Pascaline
In 1642, Blaise Pascal, a French mathematician,invented an adding machine. The machine has adopted partly the principles of the abacus but did away with the use of the hand to move the beads or counters. Instead,Pascal used wheels to move counters.
Pascal's calculator
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| A Pascaline, signed by Pascal in 1652 |
Blaise Pascal invented the mechanical calculator in 1642.[1][2] He conceived the idea while trying to help his father who had been assigned the task of reorganizing the tax revenues of the French province of Haute-Normandie ; first called Arithmetic Machine, Pascal's Calculator and later Pascaline, it could add and subtract directly and multiply and divide by repetition.
Pascal went through 50 prototypes before presenting his first machine to the public in 1645. He dedicated it to Pierre Séguier, the chancellor of France at the time.[3] He built around twenty more machines during the next decade, often improving on his original design. Nine machines have survived the centuries,[4] most of them being on display in European museums. In 1649 a royal privilege, signed by Louis XIV of France,[5] gave him the exclusivity of the design and manufacturing of calculating machines in France.
Its introduction launched the development of mechanical calculators in Europe first and then all over the world, development which culminated, three centuries later, in the invention of the microprocessor developed for a Busicom calculator in 1971.
The mechanical calculator industry owes a lot of its key machines and inventions to the pascaline. First Gottfried Leibniz invented his Leibniz wheels after 1671 while trying to add an automatic multiplication and division feature to the pascaline,[6] then Thomas de Colmar drew his inspiration from Pascal and Leibniz when he designed his arithmometer in 1820, and finally Dorr E. Felt substituted the input wheels of the pascaline by columns of keys to invent his comptometer around 1887. The pascaline was also constantly improved upon, especially with the machines of Dr. Roth around 1840, and then with some portable machines until the creation of the first electronic calculators.
PrecursorsA short list of precursors to the mechanical calculator must include the Antikythera mechanism from around 100 BC, early mechanical clocks and geared astrolabes ; they were all made of toothed gears linked by some sort of carry mechanisms.
Han dynasty odometer cart.
Some measuring instruments and automatons were also precursors to the calculating machine.
An odometer, instrument for measuring distances, was first described around 25 BC by the roman engineer Vitruvius in the tenth volume of his De architectura. It was made of a set of toothed gears linked by a carry mechanism ; the first one was driven by one of the chariot wheels and the last one dropped a small pebble in a bag for each Roman mile traveled.
A Chinese text of the third century AD described a chariot equipped with a geared mechanism that operated two wooden figures. One would strike a drum for every Chinese Li traveled, the other one would strike a gong for every ten Li traveled.
Around the end of the tenth century, the French monk Gerbert d'Aurillac, whose abacus taught the Hindu-Arabic numeral system to the Europeans,[9] brought back from Spain the drawings of a machine invented by the Moors that answered Yes or No to the questions it was asked (binary arithmetic) ; but its existence is contested.
Again in the thirteenth century, the monks Albertus Magnus and Roger Bacon built talking heads made of earthware without any further development (Albertus Magnus complained that he had wasted forty years of his life when Thomas Aquinas, terrified by his machine, destroyed it
The Italian polymath Leonardo da Vinci drew an odometer before 1519.
In 1525, the French craftsman Jean Fernel built the first pedometer. It was made in the shape of a watch and had 4 dials (units, tens, hundreds, thousands) linked by a single tooth carry mechanism.[12]
In 1623 and 1624, Wilhelm Schickard drew a calculating clock on two letters that he sent to Kepler. Schickard's machine was the first of five unsuccessful attempts of designing a direct entry calculating clock in the 17th century (including the designs of Tito Burattini, Samuel Morland and René Grillet).[13]
Pascal versus Schickard
From the introduction of the Pascaline and for more than three centuries Pascal was known as the inventor of the mechanical calculator, but then, in 1957, Dr. Franz Hammer, an expert in Johannes Kepler's work, challenged this fact by announcing that the drawings of a previously unknown working calculating clock, predating Pascal's work by twenty years had been rediscovered, after three centuries of absence, in two letters that Wilhelm Schickard had written to his friend Johannes Kepler in 1623 and 1624. The 1624 letter stated that the first machine to be built by a professional had been destroyed in a fire during its construction and that he was abandoning his project.
