HISTORY AND BACKGROUND OF ‘’BLAISE
PASCAL’
BLAISE PASCAL
Blaise Pascal 1642
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Born
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19 June 1623
Clermont-Ferrand, Auvergne, France |
Died
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Residence
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France
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Nationality
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French
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Era
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17th-century
philosophy
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Region
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Western
philosophy
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Religion
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Roman Catholic
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Jansenism
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Proto-existentialism
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Main interests
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Theology
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Mathematics
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Philosophy
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Physics
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Notable ideas
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Pascal's Wager
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Pascal's
triangle
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Pascal's law, Pascal's
theorem
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Blaise Pascal (French: [blɛz paskal]; 19 June 1623 – 19 August
1662) was a French mathematician, physicist, inventor, writer and Christian philosopher. He was a child prodigy who was educated by his father, a tax
collector in Rouen. Pascal's earliest work
was in the natural and applied sciences where he made important contributions
to the study of fluids, and clarified the
concepts of pressure and vacuum by generalizing the
work ofEvangelista Torricelli. Pascal also wrote in
defense of the scientific method.
In 1642, while still a teenager, he started
some pioneering work on calculating machines. After three years of effort and
fifty prototypes, he invented the mechanical calculator. He built 20 of these
machines (called pascal's calculator and later pascaline)
in the following ten years.7 Pascal was an important mathematician,
helping create two major new areas of research: he wrote a significant treatise
on the subject of projective geometry at the age of 16, and
later corresponded with Pierre de Fermat on probability theory, strongly influencing the
development of modern economics andsocial science. Following Galileo and Torricelli, in 1646 he refuted Aristotle's followers who insisted that nature abhors a vacuum. Pascal's results caused
many disputes before being accepted.
In 1646, he and his sister Jacqueline
identified with the religious movement within Catholicism known by its detractors as Jansenism. His father died in 1651. Following
a mystical experience in late 1654, he had his
"second conversion", abandoned his scientific work, and devoted
himself to philosophy and theology. His two most famous works date from this
period: the Lettres provinciales and the Pensées, the former set in the conflict between
Jansenists and Jesuits. In this year, he also
wrote an important treatise on the arithmetical triangle. Between 1658 and 1659
he wrote on thecycloid and its use in
calculating the volume of solids.
Pascal had poor health especially after his
18th year and his death came just two months after his 39th birthday.
Early life and education
Pascal was born in Clermont-Ferrand; he lost his mother, Antoinette Begon, at
the age of three. His father, Étienne Pascal (1588–1651), who also had an interest
in science and mathematics, was a local judge and member of the "Noblesse de Robe". Pascal had two
sisters, the younger Jacqueline and the elder Gilberte.
In 1631, five years after the death of his
wife, Étienne Pascal moved with his children to Paris. The newly arrived
family soon hired Louise Delfault, a maid who eventually became an instrumental
member of the family. Étienne, who never remarried, decided that he alone would
educate his children, for they all showed extraordinary intellectual ability,
particularly his son Blaise. The young Pascal showed an amazing aptitude for
mathematics and science.
Particularly of interest to Pascal was a work
of Desargues on conic sections. Following Desargues' thinking, the
16-year-old Pascal produced, as a means of proof, a short treatise on what was
called the "Mystic Hexagram", Essai pour les coniques ("Essay
on Conics") and sent it—his first serious work of mathematics—to Père Mersenne in Paris; it is known still today
as Pascal's theorem. It states that if a
hexagon is inscribed in a circle (or conic) then the three intersection points
of opposite sides lie on a line (called the Pascal line).
Pascal's work was so precocious that
Descartes was convinced that Pascal's father had written it. When assured by
Mersenne that it was, indeed, the product of the son not the father, Descartes
dismissed it with a sniff: "I do not find it strange that he has offered
demonstrations about conics more appropriate than those of the ancients,"
adding, "but other matters related to this subject can be proposed that
would scarcely occur to a 16-year-old child."
