Blaise Pascal

Blaise Pascal (19 June 1623 – 19 August 1662) was a prominent French polymath, recognized for his contributions as a mathematician, physicist, inventor, philosopher, and Catholic author.

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

Educated by his father, Étienne Pascal, a tax collector in Rouen, Pascal demonstrated exceptional talent as a child prodigy. His initial mathematical endeavors focused on projective geometry, culminating in a substantial treatise on conic sections authored at the age of 16. Subsequent correspondence with Pierre de Fermat regarding probability theory profoundly impacted the evolution of modern economics and social science. In 1642, Pascal initiated groundbreaking work on calculating machines, known as Pascal's calculators or Pascalines, thereby establishing himself as one of the earliest inventors of the mechanical calculator.

Similar to his contemporary René Descartes, Pascal distinguished himself as a pioneer in both the natural and applied sciences. He advocated for the scientific method and generated several contentious findings. His significant contributions to fluid dynamics included clarifying the principles of pressure and vacuum through the generalization of Evangelista Torricelli's research. The SI unit for pressure is designated in Pascal's honor. In 1647, building upon the work of Torricelli and Galileo Galilei, Pascal challenged the assertions of figures such as Aristotle and Descartes, who maintained that nature inherently resists a vacuum.

Pascal is also recognized for inventing modern public transportation, having launched the carrosses à cinq sols, the inaugural modern public transport service, shortly before his demise in 1662.

In 1646, Pascal and his sister Jacqueline aligned themselves with Jansenism, a Catholic religious movement criticized by its opponents. After a profound religious experience in late 1654, he commenced authoring influential philosophical and theological texts. His two most renowned works, the Lettres provinciales and the Pensées, originate from this era; the former addresses the conflict between Jansenists and Jesuits. The latter includes Pascal's wager, originally termed the Discourse on the Machine, which presents a fideistic probabilistic argument for belief in God. During the same year, he also composed a significant treatise on the arithmetical triangle. From 1658 to 1659, he explored the cycloid and its application in determining the volume of solids. After enduring several years of illness, Pascal passed away in Paris at the age of 39.

Early Life and Education

Born in Clermont-Ferrand, located in France's Auvergne region near the Massif Central, Pascal experienced the loss of his mother, Antoinette Begon, at the age of three. His father, Étienne Pascal, an amateur mathematician, served as a local judge and belonged to the "Noblesse de Robe." Pascal had two sisters: Jacqueline, who was younger, and Gilberte, who was older.

Relocation to Paris

In 1631, five years subsequent to his wife's passing, Étienne Pascal relocated to Paris with his children. The family soon employed Louise Delfault, a maid who ultimately became an integral part of their household. Étienne, who remained unmarried, chose to personally undertake the education of his children.

The young Pascal exhibited remarkable intellectual prowess, demonstrating an exceptional aptitude for mathematics and science. Although Étienne initially attempted to deter his son from studying mathematics, by the age of 12, Pascal independently rediscovered Euclid's first thirty-two geometric propositions by drawing with charcoal on a tile floor. Consequently, he was provided with a copy of Euclid's Elements.

Essay on Conics

Pascal developed a particular interest in Desargues' work concerning conic sections. Adopting Desargues' methodology, the 16-year-old Pascal authored a concise treatise, intended as a proof, on the concept known as the Mystic Hexagram, titled Essai pour les coniques (Essay on Conics). This work, his inaugural significant mathematical contribution, was dispatched to Père Mersenne in Paris and is recognized today as Pascal's theorem. The theorem posits that if a hexagon is inscribed within a circle (or conic section), the three intersection points of its opposite sides will be collinear, forming what is termed the Pascal line.

The precocity of Pascal's work led René Descartes to initially believe it had been authored by Pascal's father. Upon Mersenne's confirmation that the treatise was, in fact, the creation of the son, Descartes responded, "I do not find it strange that he has offered demonstrations about conics more appropriate than those of the ancients," further remarking, "but other matters related to this subject can be proposed that would scarcely occur to a 16-year-old child."

