Pascal, Blaise (1623-1662)

French philosopher and mathematician. He contributed to the development of hydraulics, calculus, and the mathematical theory of probability.

Mathematics

Pascal's work in mathematics widened general understanding of conic sections, introduced an algebraic notational system that rivalled that of Descartes and made use of the arithmetical triangle (called Pascal's triangle) in the study of probabilities.

Together with Fermat, Pascal studied two specific problems of probability: the first concerned the probability that a player will obtain a certain face of a dice in a given number of throws; and the second was to determine the portion of the stakes returnable to each player of several if a game is interrupted. Pascal used the arithmetical triangle to derive combinational analysis. Pascal's triangle is a triangular array of numbers in which each number is the sum of the pair of numbers above it. In general the nth (n = 0, 1, 2, ...) row of the triangle gives the binomial coefficients ⁿC_r, with r = 0, 1, ..., n.

In 1657-59, Pascal also perfected his ‘theory of indivisibles’ - the forerunner of integral calculus - which enabled him to study problems involving infinitesimals, such as the calculations of areas and volumes.

Hydrostatics, Pascal's principle and hydraulics

Pascal's work in hydrostatics involved repeating the experiment by Italian physicist Evangelista Torricelli to prove that air pressure supports a column of mercury. He confirmed that a vacuum must exist in the space at the top of the tube, and set out to prove that the column of mercury is held up by the weight of air exerted on the container of liquid at the base of the tube. Pascal suggested that at high altitudes there would be less air above the tube and that the column would be lower. Poor health prevented him from undertaking the experiment himself, so he entrusted it to his brother-in-law who obtained the expected results using a mercury column in the mountains of the Puy de Dôme in 1648. This led rapidly to investigations of the use of the mercury barometer in weather forecasting.

Pascal then turned to a study of pressure in liquids and gases, and found that pressure is transmitted equally in all directions throughout a fluid and is always exerted perpendicular to any surface in or containing the fluid. Propounded in a treatise on hydrostatics in 1654, Pascal's principle is fundamental to applications of hydrostatics and governs the operation of hydraulic machines, such as the hydraulic press and jack.

Calculating machine

Between 1642 and 1645, Pascal constructed a machine to carry out the processes of addition and subtraction, and then organized the manufacture and sale of these first calculating machines. At least seven of these ‘computers’ still exist. One was presented to Queen Christina of Sweden in 1652.

Pascal was born in Clermont-Ferrand. In Paris in his teens he met mathematicians Descartes and Fermat. From 1654 Pascal was closely involved with the Jansenist monastery of Port Royal. He defended a prominent Jansenist, Antoine Arnauld (1612-1694), against the Jesuits in his Lettres provinciales/Provincial Letters (1656). His Pensées (1670) was part of an unfinished defence of the Christian religion. His last project was to design a public transport system for Paris, which was inaugurated in 1662.

Pascal's pioneering work on fluid pressure laid the foundations for both hydraulics and meteorology. In his honour, the SI unit for pressure is called the pascal. It is equal to one newton per square metre.