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Blaise Pascal
Born: 19 June 1623 in Clermont
(now Clermont-Ferrand), Auvergne, France
Died: 19 Aug 1662 in Paris, France
Blaise Pascal was the third of Étienne
Pascal's children and his only son. Blaise's mother died when
he was only three years old. In 1632 the Pascal family, Étienne
and his four children, left Clermont and settled in Paris.
Blaise Pascal's father had unorthodox educational views and
decided to teach his son himself. Étienne Pascal decided
that Blaise was not to study mathematics before the age of
15 and all mathematics texts were removed from their house.
Blaise 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 Blaise
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.
In December 1639 the 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 but, as Adamson writes ,
By 1652 fifty prototypes had been produced,
but few machines were sold, and manufacture of Pascal's arithmetical
calculator ceased in that year.
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.
From about this time 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. Descartes wrote, rather cruelly, in a letter to Huygens
after this visit that Pascal
...has too much vacuum in his head.
In August of 1648 Pascal observed that the
pressure of the atmosphere decreases with height and deduced
that a vacuum existed above the atmosphere. Descartes wrote
to Carcavi in June 1647 about Pascal's experiments saying:-
It was I who two years ago advised him to
do it, for although I have not performed it myself, I did
not doubt of its success ...
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.
Étienne Pascal died in September 1651
and following this Blaise 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. 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.
He 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.
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.
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.
Through the period of this correspondence
Pascal was unwell. In one of the letters to Fermat written
in July 1654 he writes
... though I am still bedridden, I must tell
you that yesterday evening I was given your letter.
However, despite his health problems, he worked
intensely on scientific and mathematical questions until October
1654. Sometime around then 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 defence 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.
With 'Pascal's wager' he uses probabilistic
and mathematical arguments but his main conclusion is that
...we are compelled to gamble...
His 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.
Pascal died at the age of 39 in intense pain
after a malignant growth in his stomach spread to the brain.
He is described in [3] as:-
... a man of slight build with a loud voice
and somewhat overbearing manner. ... he lived most of his
adult life in great pain. He had always been in delicate health,
suffering even in his youth from migraine ...
His character is described as:-
... precocious, stubbornly persevering, a
perfectionist, pugnacious to the point of bullying ruthlessness
yet seeking to be meek and humble ...
In
the following assessment is given:-
At once a physicist, a mathematician, an eloquent
publicist in the Provinciales ... Pascal was embarrassed by
the very abundance of his talents. It has been suggested that
it was his too concrete turn of mind that prevented his discovering
the infinitesimal calculus, and in some of the Provinciales
the mysterious relations of human beings with God are treated
as if they were a geometrical problem. But these considerations
are far outweighed by the profit that he drew from the multiplicity
of his gifts, his religious writings are rigorous because
of his scientific training...
- J J O'Connor and E F Robertson |
