Pascaline (1642): Blaise Pascal's Mechanical Calculator

The Pascaline is the mechanical calculator that the French mathematician Blaise Pascal began to design in 1642, when he was 18 years old. He built it to ease his father’s tax calculations in Rouen. It was one of the first working calculating machines and the first to be produced in several copies, a landmark in the long road towards modern computing.

Background: tax work in Rouen

Blaise Pascal was born in Clermont, in Auvergne, on 19 June 1623. He was educated at home by his father, Étienne Pascal, a lawyer and amateur mathematician who moved the family to Paris and took part in its learned circles.

In 1639 Cardinal Richelieu’s government appointed Étienne a royal commissioner for tax collection in Upper Normandy, based in Rouen. The work involved endless sums in the old French currency of livres, sols and deniers, where 20 sols made a livre and 12 deniers made a sol. Blaise decided to build a machine to do this arithmetic.

Building the machine

Pascal started work in 1642 and, by his own account, built around 50 prototypes over about three years, struggling with the skills of local craftsmen and the materials of the time. In 1645 he presented a finished machine with a dedication to the chancellor of France, Pierre Séguier.

On 22 May 1649 a royal privilege in the name of the young Louis XIV gave Pascal the exclusive right to make and sell calculating machines in France. In all about 20 Pascalines were built, some for scholars and wealthy patrons, others as gifts.

How it worked

A Pascaline is a brass box with a row of numbered wheels on the top, one for each digit. The user turned a wheel with a stylus to enter a number, and the result appeared in small windows above.

Its key innovation was the automatic carry. When a wheel passed from 9 back to 0, a weighted lever called the sautoir dropped and pushed the next wheel forward by one. Because the sautoir fell by gravity, it could carry through many wheels at once, as in adding 1 to 999.

The machine was designed for addition. Subtraction was carried out with the method of nines’ complements, using a second set of numbers shown in the windows. There were versions for ordinary decimal arithmetic, for accounting in livres, sols and deniers, and for surveying in toises and pieds, old French units of length.

Limits and reception

The Pascaline impressed scholars, and Pascal sent one to Queen Christina of Sweden in 1652, with a letter praising her as a patron of learning. Each machine had to be made by hand by a skilled craftsman, and Pascal personally supervised their manufacture. But it was expensive, delicate and hard to repair, and the wheels could only turn one way. Few buyers wanted it, and it never became a commercial success.

Pascal moved on to other work, including experiments on air pressure that followed Torricelli’s barometer, mathematics of probability with Pierre de Fermat in 1654, and religious writing. He died in Paris on 19 August 1662, aged 39.

Myths and facts

Myth: Pascal built the first calculator ever. The German professor Wilhelm Schickard designed a “calculating clock” and described it to Johannes Kepler in 1623, but his machine was lost and was unknown until historians found his letters in the twentieth century. Pascal’s machine was the first to be made in numbers and widely known.

Myth: the Pascaline could do all four operations. It added directly and subtracted with complements; multiplication and division required repeated steps by the user.

Legacy

Pascal’s design inspired later inventors. Gottfried Wilhelm Leibniz studied it before designing his stepped reckoner in the 1670s, which aimed to multiply directly; he showed a model to the Royal Society in London in 1673. Reliable mass-produced calculators arrived only in the nineteenth century with the arithmometer of Thomas de Colmar.

Several original Pascalines survive, most of them in France. The Musée des Arts et Métiers in Paris holds several, and others are in Clermont-Ferrand and in German collections such as the Zwinger in Dresden. In 1970 the computer scientist Niklaus Wirth named his new programming language Pascal in the inventor’s honour.

Timeline

• 1623, 19 June: Blaise Pascal is born in Clermont, Auvergne.
• 1639: Étienne Pascal becomes a royal tax commissioner in Rouen.
• 1642: Blaise begins designing his calculating machine.
• 1645: Pascal presents a finished machine to Chancellor Pierre Séguier.
• 1649, 22 May: A royal privilege grants Pascal a monopoly on calculating machines.
• 1652: Pascal sends a Pascaline to Queen Christina of Sweden.
• 1662, 19 August: Pascal dies in Paris.

Why it matters

The Pascaline proved that arithmetic, once thought to need human reasoning, could be carried out by gears and levers. Its automatic carry mechanism solved a problem every later calculator had to face, and it stands at the start of the history of mechanical computing.