Departure from Paris

In 17th-century France, public offices and positions were subject to purchase and sale. In 1631, Étienne Pascal divested his role as second president of the Cour des Aides for 65,665 livres. This capital was invested in a government bond, which initially secured a comfortable, though not extravagant, income, enabling the Pascal family to reside in Paris. However, in 1638, Cardinal Richelieu, facing financial exigencies due to the Thirty Years' War, defaulted on these government bonds. Consequently, Étienne Pascal's assets plummeted from approximately 66,000 livres to under 7,300.

Étienne Pascal, like numerous contemporaries, was compelled to depart Paris due to his dissent against Richelieu's fiscal policies. He entrusted his three children to his neighbor, Madame Sainctot, a renowned beauty with a notable past, who hosted one of France's most distinguished intellectual salons. Étienne's pardon was secured only after Jacqueline's commendable performance in a children's play attended by Richelieu. Subsequently, Étienne regained favor with the Cardinal and, in 1639, received an appointment as the king's commissioner of taxes in Rouen, a city whose tax records were in disarray following civil unrest.

Pascaline

In 1642, at the age of 18, Pascal developed a mechanical calculator, known as Pascal's calculator or the Pascaline, to alleviate his father's arduous and repetitive tax calculations, a task in which young Pascal had also been involved. Of the eight surviving Pascalines, four are housed at the Musée des Arts et Métiers in Paris, and another is located at the Zwinger museum in Dresden, Germany, which displays two of his original mechanical devices.

Despite these machines being pioneering precursors to four centuries of mechanical calculation advancements and, in a broader sense, to the subsequent field of computer engineering, the Pascaline did not achieve significant commercial success. Its practical use was somewhat cumbersome, but its prohibitive cost was likely the primary factor, relegating it to the status of a luxury item and a symbol of affluence for the wealthy elite across France and Europe. Pascal presented the initial mechanical calculator to Christina, Queen of Sweden, in 1632. Over the subsequent decade, Pascal continuously refined his design, mentioning the construction of approximately 50 machines based on his specifications, with 20 finished units completed within that ten-year period.

Mathematics

Probability

In 1654, at the instigation of his friend, the Chevalier de Méré, Pascal engaged in correspondence with Pierre de Fermat concerning problems related to gambling, a collaboration that led to the genesis of the mathematical theory of probability. A specific challenge involved two players seeking to conclude a game prematurely and equitably divide the stakes based on each player's probability of winning from that juncture. This discourse introduced the concept of expected value. John Ross observes, "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." In his Pensées, Pascal employed a probabilistic argument, known as Pascal's Wager, to rationalize belief in God and a virtuous existence. Nevertheless, despite their significant foundational contributions to probability theory, Pascal and Fermat did not extensively advance the field. Christiaan Huygens, having learned about the subject through their correspondence, authored the first book dedicated to probability. Subsequent contributors to the theory's development include Abraham de Moivre and Pierre-Simon Laplace. The work undertaken by Fermat and Pascal on the calculus of probabilities established crucial groundwork for Leibniz's formulation of calculus.

Treatise on the Arithmetical Triangle

Pascal's Traité du triangle arithmétique, composed in 1654 and posthumously published in 1665, detailed a practical tabular arrangement for binomial coefficients. He referred to this as the arithmetical triangle, which is now universally known as Pascal's triangle. The triangular structure can also be depicted as follows:

Pascal defined the numbers within the triangle recursively: Designating the number in the (m + 1)th row and (n + 1)th column as t_mn, the recursive relation is t_mn = t_m−1,n + t_m,n−1, applicable for m = 0, 1, 2, ... and n = 0, 1, 2, ... The specified boundary conditions are t_m,−1 = 0 and t_−1,n = 0 for m = 1, 2, 3, ... and n = 1, 2, 3, ... The initial generator value is t₀₀ = 1. Pascal subsequently presented the proof.

t m n = ( m + n ) ( m + n −<!-- − --> §4243§ ) ⋯ ( m + §5556§ ) n ( n − §7071§ ) ⋯ §7778§ . {\displaystyle t_{mn}={\frac {(m+n)(m+n-1)\cdots (m+1)}{n(n-1)\cdots 1}}.}

Within the same publication, Pascal articulated the principle of mathematical induction. In 1654, he established Pascal's identity, which relates the sums of the p-th powers of the initial n positive integers, where p ranges from 0, 1, 2, ..., to k.

