Great scientists. Blaise Pascal. Pascal's adding machine: history of creation, structure and its development Blaise Pascal's adding machine
History of technology: Pascalina arithmetic machine
In the seventeenth century, there lived a simple French youth, his name was Blaise Pascal. Blaise's father worked as a tax collector and, when he came home, he spent a lot of time on calculations. Therefore, the above-mentioned young man decided to make his father’s work easier. This is how the world's first calculating machine appeared, working on a new, previously unknown principle. Without further ado, they called her “Pascalina”.
History in brief
Blaise Pascal (1623 – 1662) invented his device in 1640. It took another two years to create the device. And at the age of nineteen, the young man still pleased his parent. Like, now you will have more free time.
Naturally, there was no computer industry at that time even in our wildest dreams, so each copy of Pascalina had to be made independently, in a handicraft way.
Pascal presented one of the first products to the then Chancellor Seguier, a patron of science and a lover of all sorts of interesting things. And as gratitude, the inventor received in 1649 something like a patent for a “adder machine”, the exclusive right to produce and sell it.
A friend named Roberval began to help with the sale. History has not preserved information about him. Perhaps because they managed to sell not so many copies of Pascalina, about ten or fifteen.
It is also not very clear how many variations of the arithmetic machine were made. Researchers believe fifty. The first copies made it possible to count numbers up to 9999, later eight-digit numbers appeared.
In other words, the matter happened a very long time ago, and very little reliable evidence and documents have survived to this day.
The essence of the device
The adder machine, a box in the shape of a large brick, consisted of gears on which wheels with numbers were put on. Each gear clung to the other in such a way as to turn it and change the numbers in the windows of the box.
After each nine, as expected, a new ten began, into which something that went beyond the previous one was inserted. The principle is the same as that of ordinary abacus, which can still be seen in museums. But only if in the abacus it was necessary to move the knuckles on the rods with your fingers, then in Pascal’s device it was enough to set the gears in motion.
Reasons for failure
Firstly, despite some public recognition (the chancellor did intervene), artisanal production was slow and expensive. Accordingly, the price of the finished “Pascalina” turned out to be rather high, and not every accountant was ready to fork out for something new, unknown.
Secondly, even those who shelled out the cash faced difficulties. The fact is that in France at that time there was no decimal monetary system. A livre contained twenty sous, and a sous contained twelve deniers. The situation lasted until 1799. And Pascalina worked in the decimal system.
Thirdly, the device could only add numbers. Of course, you can perform multiplication operations using multiple summations, but this is not so convenient. And it contradicts the original purpose of creating the apparatus - to provide everyone with a convenient arithmetic device. Even for those who are not very good at mathematics.
Fourthly, Blaise Pascal was not in good health, suffered from severe headaches, could not organize a large-scale business, and died young. Only 11 years after his death, the German mathematician Gottfried Leibniz picked up the baton. But more on this later.
Meaning
In this case, a cliché is very appropriate, formulated approximately as “the influence of the invention on the subsequent development of mechanical computing technology is difficult to overestimate.” Or something like that. After all, Pascal's contribution was truly significant. If only because the young man came up with a simple and effective system of mechanical summation, based on the rotation of banal gears.
Before this, humanity only had Wilhelm Schickard’s “counting clocks,” which were so complex and incomprehensible that no one bothered to puzzle over them. But Pascal’s followers could only improve the quite obvious and clear design and expand its functionality.
In particular, the mechanical calculator of Gottfried Wilhelm Leibniz, presented in 1673, consisted of wheels that connected each other and actually became the successor to the Pascalina. He already knew how to subtract, multiply and divide.
Later, Leibniz “lengthened” the gear wheels, turning them into cylinders. After all, on the surface of the cylinder there is room for placing different configurations of catching protrusions, and one rotational movement can initiate several useful actions at once.
If you look closely at the “difference engine” of the Englishman Charles Babbage, created in 1822, you can also see the same gears on the rollers.
Well, then adding machines were, as they say, just a stone's throw away. All those mechanical things on the shelves of shops and bars in old films, which lasted until the creation of electronic calculators in the second half of the twentieth century, were the results of an evolution that began with Pascalina.
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| Pascal's summing machine
Pascalina (Pascal's adding machine) is a mechanical adding machine invented by the brilliant French scientist Blaise Pascal (1623-1662) in 1642.
Pascal became the first inventor of mechanical calculating machines. Blaise began work on the machine at the age of 19, after observing the work of his father, who was a tax collector and often performed long and tedious calculations.