In France at that time offices and positions
could be—and were—bought and sold. In 1631 Étienne sold his position as second
president of the Cour des Aides for 65,665 livres. The money was
invested in a government bond which provided if not
a lavish then certainly a comfortable income which allowed the Pascal family to
move to, and enjoy, Paris. But in 1638 Richelieu, desperate for money to carry
on the Thirty Years' War, defaulted on the government's
bonds. Suddenly Étienne Pascal's worth had dropped from nearly 66,000 livres to
less than 7,300.
Like so many others, Étienne was eventually
forced to flee Paris because of his opposition to the fiscal policies of Cardinal Richelieu, leaving his three
children in the care of his neighbor Madame Sainctot, a great beauty with an
infamous past who kept one of the most glittering and intellectual salons in
all France. It was only when Jacqueline performed well in a children's play
with Richelieu in attendance that Étienne was pardoned. In time Étienne was
back in good graces with the cardinal, and in 1639 had been appointed the
king's commissioner of taxes in the city of Rouen — a city whose tax
records, thanks to uprisings, were in utter chaos.
In 1642, in an effort to ease his father's
endless, exhausting calculations, and recalculations, of taxes owed and paid,
Pascal, not yet 19, constructed a mechanical calculator capable of addition and
subtraction, called Pascal's calculator or the Pascaline.
The Musée des Arts
et Métiers in
Paris and theZwinger museum in Dresden, Germany, exhibit two of his original mechanical calculators.
Though these machines are early forerunners to computer engineering, the calculator failed to
be a great commercial success. Because it was extraordinarily expensive
the Pascaline became little more
than a toy, and status symbol, for the very rich both in
France and throughout Europe. However, Pascal continued to make improvements to
his design through the next decade and built 20 machines in total.
Contributions to
mathematics
Pascal's triangle. Each number is the sum of
the two directly above it. The triangle demonstrates many mathematical
properties in addition to showing binomial coefficients.
Pascal continued to influence mathematics throughout
his life. His Traité du triangle arithmétique ("Treatise
on the Arithmetical Triangle") of 1653 described a convenient tabular
presentation for binomial coefficients, now called Pascal's triangle. The triangle can also be
represented:
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He defines the numbers in the triangle
by recursion: Call the number in the
(m+1)st row and (n+1)st column tmn. Then tmn = tm-1,n +
tm,n-1, for m = 0, 1, 2... and n = 0, 1, 2... The boundary
conditions are tm, −1 = 0, t−1, n = 0 for m =
1, 2, 3... and n = 1, 2, 3... The generator t00 = 1. Pascal
concludes with the proof,
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. From this discussion, the notion
of expected value was introduced.
Pascal later (in the Pensées) used a probabilistic argument, Pascal's Wager, to justify belief in God and a virtuous life.
The work done by Fermat and Pascal into the calculus of probabilities laid
important groundwork for Leibniz' formulation of theinfinitesimal calculus.
After a religious
experience in 1654, Pascal mostly gave up work in mathematics.
Philosophy of mathematics
Pascal's major contribution
to the philosophy of
mathematics came
with his De l'Esprit géométrique ("Of the Geometrical Spirit"),
originally written as a preface to a geometry textbook for one of the famous
"Petites-Ecoles
de Port-Royal"
("Little Schools of Port-Royal"). The work was unpublished until over a
century after his death. Here, Pascal looked into the issue of discovering
truths, arguing that the ideal of such a method would be to found all
propositions on already established truths. At the same time, however, he
claimed this was impossible because such established truths would require other
truths to back them up—first principles, therefore, cannot be reached. Based on
this, Pascal argued that the procedure used in geometry was as perfect as possible,
with certain principles assumed and other propositions developed from them.
Nevertheless, there was no way to know the assumed principles to be true.