During that same year, Pascal underwent a profound religious experience, which led him to largely discontinue his mathematical endeavors.

Cycloid

In 1658, during a period of suffering from a toothache, Pascal commenced investigating various problems concerning the cycloid. The subsequent disappearance of his toothache was interpreted by him as a divine indication to continue his investigations. Eight days later, he finalized his treatise and, to disseminate his findings, he initiated a public contest.

Pascal posed three inquiries regarding the centroid, area, and volume of the cycloid, stipulating that the victors would be awarded prizes of 20 and 40 Spanish doubloons. Pascal, Gilles de Roberval, and Pierre de Carcavi served as judges, and neither of the two entries (submitted by John Wallis and Antoine de Lalouvère) was deemed satisfactory. While the competition was in progress, Christopher Wren submitted a proposed proof to Pascal concerning the rectification of the cycloid curve; Roberval promptly asserted prior knowledge of this proof for several years. Wallis subsequently published Wren's proof, with due credit, in his work Tractus Duo, thereby establishing Wren's priority for the initial published demonstration.

Physics

Pascal made significant contributions across various domains in physics, particularly in the areas of fluid mechanics and pressure. Commemorating his scientific advancements, the name Pascal designates the SI unit of pressure, and Pascal's law represents a fundamental principle of hydrostatics. He devised an early iteration of the roulette and its corresponding wheel as part of his quest for a perpetual motion device. Furthermore, the Blaise Pascal Chairs are awarded to distinguished international scientists for conducting research within the Île-de-France region.

Fluid dynamics

His work in the fields of hydrodynamics and hydrostatics focused on the foundational principles of hydraulic fluids. Notable among his inventions are the hydraulic press, which utilizes hydraulic pressure for force multiplication, and the syringe. He demonstrated that hydrostatic pressure is contingent not upon the fluid's weight but rather on the difference in elevation. This principle was purportedly illustrated by his experiment involving a thin tube affixed to a water-filled barrel, with the tube subsequently filled to the height of a building's third floor. This action resulted in the barrel leaking, an event now recognized as Pascal's barrel experiment.

Vacuum

By 1647, Pascal became aware of Evangelista Torricelli's experiments involving barometers. After replicating an experiment where a mercury-filled tube was inverted into a basin of mercury, Pascal investigated the force sustaining the mercury column and the composition of the space above it. During this period, the prevailing scientific consensus, including René Descartes' view, posited the existence of a plenum—an invisible substance occupying all space—rather than a vacuum, encapsulated by the maxim "Nature abhors a vacuum." This perspective originated from the Aristotelian concept that all motion resulted from one substance moving another. Additionally, the passage of light through the glass tube was interpreted as evidence for a substance like aether, rather than a void, filling the space.

Subsequent to further experimentation in this area, Pascal published Experiences nouvelles touchant le vide ("New experiments with the vacuum") in 1647. This publication outlined fundamental principles concerning the extent to which different liquids could be sustained by atmospheric pressure. It also presented arguments supporting the existence of a vacuum above the liquid column within a barometer tube. This foundational work was succeeded by Récit de la grande expérience de l'équilibre des liqueurs ("Account of the great experiment on equilibrium in liquids"), released in 1648.

Initial Experiment on Atmospheric Pressure and Altitude

The concept of the Torricellian vacuum established that atmospheric pressure corresponds to the weight of a 30-inch mercury column. Pascal hypothesized that if air possessed a finite weight, the Earth's atmosphere would necessarily have a defined maximum height. Consequently, he deduced that air pressure should decrease with increasing altitude. Despite residing near the 4,790-foot (1,460 m) Puy de Dôme mountain, Pascal's precarious health prevented him from undertaking the ascent personally. Therefore, on September 19, 1648, following persistent encouragement from Pascal, his brother-in-law, Florin Périer (husband of Pascal's elder sister Gilberte), conducted the crucial experimental verification of Pascal's theory. Périer's written account details the event:

The weather conditions were uncertain last Saturday...[but] at approximately five o'clock that morning...the Puy-de-Dôme became visible...prompting my decision to proceed. Several prominent citizens of Clermont had requested notification of my ascent...I was pleased to have their company in this significant undertaking...