For its time, Pascalina, of course, had a rather futuristic appearance: a mechanical “box” with a bunch of gears. Over ten years, Pascal managed to assemble more than 50 different versions of the device. The numbers to be added were entered into the machine by turning the dials, each of which was marked with divisions from 0 to 9, because one wheel corresponded to one decimal place of a number. Thus, to enter a number, the wheels scrolled to the corresponding number. When making a full revolution, the excess over the number 9 was transferred to the adjacent digit, shifting the adjacent wheel by 1 position.
The first copies of Pascal's machine had five gears, after a while their number increased to six, and a little later to eight, which made it possible to work with multi-digit numbers, up to 9,999,999. The answer to arithmetic operations was visible in the upper part of the metal body of the device. The rotation of the wheels was only possible in one direction, thereby eliminating the possibility of working with negative numbers. It is noteworthy that Pascal's machine was able to perform both addition and other operations, but it required the use of a rather inconvenient procedure for repeated additions. Subtraction was performed by additions to nine, which, as an aid to the counting, appeared in the window located above the set original value.
The advantages of automatic calculations did not change the situation in any way, because... Using the decimal machine for financial calculations within the framework of the monetary system in force in France until 1799 was not an easy task. Calculations were carried out in livres, sous and deniers. A livre had 20 sous, while a sous had 12 deniers. There was a similar system in Great Britain. As a result, the use of the decimal number system in non-decimal financial calculations complicated the already difficult process of calculations.
Despite the enormous delight Pascalina caused, the machine did not make its creator rich. The technical complexity and high cost of the machine, combined with small computing abilities even for those years, served as a serious barrier to its widespread use. And yet, Pascal’s Machine deservedly went down in history, because the principle of connected wheels underlying it became the basis for almost 300 years for most of the computers created.
Pascal's summing machine(Pascalina) is a computing device invented by the French scientist Blaise Pascal (1641, according to other sources 1643). In Pascal's machine, each digit corresponded to a specific position of the bit wheel, divided into 10 sectors. Addition in such a machine was carried out by turning the wheel into the corresponding number of sectors. The idea of using the rotation of a wheel to perform the operation of addition (and subtraction) had been proposed before Pascal (for example, Wilhelm Schickard, 1623), but the innovation in Pascal's machine was the automatic transfer of the unit to the next, higher digit when the wheel of the previous digit was fully rotated (the same as in the usual addition of decimal numbers, the tens resulting from the addition of units are transferred to the most significant digit, and the hundreds - from the addition of tens). This made it possible to add multi-digit numbers without human intervention in the operation of the mechanism. This principle was used from the mid-17th to the 20th century in the construction of adding machines (powered by hand) and electric keyboard computers (powered by an electric motor).
Blaise Pascal began building a summing machine as a young man, watching his father work as a tax collector who was forced to perform long and tedious calculations. Pascalina was a mechanical device in the form of a box with numerous gears connected to one another. The numbers to be added were entered into the machine by turning the dial wheels. Each of these wheels, corresponding to one decimal place of a number, was marked with divisions from 0 to 9. When entering a number, the wheels scrolled to the corresponding number. Having completed a full revolution, the wheel transferred the excess over the number 9 to the adjacent digit, shifting the adjacent wheel by one position. The first versions of the Pascalina had five gears - decimal places, later their number increased to six or eight. The answer appeared at the top of the metal case. Rotation of the wheels was possible only in one direction, excluding the possibility of operating with negative numbers. Pascal's machine made it possible to perform not only addition, but also required the use of an inconvenient procedure for repeated additions.
Despite the advantages of automatic calculations, the use of a decimal machine for financial calculations within the framework of the monetary system in force in France at that time was difficult. Calculations were carried out in livres (pounds), sous (solids) and deniers (denarii). There were 20 sous in a livre and 12 deniers in a sous. Under such conditions, the use of the decimal system complicated the calculation process.
In about 10 years, Pascal built about 50 devices and managed to sell about a dozen variations of his machine. Despite the general excitement it caused, the complexity of manufacturing and the high cost of the machine served as an obstacle to its distribution. Nevertheless, the principle of connected wheels underlying Pascalina became the basis for most later computing devices. Pascal's machine was the second really working computing device after Wilhelm Schickard's counting clock.
The first inventor of mechanical calculating machines was the brilliant Frenchman Blaise Pascal. The son of a tax collector, Pascal conceived the idea of building a computing device after observing his father's endless tedious calculations. In 1642, when Pascal was only 19 years old, he began work on creating a adding machine. Pascal died at the age of 39, but despite such a short life, he will forever go down in history as an outstanding mathematician, physicist, writer and philosopher. One of the most common modern programming languages is named in his honor.