Dr. Hammer asserted that because these letters had been lost for three hundred years, Blaise Pascal had been called and celebrated as the inventor of the mechanical calculator in error during all this time.
After careful examination it was found that Schikard's drawings had been published at least once per century starting from 1718, This alone invalidated Dr. Hammer's claim.
Dr. von Freytag Loringhoff, a mathematics professor at the University of Tübingen built the first replica of Schickard's machine but he had to improve on the design of the carry mechanism:
This simple-looking device actually presents a host of problems to anyone attempting to construct an adding machine based on this principle. The major problem is caused by the fact that the single tooth must enter into the teeth of the intermediate wheel, rotate it 36 degrees (one tenth of a revolution), and exit from the teeth, all while only rotating 36 degrees itself. The most elementary solution to this problem consists of the intermediate wheel being, in effect, two different gears, one with long and one with short teeth together with a spring-loaded detente (much like the pointer used on the big wheel of the gambling game generally known as Crown and Anchor) which would allow the gears to stop only in specific locations. It is not known if Schickard used this mechanism, but it certainly works well on the reproductions constructed by von Freytag Loringhoff.
—Michael R. Williams, History of Computing Technology, IEEE (1997)
Without this twentieth century improvement in the carry mechanism, which is not described in any of Schickard's letters or drawings, the replicas would not have worked. Another problem was found after the replicas were built:
Pascal seems to have realized right from the start that the single-tooth gear, like that used by Schickard, would not do for a general carry mechanism. The single-tooth gear works fine if the carry is only going to be propagated a few places but, if the carry has to be propagated several places along the accumulator, the force needed to operate the machine would be of such magnitude that it would do damage to the delicate gear works.
—Michael R. Williams[20], History of Computing Technology, IEEE (1997)
Clément Ader: precursor
Schickard's machine used clock wheels which were made stronger and were therefore heavier, to prevent them from being damaged by the force of an operator input. Each digit used a display wheel, an input wheel and an intermediate wheel. During a carry transfer all these wheels meshed with the wheels of the digit receiving the carry. The cumulative inertia of all these wheels could "...potentially damage the machine if a carry needed to be propagated through the digits, for example like adding 1 to a number like 9,999".[21]
In Pascal's calculator each input wheel is totally independent from all the others and carries are propagated in sequence. Pascal chose, for his machine, a method of re-zeroing that propagates a carry right through the machine.[22] It is the most demanding operation to execute for a mechanical calculator and proved, before each operation, that the Pascaline was fully functional. This is a testament to the quality of the Pascaline because none of the 18th century criticisms of the machine mentioned a problem with the carry mechanism and yet this feature was fully tested on all the machines, by their resets, all the time.[23]
Even though Schickard designed his machine twenty years earlier, Pascal is still the inventor of the mechanical calculator because the drawings of Schickard's calculating clock described a machine that was neither complete nor fully usable. It took a hundred years to get a calculating clock worthy of this name, it was made of wood and was built by the Italian Giovanni Poleni ; it was a two-motion calculating clock (the numbers are inscribed first and then they are processed).
Just as the Wright brothers were credited for the first flight and therefore the invention of the airplane while Clément Ader flew 13 years before them, and Thomas Edison was credited with the invention of the incandescent light bulb while ten people had already worked on it before, Blaise Pascal is credited as the inventor of the mechanical calculator because he was the first person to present a machine that had all the parts required for its use, that had adequate solutions to all its challenges, a primitive machine, complete and ready to evolve.
Schickard's calculating clock had no influence on the development of mechanical calculators.
Achievements
View through back of calculator above showing wheels.
This machine once belonged to Louis Perrier, Pascal's nephew
Besides being the first calculating machine made public during its time, the pascaline is also:
the first calculator to be used in an office (his father's to compute taxes)
the first calculator commercialized (with around twenty machines built)
the first calculator to be patented (royal privilege of 1649)
View through back of calculator above showing wheels.