...at eight o'clock, we convened in the gardens of the Minim Fathers, the lowest point in the town....Initially, I poured 16 pounds of mercury...into a container...then procured several glass tubes...each four feet in length, hermetically sealed at one end and open at the other...which I subsequently inverted into the vessel [of mercury]...I observed the mercury column stood at 26 inches and 3+§34§⁄§56§ lines above the mercury level in the vessel...I replicated this experiment twice more from the identical location...[and] consistently obtained the same outcome...

I affixed one of the tubes to the vessel, marking the mercury's height, and...requested Father Chastin, a Minim Brother...to monitor for any diurnal variations...Taking the other tube and a quantity of mercury...I ascended to the summit of Puy-de-Dôme, approximately 500 fathoms above the monastery. There, upon conducting the experiment...I observed the mercury column reached a height of merely 23 inches and 2 lines...I meticulously repeated the experiment five times...at various locations on the summit...and consistently recorded the same mercury height...in every instance...

Pascal subsequently replicated this experiment in Paris, transporting a barometer to the apex of the bell tower at the church of Saint-Jacques-de-la-Boucherie, an elevation of approximately 50 meters. This ascent resulted in a two-line drop in the mercury level. Both experiments demonstrated that an elevation gain of 7 fathoms corresponds to a half-line decrease in the mercury column. Note: Pascal employed the terms pouce and ligne for "inch" and "line," respectively, and toise for "fathom."

Responding to Étienne Noël, a proponent of the plenum theory, Pascal articulated a statement reflecting contemporary scientific principles and the concept of falsifiability: "To demonstrate the validity of a hypothesis, it is insufficient for all observed phenomena to align with it; rather, if it yields a consequence contradictory to even a single phenomenon, that is enough to establish its falsehood."

Adult Life: Religious Convictions, Literary Contributions, and Philosophical Engagements

Religious Conversion

During the winter of 1646, Pascal's 58-year-old father sustained a hip fracture after slipping on an icy street in Rouen. Given his age and the rudimentary medical practices of the 17th century, such an injury posed a significant, potentially fatal, risk. Fortunately, Rouen hosted two of France's most esteemed physicians, Deslandes and de la Bouteillerie, whom the elder Pascal insisted attend him. This decision proved judicious, as he recovered and regained his ability to walk, though the treatment and rehabilitation process extended over three months, during which the doctors became frequent visitors.

Both physicians adhered to Jansenism, a theological movement founded by Jean Guillebert that diverged from mainstream Catholic doctrine. This relatively minor sect was, at the time, gaining considerable traction within the French Catholic community, advocating a stringent form of Augustinism. Blaise Pascal frequently conversed with the doctors, and following his father's successful treatment, he borrowed works by Jansenist authors from them. This period marked Pascal's "first conversion," prompting him to commence writing on theological topics over the subsequent year.

Pascal subsequently disengaged from this initial religious fervor, entering what some biographers term his "worldly period" (1648–54). In 1651, his father passed away, bequeathing his estate to Pascal and his sister Jacqueline, for whom Pascal served as conservator. Jacqueline soon declared her intention to become a postulant at the Jansenist convent of Port-Royal. Pascal was profoundly distressed, not by her spiritual choice, but by his own persistent ill health, feeling a reciprocal need for her presence.

A significant conflict erupted within the Pascal household. Blaise implored Jacqueline to reconsider her decision, but she remained resolute. His commands for her to stay were equally ineffective. Underlying this dispute was Blaise's profound fear of abandonment, compounded by the fact that Jacqueline's entry into Port-Royal would necessitate relinquishing her inheritance. Nevertheless, her determination was unwavering.

By late October 1651, a resolution was achieved between the siblings. Jacqueline transferred her portion of the inheritance to her brother in exchange for a substantial annual stipend. Gilberte had previously received her inheritance as a dowry. In early January, Jacqueline departed for Port-Royal. Gilberte recounted that on this day, her brother "retired very sadly to his rooms without seeing Jacqueline, who was waiting in the little parlor..." In early June 1653, following what appeared to be persistent persuasion from Jacqueline, Pascal formally transferred the entirety of his sister's inheritance to Port-Royal, an institution he increasingly perceived as "a cult." With two-thirds of his father's estate now dissipated, the 29-year-old Pascal found himself in a state of genteel poverty.