Pascal's adding machine, "pascaline", was a mechanical device - a box with numerous gears. In just about a decade, he built more than 50 different versions of the machine. When working on Pascaline, the numbers to be added were entered by turning the dials accordingly. Each wheel with divisions from 0 to 9 marked on it corresponded to one decimal place of the number - units, tens, hundreds, etc. The wheel “transferred” the excess over 9, making a full revolution and moving the “highest” wheel adjacent to the left by 1 forward. Other operations were performed using a rather awkward procedure of repeated additions.
1642 Pascal's adding machine performed arithmetic operations by rotating connected wheels with digital divisions.
Although the car caused widespread admiration, it did not bring Pascal wealth. Nevertheless, the principle of linked wheels he invented was the basis on which the axles of most computing devices were built over the next three centuries.
The main disadvantage of the Pascaline was the inconvenience of performing all operations on it except simple addition. The first machine, which made it easy to perform subtraction, multiplication and division, was invented later in the same 17th century. in Germany. The credit for this invention goes to a brilliant man whose creative imagination seemed inexhaustible. Gottfried Wilhelm Leibniz was born in 1646 in Leipzig. He belonged to a family famous for its scientists and politicians. His father, a professor of ethics, died when the child was only 6 years old, but by this time Leibniz was already possessed by a thirst for knowledge. He spent his days in his father's library, reading books and studying history, Latin and Greek and other subjects.
Having entered the University of Leipzig at the age of 15, he was perhaps not inferior to many professors in his erudition. Yet now a whole new world had opened up to him. At the university, he first became acquainted with the works of Kepler, Galileo and other scientists who were rapidly expanding the boundaries of scientific knowledge. The pace of scientific progress amazed the young Leibniz, and he decided to include mathematics in his curriculum.
At the age of 20, Leibniz was offered a professorship at the University of Nuremberg. He rejected this offer, preferring a diplomatic career to the life of a scientist. However, while he was traveling in a carriage from one European capital to another, his restless mind was tormented by all sorts of questions from various fields of science and philosophy - from ethics to hydraulics and astronomy. In 1672, while in Paris, Leibniz met the Dutch mathematician and astronomer Christian Huygens. Seeing how many calculations an astronomer had to do, Leibniz decided to invent a mechanical device that would make the calculations easier. “Because it is unworthy of such wonderful people,” wrote Leibniz, “like slaves, to waste time on computational work that could be entrusted to anyone using a machine.”
In 1673 he made a mechanical calculator. The axle on it folded in essentially the same way as on the Pascaline, but Leibniz included in the design a moving part (a prototype of the movable carriage of future desktop calculators) and a handle with which it was possible to turn a stepped wheel or - in subsequent versions of the machine - cylinders located inside the device. This moving element mechanism made it possible to speed up the repetitive addition operations needed to multiply or divide numbers. The repetition itself was also automatic.
1673 Leibniz's calculator speeded up multiplication and division operations.
Leibniz demonstrated his machine at the French Academy of Sciences and the Royal Society of London. One copy of Leibniz's machine came to Peter the Great, who presented it to the Chinese emperor, wanting to amaze him with European technical achievements. But Leibniz became famous primarily not for this machine, but for the creation of differential and integral calculus (which was independently developed in England by Isaac Newton). He also laid the foundations of the binary number system, which later found application in automatic computing devices.
Leibniz adding machine
Arithmometer (from the Greek αριθμός - “number”, “counting” and the Greek μέτρον - “measure”, “meter”) - a desktop (or portable) mechanical computing machine designed for accurate multiplication and division, as well as for addition and subtraction .
Desktop or portable: Most often, adding machines were desktop or “knee-mounted” (like modern laptops); occasionally there were pocket models (Curta). This distinguished them from large floor-standing computers such as tabulators (T-5M) or mechanical computers (Z-1, Charles Babbage's Difference Engine).
Mechanical: Numbers are entered into the adding machine, converted and transmitted to the user (displayed in counter windows or printed on tape) using only mechanical devices. In this case, the adding machine can use exclusively a mechanical drive (that is, to work on them you need to constantly turn the handle. This primitive option is used, for example, in “Felix”) or perform part of the operations using an electric motor (The most advanced adding machines are computers, for example “Facit CA1-13", almost any operation uses an electric motor).
Precise calculation: Adding machines are digital (not analog, such as a slide rule) devices. Therefore, the calculation result does not depend on the reading error and is absolutely accurate.
