Blaise Pascal


The great mathematician and philosopher Blaise Pascal was born on June 16, 1623, in Clermont (now Clermont-Ferrand) in Auvergne in southern France. He was the third child of Étienne Pascal and was his only son. Étienne, being well schooled in mathematics himself, had decided that his son could best be educated at home and that he should not be exposed to mathematics before the age of 15, as he saw no future for the boy in this subject, so all text books on mathematics were ruled out of bounds for him. Like most boys who are not allowed to read certain books, Blaise took an early interest in the forbidden subject and started with geometry. When he discovered at the age of 12, that the sum of the angles of a triangle are two right angles (i.e. 180°), his father realised his talents, relented and gave him a copy of Euclid's Elements, a subject soon mastered by the young Blaise.

The Pascaline

The family, which had settled in Paris in 1632, moved to Rouen in 1639 where Étienne had been appointed by Cardinal Richelieu as a collector of taxes in Upper Normandy. Shortly after that, Blaise published his first work in mathematics in 1640, an essay on conic sections. He sent his essay to the Mersenne Academy in Paris to become the subject of an evening group discussion. At home however the budding mathematician was kept busy by his father who asked for his assistance in manually adding up long columns of tax figures. The young Pascal found this activity so boring that he set himself to design a machine that would alleviate the tedious work, a machine that would enable him to add up figures. His mechanical calculator, called the Pascaline, initially could only handle 5-digit numbers, but later Pascal developed 6- and 8-digit versions as well.


One of the problems Pascal had to solve was the mechanism to carry tens and hundreds. His solution was ingenious: using a geared wheel with ten teeth, every full rotation would result in the next geared wheel (tens) being shifted one tooth through a gravity-assisted carry mechanism. When that wheel had also made a full rotation the next wheel (hundreds) would shift one tooth, etc. The same principle can still be seen today in a car's odometer, or your water or electricity meter at home, etc.

It was obvious that construction of such a machine would need very fine mechanics, something that Pascal found sorely lacking in the local workmen who were more used to constructing farming equipment and houses. This led him to be trained himself as a mechanic in order to produce the Pascalines with the necessary quality and precision. Although about fifty machines were built, all based on the original concept of 1642, the Pascaline never became the commercial success Pascal had hoped for. There were a few reasons for this: firstly the machine's delicate mechanics tended to jam occasionally, so despite looking impressive in its finely crafted box the size of a shoebox, it failed sometimes in its operations. Its time-consuming production process, mainly handwork, also resulted in a price that was often outside the potential buyer's budget. In addition many white-collar workers (accounting clerks) feared that the new machine would cause unemployment and thus the Pascaline caused resentment. The machine's functionality was limited primarily to additions, with more complex solutions for subtraction, multiplication and division. Subtractions could be done by adding the nines-complement of the number, an approach which even today is still used in modern computers. Multiplication and division was done by repeated additions and subtractions, a slightly cumbersome practice which has also been used by many mechanical calculators of only a few decades ago. From the original fifty Pascalines built by Pascal, less than ten have survived to the present, a few of these are on display in the Musée des Arts et Métiers in Rue Saint Martin, Paris (see maxicard below).

In the late 1640's Pascal turned more and more to religion. When his father Étienne died in 1651, he wrote a letter to one of his sisters on the meaning of death in general and on his father's death in particular. These ideas and thoughts would later form the basis of his philosophical work Les Pensées, which encapsulated his thoughts on human suffering and faith in God.
Having suffered during his adult life of a rather delicate health, Pascal died at the age of 39 on August 19, 1662 in Paris.

On May 6, 1827, the city of Paris named a street in the Vth and XIIIth arrondissements after him, the Rue Pascal. This is of philatelic interest as well as there is a local post office in the Rue Pascal. This post office opened in December 1884 and was closed 8½ years later. Shown is a folded letter from 12 January 1871, when Paris was under siege during the Franco-Prussian war.

Folded letter flown by Ballon Monté “Le Jules Favres No.2”, departing from Gare du Nord on 30 November 1870,
landing the next day on Belle-Île-en-Mer. Cancelled 29 November 1870 with Star of Paris 29 combined with Rue Pascal cds.
After the Rue Pascal post office closed in April 1873, the Star of Paris 29 was assigned to Rue Monge.

Was the Pascaline the first mechanical calculator?

From two letters written in 1623-24, found in Johannes Kepler’s papers, we know that an earlier adding machine containing a carrying mechanism must have existed. The letters were from Wilhelm Schickard (1592-1635), a professor in Oriental Languages, Mathematics and Astronomy at the University of Tübingen, Germany. In his letters to Kepler Schickard described his newly constructed calculating machine which used sprocket wheels and he explained its workings through several detailed technical drawings. It is clear from the correspondence that Schickard himself did have a working version.

Although no actual copy of the Schickard machine has ever been found, his annotated sketches to Kepler made it possible to reconstruct a working replica of his calculator. This machine was featured on a West-Germany stamp in 1973 commemorating the 350th year of the Schickard calculator. The stamp shows the number 100722 (visible in the upper dials) being multiplied by 4. Although the Schickard calculator was built around the time Pascal was born, it is considered unlikely that Pascal was aware of Schickard’s invention when he designed and constructed his famous Pascaline.

A fitting tribute

When Niklaus Wirth, professor of the Polytechnic of Zurich, Switzerland, developed a new programming language in 1971, he decided to name the language after the great mathematician and calculator builder Pascal. The Pascal programming language was a simplified version of ALGOL which Wirth also had helped to develop. Pascal's prime area of application is the learning environment where it is used to teach students the basics of computer programming and the development of well structured and well organized programs. Pascal has been the language of choice for most colleges and universities for teaching programming techniques since the early 1970's. Many a Computer Science graduate will remember with fondness his first computer program written in Pascal.

            © Wobbe Vegter, 2005

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