For a period, Pascal adopted a bachelor's lifestyle. During his 1654 visits to his sister at Port-Royal, he expressed disdain for worldly matters but remained spiritually uninclined towards God.

Memorial

On the night of November 23, 1654, between 10:30 PM and 12:30 AM, Pascal underwent a profound religious experience. He promptly documented this event in a personal note, commencing with "Fire. God of Abraham, God of Isaac, God of Jacob, not of the philosophers and the scholars..." and concluding with a quotation from Psalm 119:16: "I will not forget thy word. Amen." Pascal reportedly meticulously stitched this document into his coat, transferring it with each change of clothing; it was only fortuitously discovered by a servant after his death. This text is now recognized as the Memorial. The narrative attributing this experience, as described in the Memorial, to a carriage accident is contested by some scholars. With his faith and religious devotion reinvigorated, Pascal undertook a two-week retreat at the elder of the two Port-Royal convents in January 1655. Over the subsequent four years, he frequently journeyed between Port-Royal and Paris. It was immediately following this conversion that he commenced writing his seminal literary work on religion, the Provincial Letters.

Literature

Within the realm of literature, Pascal is esteemed as a pivotal author of the French Classical Period and is presently recognized as one of the foremost masters of French prose. Seymour Eaton lauded him as "the greatest of all French thinkers." His distinctive application of satire and wit significantly impacted subsequent polemicists.

The Provincial Letters

Pascal initiated a notable critique of casuistry, a prevalent ethical methodology employed by Catholic intellectuals during the early modern era, particularly by the Jesuits and Antonio Escobar, starting in 1656–57. He condemned casuistry as a sophisticated form of reasoning designed solely to rationalize moral permissiveness and various transgressions. This series of 18 letters, issued between 1656 and 1657 under the pseudonym Louis de Montalte, provoked the ire of Louis XIV, who subsequently ordered the book's destruction by shredding and burning in 1660. Amidst the formulary controversy in 1661, the Jansenist institution at Port-Royal faced condemnation and closure. Individuals associated with the school were compelled to endorse a 1656 papal bull that declared Jansen's doctrines heretical. Pascal's concluding letter in 1657 directly challenged Pope Alexander VII, who, despite public opposition, was reportedly swayed by Pascal's arguments.

Beyond their theological impact, the Provincial Letters achieved widespread acclaim as a significant literary contribution. Pascal's deployment of humor, derision, and sharp satire within his arguments rendered the letters highly accessible to the public and profoundly shaped the prose styles of subsequent French authors, including Voltaire and Jean-Jacques Rousseau.

Within the Provincial Letters, Pascal famously offered an apology for the length of his correspondence, attributing it to a lack of time for conciseness. In Letter XVI, translated by Thomas M'Crie, he stated: "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 remarked on the Letters, asserting: "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

Émile Faguet characterized Pascal as "one of the greatest of French philosophers." Pascal adhered to dualism and scientific principles, aligning with the philosophical tradition of René Descartes.

Philosophy of Religion

Pascal's primary intellectual focus was the philosophy of religion, leading him to describe Descartes' philosophy as "useless and uncertain." He further articulated his critique: "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."

Pascal rejected both the rationalism exemplified by thinkers such as Descartes, asserting that "reason can decide nothing here," and the opposing epistemological framework of empiricism, instead favoring fideism. He contended that God's nature precluded revelation through proofs, stating that humans "are in darkness and estranged from God" because "he has hidden Himself from their knowledge." Pascalian theology stems from his view that humanity, as articulated by Wood, is "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."

Pensées

Man is only a reed, the weakest in nature, but he is a thinking reed.

Pascal's most significant theological contribution, posthumously titled the Pensées ("Thoughts"), is broadly recognized as a masterpiece and a seminal work in French prose. Sainte-Beuve, commenting on a specific section (Thought #72), lauded it as among the most exquisite passages in the French language. Similarly, Will Durant acclaimed the Pensées as "the most eloquent book in French prose."

