In the early seventeenth century, a 12-year-old boy was so involved working out on principles of Geometry, calling straight lines 'bars' and circles 'rounds' trying trying to put forth a method to prove his guess or conviction. It was that the three angles of a triangles must add up to two right angles. Being unaware of the fact that his father was arround, he was busy working on the mathematical diagram. When his father came to know about it, he felt proud of his son; and a few years later, the entire world was to take note of him and his achievements.The young boy turned out to be none other than the great mathematician, Blaise Pascal.
On June 19, 1623, Blaise Pascal was born at Clermont – Ferrand, the capital of Auvergne, France and christened eight days later. Clermont was a small town with a population of about 9,000 people. His father Etienne Pascal was a high public official in the Department, being Conseiller Elu pour le Roi in the elctorate of Bas-Auvergne at Clermont and about to be President from 1624 of the Cour des Aides. Blaise’s mother Antoinette Begon was a daughter of Victor Begon, a burgess and merchant of Clermont, who aspired to public service position. Of the four children of Etienne and Antoinette, only three - Gilberte, Blaise and Jacqueline, survived.
When Blaise was only three, his mother at the age of 30, died. Blaise’s father Etienne though grief – stricken resolved to father, mother and tutor his children - a unique resolve of those times. Etienne Pascal nurtured his children in his own style educating the kids; he used to teach them through open talks and debates. He was a wonderful teacher, who never suppressed his children’s qualities by resorting to harsh educational methods. He himself was a prominent mathematician and meticulously undertook the task of educating Blaise.
In 1631, when Blaise’s family settled in Paris, Blaise was eight years old. In Paris, Etienne Pascal engaged a governess named Louise Default to look after his young children. She remained attached throughtout her life with the Pascal's. Etienne who lived the spirit of Renaissance, wanted his son to become a humanist. He taught Blaise Greek and Latin languages. Due to such a cultured upbringing in Paris, Blaise’s sister Jacqueline too figured as an infant prodigy in literary circles, as Blaise himself achieved fame in mathematics.
At the age of twelve, Blaise set himself to reflect upon and draw figures on the tiles of his playroom. He did not even know the names of the figures and started naming them. He called a circle ‘round’ and a line ‘bar’! His curiosity and intelligence pushed him to reach the 32nd theorem of the first book of Euclid. The theorem was: The sum of the angles of a triangle is equal to two right angles. His father was surprised at what Blaise was doing. It seemed that Blaise was seeking something; and that something turned out to be the 37th proposition of the first book of Euclid's theorem! Blaise’s father was deeply struck by his son's ability and gifted him a copy of Euclid’s Elements. Blaise read the book with all eagerness and soon mastered it.
At the age of 14, Blaise started attending weekly sessions, in which prominent geometricians including Roberval, Mersenne, Mydorge, Pierre Petit(young engineer), Gerard Desargues (mathematician and architect) and others met. These meetings laid the foundation for the French Academy. When Blaise was 16, he wrote an essay on conic sections. The young boy’s work was highly appreciated in the world of mathematics. It aroused the envy of none other than Rene Descartes, the great French rationalist and mathematician. Blaise was also introduced to Geometry as a seperate discipline. All volumes of arithmetic were intentionally removed from the house, so that he would focus on Geometry alone.
Towards the end of 1638, Etienne got into trouble with the authorities. He had truble over his investments in the Hotel de Ville. Richelieu in need of money had dispute with Etienne and his group who vociferosly protested against payments for waging war. He then fled alone to Clermont leaving his family behind. Worthy to note here is the commendable part played by Jacqueline (Blaize' sister) who performed Scudery's L'Amour Tyrannique with a cast under Mondory's direction, catching the attention of the Cardinal. Here again, Jacqueline introduced Blaize as a young genius in the making (which also attracted the attention of the authority) and alongwith Mondory's pleading was able to seek successfully a reprive from Etienne's near certain imprisonment. Etienne was thus recalled from hiding and given promotion reaching Rouen honorably to join his family.