Pascal also used De
l'Esprit géométrique to develop a theory of definition. He distinguished between definitions which
are conventional labels defined by the writer and definitions which are within
the language and understood by everyone because they naturally designate their
referent. The second type would be characteristic of the philosophy of essentialism. Pascal claimed that only definitions of the
first type were important to science and mathematics, arguing that those fields
should adopt the philosophy of formalism as formulated by
Descartes.
In De l'Art de
persuader ("On the Art of Persuasion"), Pascal looked deeper
into geometry's axiomatic method, specifically the question of how people
come to be convinced of the axioms upon which later
conclusions are based. Pascal agreed with Montaigne that achieving certainty in these
axioms and conclusions through human methods is impossible. He asserted that these
principles can be grasped only through intuition, and that this fact
underscored the necessity for submission to God in searching out
truths.
Contributions
to the physical sciences
Portrait
of Pascal
Pascal's work in the fields
of the study of hydrodynamics and hydrostatics centered on the principles ofhydraulic fluids. His inventions include the hydraulic press (using hydraulic pressure to multiply
force) and the syringe. He proved that
hydrostatic pressure depends not on the weight of the fluid but on the
elevation difference. He demonstrated this principle by attaching a thin tube
to a barrel full of water and filling the tube with water up to the level of
the third floor of a building. This caused the barrel to leak, in what became
known as Pascal's barrel experiment. By 1646,
Pascal had learned of Evangelista Torricelli's experimentation withbarometers. Having replicated an experiment that
involved placing a tube filled with mercury upside down in a bowl of mercury,
Pascal questioned what force kept some mercury in the tube and what filled the
space above the mercury in the tube. At the time, most scientists contended
that, rather than a vacuum, some invisible matter was
present. This was based on the Aristotelian notion that creation was a thing of
substance, whether visible or invisible; and that this substance was forever in
motion. Furthermore, "Everything that is in motion must be moved by
something," Aristotle declared. Therefore,
to the Aristotelian trained scientists of Pascal's time, a vacuum was an
impossibility. How so? As proof it was pointed out:
·
Light
passed through the so-called "vacuum" in the glass tube.
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Aristotle
wrote how everything moved, and must be moved by something.
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Therefore,
since there had to be an invisible "something" to move the light
through the glass tube, there was no vacuum in the tube. Not in the glass tube
or anywhere else. Vacuums – the absence of any and everything – were simply an
impossibility.
Following more
experimentation in this vein, in 1647 Pascal produced Experiences
nouvelles touchant le vide ("New Experiments with the
Vacuum"), which detailed basic rules describing to what degree various
liquids could be supported by air pressure. It also provided reasons why it was
indeed a vacuum above the column of liquid in a barometer tube.
On 19 September 1648, after
many months of Pascal's friendly but insistent prodding, Florin
Périer,
husband of Pascal's elder sister Gilberte, was finally able to carry out the
fact-finding mission vital to Pascal's theory. The account, written by Périer,
reads:
"The
weather was chancy last Saturday...[but] around five o'clock that morning...the Puy-de-Dôme was visible...so I decided to give it a
try. Several important people of the city ofClermont had asked me to let them know when I
would make the ascent...I was delighted to have them with me in this great
work... "...at eight o'clock we met in the gardens of the Minim Fathers,
which has the lowest elevation in town....First I poured 16 pounds of quicksilver...into a vessel...then took several glass
tubes...each four feet long and hermetically sealed at one end and opened at the
other...then placed them in the vessel [of quicksilver]...I found the quick
silver stood at 26" and 3½ lines above the quicksilver in the vessel...I
repeated the experiment two more times while standing in the same spot...[they]
produced the same result each time... "I attached one of the tubes to the
vessel and marked the height of the quicksilver and...asked Father Chastin, one
of the Minim Brothers...to watch if any changes should occur through the
day...Taking the other tube and a portion of the quick silver...I walked to the
top of Puy-de-Dôme, about 500 fathoms higher than the monastery, where upon
experiment...found that the quicksilver reached a height of only 23" and 2
lines...I repeated the experiment five times with care...each at different
points on the summit...found the same height of quicksilver...in each
case..."
