

Quotations:
"I made this one [letter] longer only because I have not had the leisure to make it shorter."

"People almost invariably arrive at their beliefs not on the basis of proof but on the basis of what they find attractive."

"Do not imagine that it is less an accident by which you find yourself master of the wealth which you possess, than that by which this man found himself king."

"If you act externally with men in conformity with your rank, you should recognize, by a more secret but truer thought, that you have nothing naturally superior to them."

"The mind must not be forced; artificial and constrained manners fill it with foolish presumption, through unnatural elevation and vain and ridiculous inflation, instead of solid and vigorous nutriment."

Personality

Pascal, a complex personality, was described by biographer Donald Adamson as precocious, stubbornly persevering, a perfectionist, pugnacious to the point of bullying ruthlessness yet seeking to be meek and humble.

Physical Characteristics:
Pascal had struggled with insomnia and a digestive disorder from the time he was a teen, and as such he was known to have suffered greatly from pain throughout his life. Over the years, Pascal’s constant work took a further toll on his already fragile health.

Pascal died of a malignant stomach tumor at his sister Gilberte's home in Paris on August 19, 1662. By then, the tumor had metastasized in his brain. He was 39 years old.

Quotes from others about the person

"[Pascal] has too much vacuum in his head." - René Descartes

Interests

Philosophers & Thinkers

Augustine of Hippo, René Descartes, Cornelius Jansen, Epictetus