In 1639, Blaise’s father was appointed a tax collector at Rouen. It was such a tough job that he could never sleep till two at night. Etienne would pour over voluminous figures copying and calculating into the night, ceaselessly. Blaise wanted to relieve his father from such tedium and therefore worked hard for three consequitive years finally inventing a calculating device. Blaise’s contemporaries regarded this machine, which he further improved. In 1652, he came out with the final standard workable model. It was placed for sale at 100 livres, a piece that is on exhibit at Paris Conservatoire des Arts et Metiers.This was his major claim to fame and all of it was achieved in his early twenties only.
From 1640 to 1646, Blaise lived in Rouen with his father. The Pascal family practised religion sincerely, regularly and unquestioningly; perhaps without notable fervor. Though born and raised a Catholic, at the age of 23, Blaise became a convert. The necessity of conversion – abandonment of the world and submission to God – became the foundation for life and work of Blaise Pascal.It is said that the only form of conflict between religion and science that Blaise would encounter in his own experience, would be the struggle between the two rival attractions.
Blaise continued his research. Through some ingenious experiments in physics, he demonstrated the existence of vacuum and the weight of air. It is pertinent to note that around 1645, Evangelista Torricelli had found that if a tube filled in mercury was inverted in a basin of mercury with the lower end open, the mercury in the tube would fall a certain distance. The two questions raised then were; what was in the emtpy space and why did the mercury fall so far and no further? It was a vacuum that was left in the tube that came to be known as the Torricellian Vacuum in honor of the scientist on which Pascal had proposed several scientific as well as dogmatic hypotheses. Simultaneously, he advanced the principles of modern philosophy and attempted to bridge the gap between science and metaphysics.
In 1647, Pascal’s health deteriorated due to his long labors on his arithmetical machine. Doctors advised him to avoid excessive mental strain. To receive proper treatment Pascal left Rouen for Paris. In Paris, friendships that developed with other intellectuals influenced Blaise and he began to grow as a ‘free-thinker’. During this period, he became a firm believer that the science of man is greater than the science of things.
Again, he continued his work and laid the groundwork for the Calculus of Probabilities. Between 1647 and 1651, Pascal did his most important research connected with the problem of vacuum. He published his preliminary conclusions in a pamphlet Nouvelles Experiences touchant le Vide in October 1647. After this, Pascal became a well-known experimentalist.
Blaise patented his invention of calculator, on which Leibnitz worked later. Blaise also invented the syringe, and refined Torricelli’s barometer. He created the hydraulic press, an instrument based upon the principles known today as Pascal’s Laws of Pressure.
In 1651, Pascal’s father died accidentally. Blaise' sister, Jacqueline entered the Jansenist convent at Port-Royal. The night of November 23, 1654 brought a change in Blaise’s life for he had two revelations. He had realized that his religious behavior had remained too intellectual and dry. He decided to join his sister Jacqueline in her retreat at Port-Royal. He decided to withdraw from mathematical pursuits and lead a life devoid of social affairs. He joined the battle of the Jansenists against the Jesuits of the Sorbonne, who had publicly denounced Arnauld, the Jansenist mathematician as a heretic.
Between 1656 and 1658 Pascal composed those works, which lay at the heart of his achievement. He completed The Provincial Letters. He also accumulated the requisite material for his Apology for Christianity, directed against the unbelievers. Though he had given up science after his second conversion in 1654, he came back to his abandoned work in 1657. His friends convinced him that the publication of another important discovery would add weight to his apologetic arguments.
Later, Pascal was afflicted with serious illness. This illness caused hinderence in his intellectual efforts. He thus sought refuge and turned towards mysticism and charity. In 1657 and 1658, he wrote apologetic notes with an intention to organize them into a book, but unfortunately these writings were published posthumously as Pensees .Thus, his work on Cycloid was published in 1658. This work provided the foundation for differential and integral calculus. It also laid the base for the Theory of Probability, one of the most important theories in mathematics.
Towards the end of his life, Pascal was rather a sick man suffering from severe pain. He withdrew himself from all creative activities and devoted himself to spiritualism. His illness rendered him capable only for a one last short writing, Prayer asking God to make good use of his illness. In this writing, he had expressed his ardent desire for an ultimate conversion. In his last days, this great mathematician attained spiritual ascension and sainthood. Eventually, on the midnight of August 17, 1662, Blaise Pascal who lived bachelors life, died young at the age of 39. His last words, as a reader of his Ecrits sur la Grace would expect, were – ‘May God never abandon me !’
