Archive from December, 2012

Blaise Pascal

The French scientist and philosopher Blaise Pascal (1623 1662) was a precocious and influential
mathematical writer, a master of the French language and a great religious philosopher.

Blaise Pascal was born at Clermont Ferrand on June 19, 1623. He was the son of Etienne Pascal, king’s counselor and later president of the Court of Aids at Clermont. Blaise’s mother died in 1626, and he was left with his two sisters, Gilberte and Jacqueline. In 1631 the family moved to Paris.

Young Geometer
When Pascal was 12, he began attending meetings of a mathematical academy. His father taught him languages, especially Latin and Greek, but not mathematics. This ban on mathematics merely served to whet the boy’s curiosity. He experimented with geometrical figures, inventing his own names for standard geometrical terms.

In 1640 the Pascal family moved to Rouen. There, still taught mainly by his father, Blaise worked with such intensity that his health deteriorated. Nevertheless, he had arrived at one of the most beautiful theorems in geometry.

Sometimes called by him his “mystic hexagram” it is a theorem concerned with the collinearity of intersections of lines. It does not concern metrical properties of figures but is, in fact, at the very foundation of an important, and at the time almost entirely undeveloped, branch of mathematics — projective geometry. Pascal then set to work on a book, Essay on Conics, finished in 1640, in which the mystics hexagram was given central importance. It contained several hundred propositions on conitc sections, bringing the work of Apollonius and his successors, and was remarkable not only because of the writer’s age (16) but also because of its treatment of tangency, among other things.

Jansenists and Port Royal
In 1646 Pascal’s father had an accident and was confined to his house. He was visited by some neighbors who were Jansenists, a group formed by Cornelis Jansen, a Dutch-born professor of theology at Louvain. Their beliefs were contrary to the teachings of the Jesuits. The Pascals came under the influence of the Jansenists, with resultant fierce opposition to, and from, the Jesuits. Jacqueline wish to join the Jansenist convent at Port Royal. Etienne Pascal disliked the idea and took the family away to Paris, but after his death in 1651 Jacqueline joined Port Royal. Pascal still enjoyed a more worldly life, having a number of aristocratic friends and a little more money to spend from his patrimony. In 1614, however, he was completely converted to Jansenism, and he commenced an austere life at Port Royal.

Provincial Letters
In 1655 Antoine Arnauld, a prolific writer in defense of Jansen, was formally condemned by the Sorbonne for heretical teaching, and Pascal took up his defense in the first part of the famous Provincial Letters. Their framework is that of a correspondence between a Parisian and a friend in the provinces from Jan. 13, 1656, to March 24, 1657. They were circulated in the thousands through Paris under a pseudonym (Louis de Montalte), and the Jesuits tried to discover the author, whose wit, reason, eloquence, and humor made the order a laughingstock.

The Pensees
Knowledge of Pascal’s personal life is slight after his entry to Port Royal. His sister Gilberte tells of his asceticism, of his dislike of seeing her caress her children, and of his apparent revulsion from talk of feminine beauty. He suffered increasingly after 1658 from head pains, and he died on Aug. 19, 1662.

At his death Pascal left an unfinished theological work, the Pensees, an apology for Christianity, in effect, which was published 8 years later by the Port Royal community in a thoroughly garbled and incoherent form. A reasonably authentic version first appeared in 1844. It deals with the great problems of Christian thought, faith versus reason, free will, and preknowledge. Pascal explains the contradictions and problems of the moral life in terms of the doctrine of the Fall and makes faith and revelation alone sufficient for their mutual justification.

The Pensees, unlike the Provincial Letters, were not worked over and over by their author, and in style they would not, perhaps, mark him out as a great literary figure. The Letters, however, give Pascal a place in literary history as the first of several great French writers practicing the polite irony to which the language lends itself. The Pensees could almost have been written by another man, for in them reason is ostensibly made to take second place to religion. But they are both, in their different ways, among the great books in the history of religious thought.

Later Mathematical and Scientific Work
Pascal’s writings on hydrostatics, relating his experi¬ments with the barometer to his theoretical ideas on the equilibrium of fluids, were not published until a year after his death. His Treatise on the Equilibrium of Liquids extends Simion Stevin’s analysis of the hydrostatic paradox and enunciates what may be called the final law of hydrostatics: in a fluid at rest the pressure is transmitted equally in all directions (Pascal’s principle). Pascal is important as having  forged links between the theories of liquids and gases, and between the dynamics of rigid bodies and hydrodynamics.

Pascal’s principal contribution to mathematics after his entry to Port Royal related to problems associated with the cycloid—a curve, with the area of which the best mathematicians of the day were occupied. He published many of his theorems without proof, as a challenge to other mathematicians. Solutions were found by John Wallis, Christopher Wren, Christian Huygens, and others. Pascal published his own solutions under the assumed name of Amos DettonviIle (an anagram of Louis cle Montalte), and contemporary mathematicians often referred to him by this name.

The mathematical theory of probability made its first great step forward when a correspondence between Pascal and Pierre de Fermat revealed that both had come to similar conclusions independently. Pascal planned a treatise on the subject, but again only a fragment survived, to be published after his death. He never wrote at great length on mathematics, but the many short pieces which survive are almost always concise and incisive.

 

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