This machine once belonged to Louis Perrier, Pascal's nephew
Besides being the first calculating machine made public during its time, the pascaline is also:
the first calculator to be used in an office (his father's to compute taxes)
the first calculator commercialized (with around twenty machines built)
the first calculator to be patented (royal privilege of 1649)
the first calculator to be described in an encyclopaedia (Diderot & d'Alembert, 1751):
"...The first arithmetic machine presented to the public was from Blaise Pascal, born in Clermont, Auvergne on June 19, 1623 ; he invented it at the age of 19. Other machines have been designed since which, in the judgement of Mr of the Academy of Sciences, seem to have more practical advantages ; but Pascal's machine is the oldest one ; it could have served as model to all the others ; this is why we preferred it."
the first calculator sold by a distributor:
"Mr de Roberval ... located in the college Maitres Gervais ... every morning until 8..."
the first calculator to be cloned (a clockmaker from Rouen before 1645)
the first calculator to have a controlled carry mechanism which allowed for an effective propagation of multiple carries
Development
Pascal began to work on his calculator in 1642, when he was only 19 years old. He had been assisting his father, who worked as a tax commissioner, and sought to produce a device which could reduce some of his workload. Pascal received a Royal Privilege in 1649 that granted him exclusive rights to make and sell calculating machines in France. By 1654 Pascal had sold about twenty machines, but the cost and complexity of the Pascaline was a barrier to further sales, and production ceased in that year. By that time Pascal had moved on to the study of religion and philosophy which gave us both the Lettres provinciales and the Pensées.
Literary Praise
Pascal's genius and his machine have been celebrated all around the world for centuries.
Pascal, mad genius, born a century too early
— Voltaire, Quoted by Chateaubriand, Le génie du Christianisme, (1802)
Blaise Pascal was, simply, one of the greatest men that have ever lived. Having made the discovery of mathematics at the age of twelve, at sixteen he wrote a treatise on conic sections which is the herald of modern projective geometry. At nineteen he invented, constructed, and offered for sale the first calculating machine. He gave Pascal's Law to physics, proved the existence of the vacuum, and helped to establish the science of hydrodynamics. He created the mathematical theory of probability, in a discussion of the division of gamblers' stakes. His speculations were important in the early development of the infinitesimal calculus. After a night of religious revelation, when he was but thirty-one, he abandoned science, returning to it only to solve, as a diversion from the toothache, the problems of the cycloid. Espousing the theological principles of the Jansenists, he wrote, in their defense, the Lettres provinciales, a controversial weapon which has not yet lost its edge. His prose style, novel in its strong simplicity, determined the shape and character of the French literary language. He devised a new method of teaching reading. He organized the first omnibus line. In the lucid moments of cruel illness, he wrote his Pensées, in preparation for an apology for Christianity, thoughts which have affected the mental cast of three centuries, thoughts which still stir and work and grow in modern minds. He died at 39.
—Morris Bishop[30], Pascal, The life of genius, New York, (1936)
...at the age of nineteen, when he invented the calculating machine - essentially a practical instrument - Pascal was already well known in the realm of pure mathematics. His perseverance with this invention helped one to appreciate more fully the character of Pascal. He had to fight not only ill-health but also the ignorance of his time, for his conception far out-stripped the mechanical experience and ability of those to whom the work was entrusted. It was not until Pascal had made more than fifty models that he achieved his final design.
The invention of the calculating machine illustrated Pascal's extraordinary creative imagination, allied with mathematical genius and precision, and tempered with critical penetration. These qualities were characteristic of the man throughout his life.
—Prof. René Cassin, Pascal tercentenary celebration, London, (1942)
Pascal's invention of the calculating machine, just three hundred years ago, was made while he was a youth of nineteen. He was spurred to it by seeing the burden of arithmetical labor involved in his father's official work as supervisor of taxes at Rouen. He conceived the idea of doing the work mechanically, and developed a design appropriate for this purpose ; showing herein the same combination of pure science and mechanical genius that characterized his whole life. But it was one thing to conceive and design the machine, and another to get it made and put into use. Here were needed those practical gifts that he displayed later in his inventions....
In a sense, Pascal's invention was premature, in that the mechanical arts in his time were not sufficiently advanced to enable his machine to be made at an economic price, with the accuracy and strength needed for reasonably long use. This difficulty was not overcome until well on into the nineteenth century, by which time also a renewed stimulus to invention was given by the need for many kinds of calculation more intricate than those considered by Pascal.