Blaise Pascal, the French scientist was one of the most reputed Mathematician and Physicist of his time. Being a profound thinker, well ahead of his time, he also contributed immensely to the Christian literature.
Today, he is mainly known for his Theory of Probability and Pascal’s Law of Pressure. In later years, living a life of an ascetic, he wrote his famous Provincial Letters and Pensees, the former having gained a considerable acclaim as a classic in satire.
Pascal’s style was marked by originality and bereft of artifice. He impressed his readers presenting logical thoughts and through passionate force of his dialectics. Among contemporaries of Rene Descartes, the great thinker and mathematician, there was none who exhibited such a genius, as did Pascal. Pascal proved his strength in technical matters as well as in pure sciences. His invention of the first calculating machine paved way for present day calculators and computers. The computer language Pascal is named after this great man.
If Rene Descartes contribution be likened to a free flowing river that serves large tracts of barren land, irrigating and serving people and life all along its course, then Pascal's could be likened to a trickle of a river, a short way from its source to disappear underground, only to appear miles away on the other side of the mountain, probably unrecognised, to reappear in full power and fertilize a province.
June 19, 1623
Birth of Blaise Pascal in Clermont – Ferrand, France. 1626
Death of Blaise’s mother. 1631
His father Etienne moved to Paris with his three children. Blaise proved to be exceptional in mathematics. 1638
After opposing a fiscal measure of Richelieu, Etienne went into hiding, leaving his children in Paris. 1640
He wrote Essai Pour les Coniques. 1642
Blaise began to work on his calculating machine with an aim to assist his father in the computation of taxes. 1646 Pascal's first conversion as happening in the year. 1647
Visited by Rene Descartes and a discussion ensued on atmospheric pressure and the function of barometer. 1648
Wrote Treatise on Conic Sections, after returning to Clermont. 1650
Moved to Paris. November 23, 1654
He felt a two-hour ecstatic vision that led him to second conversion. January 7, 1655 He joined his sister Jacqueline at a retreat to Port-Royal.
He defended the great mathematician Arnauld against the Jesuits who tried to expel him. 1656
Appearance of the first of The Provincial Letters. 1658
Lectures on his apologetics to the leaders of the convent Port-Royal. 1659
Became ill.
August 17, 1662
He died in his sister Gilberte' house at midnight, in Paris.
Major works of Blaise Pascal are listed below :
1640 ESSAY ON CONIC SECTIONS 1647 EXPERIMENTS CONCERNING VACUUM 1648 THE GENERATION OF CONIC SECTIONS 1653 TREATISE ON THE ARITHMETICAL TRIANGLE 1653 TREATISE ON THE EQUILIBRIUM OF LIQUIDS 1654 THEORY OF PROBABILITY 1656-57 PROVINCIAL LETTERS 1657-59 PENSEES 1658 CYCLOID
ESSAY ON CONIC SECTIONS
At the age of 16, Pascal wrote an essay on the sections of a cone, called Treatise on Conic Sections, which includes his famous theorem of hexagons. Today this essay is known as Pascal’s Theorem. Pascal’s essay was much praised, not only within his circle, but also beyond the boundaries of Paris. For this pure mathematical work, he was considered as one of the great scientific minds of those times.
His early essay on the Geometry of Conics written in 1640, had not been published till 1779. It was an essay which mentioned important and interesting results of his theorem. The first theorem, known now as Pascal’s theorem explains that if a hexagon be inscribed in a conic, the points of intersection of the opposite sides will lie in a straight line. The second theorem explains that if a quadrilateral were to be inscribed in a conic, and a straight line be drawn cutting the sides taken in order at the points A, B, C and D, and if the conic in P and Q, then the equation is :
PA x PC : PB x PD = QA x QC : QB x QD.
FIRST 'DIGITAL' CALCULATOR
Pascal gained fame early in his life with his work on conic sections. Pascal proved his genius in technical matters in 1645, when he invented the first calculating machine. He worked on it for three years, from 1642 to 1645. The automatic device, which he invented to help his father in his work of calculating taxes, was called the Pascaline. It closely resembled the first popular calculator of 1940. Pascal was the second person to have invented a calculator for it was Schickard who had manufactured the first one in 1624.