Pascal replicated the
experiment in Paris by carrying a barometer up to the top of the bell tower at
the church of Saint-Jacques-de-la-Boucherie, a height of about fifty
meters. The mercury dropped two lines.
In the face of criticism
that some invisible matter must exist in Pascal's empty space, Pascal, in his
reply to Estienne
Noel,
gave one of the 17th century's major statements on the scientific method, which
is a striking anticipation of the idea popularised by Karl Popper that scientific theories are
characterised by their falsifiability: "In order to show that a hypothesis is
evident, it does not suffice that all the phenomena follow from it; instead, if
it leads to something contrary to a single one of the phenomena, that suffices
to establish its falsity." His insistence on the existence of the
vacuum also led to conflict with other prominent scientists, including
Descartes.
Pascal introduced a
primitive form of roulette and the roulette
wheel in the 17th century in his search for a perpetual motion machine.
Adult
life, religion, philosophy, and literature
For
after all what is man in nature? A nothing in relation to infinity, all in
relation to nothing, a central point between nothing and all and infinitely far
from understanding either. The ends of things and their beginnings are
impregnably concealed from him in an impenetrable secret. He is equally
incapable of seeing the nothingness out of which he was drawn and the infinite
in which he is engulfed.
Blaise
Pascal, Pensées #72
Religious conversion
In the winter of 1646,
Pascal's 58 year-old father broke his hip when he slipped and fell on an icy
street of Rouen; given the man's age and the state of medicine in the 17th
century, a broken hip could be a very
serious condition, perhaps even fatal. Rouen was home to two of the finest
doctors in France: Monsieur Doctor Deslandes and Monsieur Doctor de La
Bouteillerie. The elder Pascal "would not let anyone other than these men
attend him...It was a good choice, for the old man survived and was able to walk
again..." But treatment and rehabilitation took three months, during
which time La Bouteillerie and Deslandes had become household guests.
Both men were followers
of Jean
Guillebert,
proponent of a splinter group from the main body of Catholic teaching known
as Jansenism. This still fairly small
sect was making surprising inroads into the French Catholic community at that
time. It espoused rigorous Augustinism. Blaise spoke with the doctors frequently,
and upon his successful treatment of Étienne, borrowed works by Jansenist
authors from them. In this period, Pascal experienced a sort of "first
conversion" and began to write on theological subjects in the course of
the following year.
Pascal fell away from this
initial religious engagement and experienced a few years of what some
biographers have called his "worldly period" (1648–54). His father
died in 1651 and left his inheritance to Pascal and Jacqueline, of which Pascal
acted as her conservator. Jacqueline announced that she would soon become
a postulant in the Jansenist convent of Port-Royal. Pascal was deeply
affected and very sad, not because of her choice, but because of his chronic
poor health; he too needed her.
"Suddenly
there was war in the Pascal household. Blaise pleaded with Jacqueline not to
leave, but she was adamant. He commanded her to stay, but that didn't work,
either. At the heart of this was...Blaise's fear of abandonment...if Jacqueline
entered Port-Royal, she would have to leave her inheritance behind...[but]
nothing would change her mind."
By the end of October in
1651, a truce had been reached between brother and sister. In return for a
healthy annual stipend, Jacqueline signed over her part of the inheritance to
her brother. Gilberte had already been given her inheritance in the form of a
dowry. In early January, Jacqueline left for Port-Royal. On that day, according
to Gilberte concerning her brother, "He retired very sadly to his rooms
without seeing Jacqueline, who was waiting in the little parlor..." In
early June 1653, after what must have seemed like endless badgering from
Jacqueline, Pascal formally signed over the whole of his sister's inheritance
to Port-Royal, which, to him, "had begun to smell like a cult." With
two-thirds of his father's estate now gone, the 29 year old Pascal was now
consigned to genteel poverty.