"...The first arithmetic machine presented to the public was from Blaise Pascal, born in Clermont, Auvergne on June 19, 1623 ; he invented it at the age of 19. Other machines have been designed since which, in the judgement of Mr of the Academy of Sciences, seem to have more practical advantages ; but Pascal's machine is the oldest one ; it could have served as model to all the others ; this is why we preferred it."
the first calculator sold by a distributor:
"Mr de Roberval ... located in the college Maitres Gervais ... every morning until 8..."
the first calculator to be cloned (a clockmaker from Rouen before 1645)
the first calculator to have a controlled carry mechanism which allowed for an effective propagation of multiple carries
Development
Pascal began to work on his calculator in 1642, when he was only 19 years old. He had been assisting his father, who worked as a tax commissioner, and sought to produce a device which could reduce some of his workload. Pascal received a Royal Privilege in 1649 that granted him exclusive rights to make and sell calculating machines in France. By 1654 Pascal had sold about twenty machines, but the cost and complexity of the Pascaline was a barrier to further sales, and production ceased in that year. By that time Pascal had moved on to the study of religion and philosophy which gave us both the Lettres provinciales and the Pensées.
Literary Praise
Pascal's genius and his machine have been celebrated all around the world for centuries.
Pascal, mad genius, born a century too early
— Voltaire, Quoted by Chateaubriand, Le génie du Christianisme, (1802)
Blaise Pascal was, simply, one of the greatest men that have ever lived. Having made the discovery of mathematics at the age of twelve, at sixteen he wrote a treatise on conic sections which is the herald of modern projective geometry. At nineteen he invented, constructed, and offered for sale the first calculating machine. He gave Pascal's Law to physics, proved the existence of the vacuum, and helped to establish the science of hydrodynamics. He created the mathematical theory of probability, in a discussion of the division of gamblers' stakes. His speculations were important in the early development of the infinitesimal calculus. After a night of religious revelation, when he was but thirty-one, he abandoned science, returning to it only to solve, as a diversion from the toothache, the problems of the cycloid. Espousing the theological principles of the Jansenists, he wrote, in their defense, the Lettres provinciales, a controversial weapon which has not yet lost its edge. His prose style, novel in its strong simplicity, determined the shape and character of the French literary language. He devised a new method of teaching reading. He organized the first omnibus line. In the lucid moments of cruel illness, he wrote his Pensées, in preparation for an apology for Christianity, thoughts which have affected the mental cast of three centuries, thoughts which still stir and work and grow in modern minds. He died at 39.
—Morris Bishop[30], Pascal, The life of genius, New York, (1936)
...at the age of nineteen, when he invented the calculating machine - essentially a practical instrument - Pascal was already well known in the realm of pure mathematics. His perseverance with this invention helped one to appreciate more fully the character of Pascal. He had to fight not only ill-health but also the ignorance of his time, for his conception far out-stripped the mechanical experience and ability of those to whom the work was entrusted. It was not until Pascal had made more than fifty models that he achieved his final design.
The invention of the calculating machine illustrated Pascal's extraordinary creative imagination, allied with mathematical genius and precision, and tempered with critical penetration. These qualities were characteristic of the man throughout his life.
—Prof. René Cassin, Pascal tercentenary celebration, London, (1942)
Pascal's invention of the calculating machine, just three hundred years ago, was made while he was a youth of nineteen. He was spurred to it by seeing the burden of arithmetical labor involved in his father's official work as supervisor of taxes at Rouen. He conceived the idea of doing the work mechanically, and developed a design appropriate for this purpose ; showing herein the same combination of pure science and mechanical genius that characterized his whole life. But it was one thing to conceive and design the machine, and another to get it made and put into use. Here were needed those practical gifts that he displayed later in his inventions....
In a sense, Pascal's invention was premature, in that the mechanical arts in his time were not sufficiently advanced to enable his machine to be made at an economic price, with the accuracy and strength needed for reasonably long use. This difficulty was not overcome until well on into the nineteenth century, by which time also a renewed stimulus to invention was given by the need for many kinds of calculation more intricate than those considered by Pascal.