Pascal had to face some problems in designing the calculator because at that time, the pattern of the French currency was strange. There were 20 sols in a livre and 12 deniers in a sol; a similar pattern had lasted in Britain till as late as 1971, while in France it expired in 1799. Pascal had to work hard to solve the technical problems. He took patent on his invention and started mass production in 1642. However, Adamson has noted, "By 1652, 50 prototypes had been produced, but few machines were sold and manufacture of Pascal’s arithmetical calculator ceased in that year."
Whatever the hurdles, Pascal’s machine was regarded as the first digital calculator. Very humbly, Pascal dedicated the machine to the chancellor of France, Pierre Siguier, in 1644.
EXPERIMENTS AS A PHYSICIST
Pascal was perhaps the first scientist who felt the necessity of turning away entirely from the world, towards God. He gave up his scientific researches and persuits for a year and spent that time as a spiritual adviser to his family. But the conflict between the scientist and the ascetic personality was not resolved. Eventually, the scientist won and Pascal forayed into the researches in 1647. He worked on the theories of Galileo Galilei and Evangelista Torricelli, an Italian physicist who discovered the principle of the barometer, as discussed earlier. Pascal began a series of experiments on atmospheric pressure. By the end of the year, he could prove that vacuum undoubtedly existed. On September 23, Rene Descartes visited him; he did not accept Pascal’s discovery. He disgracefully mentioned in a letter to Huygens, that Pascal has too many vacuums in his head.
But Pascal was not the one to give up and he continued his experiments on atmospheric pressure by constructing mercury barometers and measuring air pressure. He carried out some of his experiments on the top of the mountain of Puy de Dome. The tests opened the doors for further studies in hydrodynamics and hydrostatics. Pascal invented the syringe and created the hydraulic press. The instrument was based upon the principle that became known as Pascal’s Law of Pressure. The law states, Pressure applied to a confined liquid is transmitted undiminished through the liquid in all directions regardless of the area to which the pressure is applied.
Pascal explained his law of pressure in his Treatise on the Equilibrium of Liquids, in 1653. As Adamson writes, "This treatise is a complete outline of a system of hydrostatics, the first in the history of science, it embodies his most distinctive and important contribution to physical theory."
THEORY OF PROBABILITY
While corresponding with Fermat in 1654, Pascal laid the foundation for the Theory of Probability. As a mathematician Pascal is best known for his principles of the theory of probabilities. The root cause for this invention was a problem proposed by a gamester, the Chevalier de Mere. The problem was : Two players of equal skill want to leave the table before completion of the game. Their scores and the number of points, which constitute the game being given, it is desired to find in what proportion they should divide the stakes. Pascal communicated the problem to Fermat. Both agreed on the same solution. Pascal proceeded next to concentrate on such similar problems. The general solution was obtained by using the arithmetical triangle. Pascal’s results match the general solution available in the textbooks on algebra.
TREATISE ON THE ARITHMETICAL TRIANGLE
Pascal employed his arithmetical triangle in 1653, but it had remained unpublished till 1665. Although Pascal was not the first to study this triangle, his work on the topic in Treatise on the Arithmetical Triangle was the most important. His work on binomial coefficients helped Isaac Newton in his discovery of the general binomial theorem for fractional and negative powers.
Pascal’s triangle is constructed as in the figure given below. Each horizontal line being formed from the one above it, by making every number in it equal to the sum of those above and to the left of it in the row immediately above it. For an example, the fourth number in the fourth line, 20, is equal to 1 + 3 + 6 + 10.
PROVINCIAL LETTERS :
Pascal’s two masterpieces are the Provincial Letters and Pensees. In spite of its lucidity and perfection, Pascal’s Provincial Letters is a complex work. Even critics have often missed its significance. It is the work of an ingenious mind living in an intellectual environment.
Provincial Letters is written in a form of 18 letters, and aims to defend Pascal’s friend Antoine Arnauld. Arnauld was an opponent of the Jesuits and a defender of Jansenism, who was on trial in Paris for his controversial religious works.