The Pensées remained unfinished at the time of Pascal's death. It was conceived as a comprehensive and systematic exploration and defense of Christian doctrine, originally bearing the title Apologie de la religion Chrétienne ("Defence of the Christian Religion"). The initial compilation of the numerous manuscript fragments discovered after his passing was published in 1669 as Pensées de M. Pascal sur la religion, et sur quelques autres sujets ("Thoughts of M. Pascal on religion, and on some other subjects"), quickly establishing itself as a classic.

A primary strategy of the Apologie's involved juxtaposing the conflicting philosophies of Pyrrhonism and Stoicism, personified by Montaigne and Epictetus respectively, with the aim of inducing such profound despair and disorientation in the unbeliever that they would ultimately turn to God.

Philosophy of Mathematics

Pascal's significant contribution to the philosophy of mathematics is encapsulated in his work, De l'Esprit géométrique ("Of the Geometrical Spirit"). This text was initially conceived as a preface for a geometry textbook intended for the renowned Petites écoles de Port-Royal ("Little Schools of Port-Royal"). Despite its early composition, the manuscript remained unpublished for more than a century following his demise. In this treatise, Pascal explored the methodology for discovering truths, positing that an ideal approach would involve grounding all propositions in previously validated truths. Concurrently, he contended that such an ideal was unattainable, as established truths inherently necessitate further supporting truths, thereby precluding the ultimate identification of first principles. Consequently, Pascal asserted that the geometric method, which involves assuming certain principles and deriving other propositions from them, represented the most perfect possible procedure. However, he acknowledged the inherent uncertainty regarding the veracity of these foundational assumed principles.

Within De l'Esprit géométrique, Pascal further elaborated a comprehensive theory of definition. He differentiated between two categories: definitions functioning as conventional labels established by an author, and definitions intrinsically embedded within language, universally comprehended due to their inherent designation of a referent. The latter category aligns with the philosophical tenets of essentialism. Pascal maintained that only the former type of definition held significance for scientific and mathematical discourse, advocating for the adoption of Descartes' philosophy of formalism within these disciplines.

In his treatise De l'Art de persuader ("On the Art of Persuasion"), Pascal conducted a more profound examination of geometry's axiomatic method, particularly addressing the process by which individuals become convinced of the foundational axioms underpinning subsequent conclusions. Aligning with Montaigne's perspective, Pascal posited that attaining absolute certainty in these axioms and their derived conclusions through purely human reasoning is unattainable. He asserted that such fundamental principles are accessible solely through intuition, a realization that, for Pascal, emphasized the imperative of divine submission in the pursuit of truth.

Final Works and Demise

T. S. Eliot characterized Pascal during this period of his life as "a man of the world among ascetics, and an ascetic among men of the world." Pascal's embrace of an ascetic existence stemmed from his conviction that human suffering was both natural and essential. In 1659, Pascal experienced a severe decline in health. Throughout his final years, he often resisted medical interventions, articulating, "Do not pity me; sickness represents the natural condition of Christians, for in it we are, as we ought always to be, enduring afflictions, deprived of all sensory comforts and pleasures, liberated from all life's pervasive passions, devoid of ambition, free from avarice, and in constant anticipation of death." Driven by a desire to emulate Jesus' spiritual poverty, and imbued with a spirit of fervent devotion and benevolence, Pascal declared that should God grant him recovery from his ailment, he would dedicate the remainder of his life solely to "the service of the poor."

In 1661, Louis XIV initiated the suppression of the Jansenist movement at Port-Royal. Reacting to this, Pascal authored one of his concluding works, Écrit sur la signature du formulaire ("Writ on the Signing of the Form"), which urged the Jansenists to resist capitulation. Subsequently, later that same year, the death of his sister Jacqueline prompted Pascal to discontinue his polemical engagements concerning Jansenism.