For a while, Pascal pursued
the life of a bachelor. During visits to his sister at Port-Royal in 1654, he
displayed contempt for affairs of the world but was not drawn to God.
Brush with death
On 23 November 1654, between 10:30 and 12:30
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 the scholars..." and
concluded by quoting Psalm 119:16: "I will not forget thy word.
Amen." He seems to have carefully sewn this document into his coat and
always transferred it when he changed clothes; a servant discovered it only by chance
after his death. This piece is now known as the Memorial. The
story of the carriage accident as having led to the experience described
in the Memorial is disputed by some scholars. His belief
and religious commitment revitalized, Pascal visited the older of two convents
at Port-Royal for a two-week
retreat in January 1655. For the next four years, he regularly travelled
between Port-Royal and Paris. It was at this point immediately after his
conversion when he began writing his first major literary work on religion,
the Provincial Letters.
The Provincial
Letters
Beginning in 1656, Pascal
published his memorable attack on casuistry, a popular ethical method used by Catholic thinkers in the early
modern period (especially theJesuits, and in particular Antonio Escobar). Pascal denounced casuistry
as the mere use of complex reasoning to justify moral laxity and all sorts
of sins. The 18-letter series was published between 1656 and
1657 under the pseudonym Louis de Montalte and incensed Louis XIV. The king ordered that the
book be shredded and burnt in 1660. In 1661, in the midsts of the formulary controversy, the Jansenist school at
Port-Royal was condemned and closed down; those involved with the school had to
sign a 1656 papal bull condemning the
teachings of Jansen as heretical. The final letter from Pascal, in 1657, had
defied Alexander VII himself. Even Pope
Alexander, while publicly opposing them, nonetheless was persuaded by Pascal's
arguments.
Aside from their religious
influence, the Provincial Letters were popular as a literary
work. Pascal's use of humor, mockery, and vicious satire in his arguments made
the letters ripe for public consumption, and influenced the prose of later
French writers like Voltaire and Jean-Jacques Rousseau.
Wide praise has been given
to the Provincial Letters.
The Pensées
Pascal's most influential
theological work, referred to posthumously as the Pensées ("Thoughts"),
was not completed before his death. It was to have been a sustained and
coherent examination and defense of the Christian faith, with the original title Apologie de
la religion Chrétienne ("Defense of the Christian Religion").
The first version of the numerous scraps of paper found after his death
appeared in print as a book in 1669 titled Pensées de M. Pascal sur la
religion, et sur quelques autres sujets ("Thoughts of M. Pascal
on religion, and on some other subjects") and soon thereafter became a
classic. One of the Apologie's main strategies was to use the
contradictory philosophies of skepticism and stoicism, personalized by Montaigne on one hand, and Epictetus on the other, in order to bring the
unbeliever to such despair and confusion that he would embrace God.
Pascal's Pensées is
widely considered to be a masterpiece, and a landmark in French prose. When
commenting on one particular section (Thought #72), Sainte-Beuve praised it as the finest pages in the
French language. Will Durant hailed it as
"the most eloquent book in French prose." In Pensées,
Pascal surveys several philosophical paradoxes: infinity and nothing, faith and
reason, soul and matter, death and life, meaning and vanity—seemingly arriving
at no definitive conclusions besides humility, ignorance, and grace. Rolling
these into one he develops Pascal's Wager.
Last works and death
T. S. Eliot described him during this phase of his
life as "a man of the world among ascetics, and an ascetic among men of
the world." Pascal's ascetic lifestyle derived from a belief that it was
natural and necessary for a person to suffer. In 1659, Pascal fell seriously
ill. During his last years, he frequently tried to reject the ministrations of
his doctors, saying, "Sickness is the natural state of Christians."
Louis XIV suppressed the
Jansenist movement at Port-Royal in 1661. In response, Pascal wrote one of his
final works, Écrit sur la signature du formulaire ("Writ
on the Signing of the Form"), exhorting the Jansenists not to give in.