The Provincial Letters greatly influenced the general life of the Church. It provoked a widespread reaction against a lax moral theology. It played a very great part in the subsequent cultural history of France by influencing the ‘Freethinkers’ of that time.
The Jesuits of the 17th century did aim at a moral ideal, whereas Pascal demanded a certain healthy disquiet in the soul, a perpetual quest for moral truth. Thus, Pascal and the Jesuits had a debate. An eminent Jesuit, Father de Montcheuil once said, "Not to wish to make further progress is enough in itself to constitute sin. But for Pascal, not to wish to make further progress was – ‘the sincere search for truth", or in other words, ‘the love of God’.
Nevertheless the Provincial Letters remains an eagerly polemical work, which has established Pascal as a polemical author.
CYCLOID
Cycloid is Pascal’s last work in mathematics. The cycloid is the curve traced out by a point on the circumference of a circular hoop, which rolls along a straight line. It was Galileo who first concentrated on this curve in 1630, and suggested that the arches of bridges should be built in this form. In 1634, Roberval found the area of the cycloid. Later, Descartes and Fermat worked on it. Several questions connected with the curve, as well as with the surface and volume generated by its revolution about its axis, base and the tangent were proposed by many mathematicians. Eventually, Pascal could solve these and solved other questions related to the positions of the centres of the mass of the solids formed in 1658. It was Wallis, who succeeded in solving all the rest of the questions leaving those related with the center of mass. Pascal’s own solutions are influenced by the method of indivisibles. According to D’Alembert, Pascal’s researches including the geometry of the Archimedian spiral form a connecting linkage between the geometry of Archimedes and the infinitesimal calculus of Isaac Newton.
PENSEES
Pascal has left many manuscripts behind. Amongst these, the most important is the work of Christian apologetic. The first editors of these manuscripts have published it under the title of Pensees, in 1670.
Pensees is the most famous religious work. It is a collection of personal thoughts on human suffering and faith in God. Pensees is written, in the autumn of Pascal’s life, during 1657 to 1659. It is the first example of the religious writing, which is characteristic of the best French literature.
Pensees includes a thousand of fragmented pieces of writings. Sometime, a portion of argument is fully elaborated, while the other time; a thought is slightly touched upon. Though left unfinished, Pensees’s tone is such that would make a reader feel intimate with Pascal.
A few good lines from the Pensees follow:
I lay it down as a fact that if all men knew what others say of them, there would not be four friends left in the world.
It is the heart, which perceives God and not the reason.
One nature consists in movement, absolute rest in death.
We are usually convinced more easily by reasons we have found ourselves than by those which have occurred to others.
When the passions become masters, they are vices.
• Man is but a reed, the weakest in nature, but he is a thinking reed.
• Man’s greatness lies in his power of thought.
• Things are always at their best in their beginning.
• Most of the evils of life arise from man’s being unable to sit still in a room.
• Animals do not admire each other. A horse does not admire its companion.
• There are two types of mind… the mathematical, and what might be called the intuitive. The former arrives at its views slowly, but they are firm and rigid; the latter is endowed with greater flexibility and applies itself simultaneously to the diverse lovable parts of that which it loves.
• Habit is the second nature which destroys the first.
• The last thing one discovers in composing a work is what to put first.
• Kind words do not cost much. Yet they accomplish much.
• To go beyond the bounds of moderation is to outrage humanity.
• One must know oneself. If this does not serve to discover truth, it at least serves as a rule of life and there is nothing better.
• I maintain that, if everyone knew what others said about him, there would not be four friends in the world.
• When we play tennis, we both play with the same ball, but one of us places it better.
• Man finds nothing so intolerable as to be in a state of complete rest, without passions, without occupation, without diversion, without effort.
• Earnestness is enthusiasm tempered by reason.
• What a chimera, then, is man ! What a novelty, what a monster, what a chaos, what a subject of contradiction, what a prodigy ! A judge of all things, feeble worm of the earth, depository of the truth, cloaca of uncertainty and error, the glory and the shame of the universe !
• Do you wish people to believe good of you ? Don’t speak.
• Man is full of desires : he loves only those who can satisfy them all.
• Everything that is written merely to please the author is worthless.