Pioneer of Public Transportation

Pascal's final significant accomplishment, showcasing a return to his mechanical ingenuity, involved establishing one of the earliest land-based public transport systems: the carrosses à cinq sols. This network comprised horse-drawn, multi-seat carriages operating on five predetermined routes. Pascal also formulated the operational principles that subsequently informed the planning of public transportation; these carriages adhered to fixed routes, maintained a consistent fare (five sols, from which the name derived), and departed punctually regardless of passenger occupancy. Despite these innovations, the routes proved commercially unsuccessful, with the final line ceasing operation by 1675. Nevertheless, Pascal is recognized as a pioneering figure in the development of public transportation.

Sickness and Demise

In 1662, Pascal's health deteriorated significantly, and his emotional state worsened considerably following his sister's death. Recognizing his rapidly declining condition, he sought admission to a hospital for incurable diseases; however, his physicians deemed him too frail to be transported. On August 18, 1662, in Paris, Pascal experienced convulsions and received extreme unction. He passed away the following morning, uttering "May God never abandon me" as his final words, and was interred in the cemetery of Saint-Étienne-du-Mont.

A post-mortem examination revealed severe issues with his stomach and other abdominal organs, in addition to brain damage. Despite the autopsy, the precise etiology of his poor health remained undetermined, although prevailing theories suggest tuberculosis, stomach cancer, or a combination thereof. The headaches Pascal endured are generally attributed to the identified brain lesion.

Legacy

Université Blaise Pascal, one of the universities in Clermont-Ferrand, France, bears his name. Similarly, the Établissement scolaire français Blaise-Pascal in Lubumbashi, Democratic Republic of the Congo, is named in Pascal's honor.

The 1969 Eric Rohmer film My Night at Maud's draws inspiration from Pascal's work. Roberto Rossellini directed a biographical film, Blaise Pascal, which premiered on Italian television in 1971. Pascal was also featured in the inaugural episode of the 1984 BBC Two documentary series, Sea of Faith, presented by Don Cupitt. The chameleon character in the animated film Tangled is named Pascal.

A prominent programming language is named after Pascal. In 2014, Nvidia introduced its new Pascal microarchitecture, also named in his honor. The initial graphics cards incorporating the Pascal architecture were released in 2016.

The 2017 video game Nier: Automata features several characters named after renowned philosophers, including a sentient, pacifistic machine named Pascal, who functions as a significant supporting figure. This Pascal establishes a village where machines can coexist peacefully with the androids they are at war with, serving as a parental figure for other machines adapting to their newfound individuality.

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

The minor planet 4500 Pascal is named in his honor.

In his 1967 encyclical Populorum progressio, Pope Paul VI quoted from 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 issued an apostolic letter, Sublimitas et miseria hominis, dedicated to Blaise Pascal, commemorating the fourth centenary of his birth.

Pascal's intellectual contributions influenced both the French sociologist Pierre Bourdieu, who titled his 1997 work Pascalian Meditations after him, and the French philosopher Louis Althusser.

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; published 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; published 1670)
• Discours sur les passions de l'amour [Discourse on the Passion of Love] (possibly a forgery)
• On the Conversion of the Sinner
• Ecrits sur la grace [Writings on Grace]

Expected value

• Expected value
• Gambler's ruin
• List of pioneers in computer science
• List of works by Eugène Guillaume
• Pascal distribution
• Pascal's mugging
• Pascal's pyramid
• Pascal's simplex
• Problem of points
• Scientific Revolution

Notes

References

• Oeuvres complètes, volume 2 (1858). Paris: Libraire de L Hachette et Cie.
• Works by Blaise Pascal.
• Works by or concerning Blaise Pascal are available at the Internet Archive.
• Blaise Pascal's works are accessible through LibriVox, offering public domain audiobooks.
• Blaise Pascal's correspondence is cataloged within EMLO.
• Simpson, David. "Blaise Pascal." In Fieser, James; Dowden, Bradley (eds.). Internet Encyclopedia of Philosophy. ISSN 2161-0002. OCLC 37741658.Clarke, Desmond. "Blaise Pascal." In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy. ISSN 1095-5054. OCLC 429049174."Blaise Pascal" . Catholic Encyclopedia. 1913.O'Connor, John J.; Robertson, Edmund F., "Blaise Pascal," MacTutor History of Mathematics Archive, University of St AndrewsSource: TORIma Academy Archive