Later that year, his sister Jacqueline died, which convinced Pascal to cease
his polemics on Jansenism. Pascal's last major achievement, returning
to his mechanical genius, was inaugurating perhaps the firstbus line, moving
passengers within Paris in a carriage with many seats.
In 1662, Pascal's illness
became more violent, and his emotional condition had severely worsened since
his sister's death, which happened the previous year. Aware that his health was
fading quickly, he sought a move to the hospital for incurable diseases, but
his doctors declared that he was too unstable to be carried. In Paris on 18
August 1662, Pascal went into convulsions and received extreme unction. He died the next morning, his last words
being "May God never abandon me," and was buried in the cemetery
of Saint-Étienne-du-Mont.
An autopsy performed after his death revealed grave problems
with his stomach and other organs of his abdomen, along with damage to his brain. Despite the autopsy, the cause of his poor
health was never precisely determined, though speculation focuses on tuberculosis, stomach cancer, or a combination of the two. The
headaches which afflicted Pascal are generally attributed to his brain lesion.
Legacy
In honor of his scientific
contributions, the name Pascal has been given to the SI unit of pressure, to aprogramming
language,
and Pascal's law (an important
principle of hydrostatics), and as mentioned above, Pascal's triangle and
Pascal's wager still bear his name.
Pascal's development of
probability theory was his most influential contribution to
mathematics. Originally applied to gambling, today it is extremely important in economics, especially in actuarial science. John Ross writes, "Probability theory
and the discoveries following it changed the way we regard uncertainty, risk,
decision-making, and an individual's and society's ability to influence the
course of future events." However, it should be
noted that Pascal and Fermat, though doing important early work in probability theory,
did not develop the field very far. Christiaan Huygens, learning of the subject
from the correspondence of Pascal and Fermat, wrote the first book on the
subject. Later figures who continued the development of the theory
include Abraham de Moivre and Pierre-Simon Laplace.
In literature, Pascal is
regarded as one of the most important authors of the French Classical Period
and is read today as one of the greatest masters of French prose. His use of
satire and wit influenced later polemicists. The content of his literary work is best
remembered for its strong opposition to therationalism of René Descartes and simultaneous assertion that the
main countervailing philosophy, empiricism, was also insufficient for determining major
truths.
In France, prestigious
annual awards, Blaise Pascal Chairs are given to
outstanding international scientists to conduct their research in the Ile de France region. One of the
Universities of Clermont-Ferrand, France – Université Blaise Pascal – is named after him.
The University of Waterloo, Ontario, Canada, holds an annual math contest named in his
honour.
Roberto Rossellini directed a filmed
biopic (entitled Blaise Pascal) which originally aired on Italian
television in 1971. Pascal was a subject of the first edition of the
1984 BBC Twodocumentary, Sea of Faith, presented by Don Cupitt.
Works
·
Essai pour les coniques (1639)
·
Experiences nouvelles touchant le vide (1647)
·
Traité du triangle arithmétique (1653)
·
De l'Esprit géométrique (1657 or 1658)
·
Écrit sur la signature du formulaire (1661)
References
2.
^Marguin, Jean (1994).Histoire des instruments et
machines à calculer,trois siècles de mécanique pensante
4.
^ Mourlevat, Guy (1988). Les machines arithmétiques
de Blaise Pascal (in fr). Clermont-Ferrand: La Française
d'Edition et
d'Imprimerie. p. 12.
Further
reading
·
Adamson, Donald. Blaise Pascal: Mathematician,
Physicist, and Thinker about God (1995) ISBN 0-333-55036-6
·
Adamson,
Donald."Pascal's Views on Mathematics and the Divine,"Mathematics and the
Divine:A Historical Study (eds.T.
Koetsier
and L. Bergmans. Amsterdam: Elsevier 2005), pp. 407–21.
·
Davidson,
Hugh M. Blaise Pascal. (Boston: Twayne Publishers), 1983.
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