Multiplication and Division: Arithmometers are designed primarily for multiplication and division. Therefore, almost all adding machines have a device that displays the number of additions and subtractions - a revolution counter (since multiplication and division are most often implemented as sequential addition and subtraction; for more details, see below).
Addition and Subtraction: Adding machines can perform addition and subtraction. But on primitive lever models (for example, on the Felix) these operations are performed very slowly - faster than multiplication and division, but noticeably slower than on the simplest adding machines or even manually.
Not programmable: When working on an adding machine, the order of actions is always set manually - immediately before each operation, you must press the corresponding key or turn the corresponding lever. This feature of the adding machine is not included in the definition, since there were practically no programmable analogues of adding machines.
Charles Babbage's ideas
The Charles Babbage Difference Engine is a mechanical apparatus invented by the English mathematician Charles Babbage, designed to automate calculations by approximating functions with polynomials and calculating finite differences. The possibility of approximate representation of logarithms and trigonometric functions in polynomials allows us to consider this machine as a fairly universal computing device.
The first idea for a difference engine was put forward by the German engineer Johann Muller in a book published in 1788.
However, Charles Babbage got the idea for his project not from Müller, but from the work of Gaspard de Prony, who served as head of the French government's census bureau from 1790 to 1800.
Prony, who was tasked with calibrating and improving logarithmic trigonometric tables in preparation for the introduction of the metric system, proposed that the work be divided into three levels. At the top level, a group of prominent mathematicians was engaged in the derivation of mathematical expressions suitable for numerical calculations. The second group calculated function values for arguments spaced five or ten intervals apart. The calculated values were included in the table as reference values. After this, the formulas were sent to the third, most numerous group, whose members carried out routine calculations and were called “calculators.” They were only required to carefully add and subtract in the sequence determined by the formulas received from the second group.
The works of de Prony (never completed due to the revolutionary times), which Babbage became acquainted with while in France, led Babbage to think about the possibility of creating a machine capable of replacing the third group - calculators. In 1822, Babbage published an article describing such a machine, and soon began its practical creation. As a mathematician, Babbage was familiar with the method of approximating functions by polynomials and calculating finite differences. In order to automate this process, he began to design a machine, which was called a difference machine. This machine had to be able to calculate the values of polynomials up to the sixth power with an accuracy of up to the 18th digit.
In the same 1822, Babbage built a model of a difference engine, consisting of rollers and gears, manually rotated using a special lever. Having secured the support of the Royal Society, which considered his work “eminently worthy of public support,” Babbage approached the British government with a request to fund full-scale development. In 1823, the British government provided him with a subsidy of £1,500 (the total amount of government subsidies Babbage received for the project ultimately amounted to £17,000).
While developing the machine, Babbage did not imagine all the difficulties associated with its implementation, and not only did not meet the promised three years, but nine years later he was forced to suspend his work. However, part of the machine did begin to function and performed calculations with even greater accuracy than expected.
Replica of the difference engine at the London Science Museum
The design of the difference machine was based on the use of the decimal number system. The mechanism was driven by special handles. When funding for the Difference Engine ceased, Babbage began designing a much more general Analytical Engine, but then returned to the original design. The improved project he worked on between 1847 and 1849 was called Difference Engine No.
Blaise Pascal left a noticeable mark on the history of mankind. The scientist worked in a variety of fields of knowledge. He is rightfully considered one of the creators of mathematical analysis, design geometry, probability theory, hydrostatics (physicists and others know Pascal’s law, according to which changes in pressure in a fluid at rest are transmitted to other points without changes), the creator of a mechanical calculating device - the “Pascal wheel” "
Blaise Pascal was born in the summer of 1623 in the French town of Clermont-Ferrand in the family of the chairman of the tax department, Etienne Pascal. Life was not kind to Blaise. Even in childhood, when he was very young, the boy fell ill with an incomprehensible nervous disease. From the words of those around him, it can be assumed that he was bitten by a rabid dog: the boy was terrified of water, had convulsions, and finally fell silent, completely insensitive and seemed dead. If so, it is unclear how he survived. And he not only survived, but also quite soon recovered from his illness.
In 1631, Pascal's mother died and after that his family moved to Paris. Blaise grew up as a gifted child. From an early age, the boy was interested in exact sciences, and his upbringing played a special role in this: since Blaise’s father was himself quite good at mathematics, was friends with Marin Mersenne and Gerard Desargues, and once discovered and studied a previously unknown algebraic curve, which has since been called “Pascal’s snail” .
It was his father who gave young Blaise Euclid’s Elements. The boy read the entire book without once asking for an explanation. After that, his father began to give him other works in mathematics. Blaise was also allowed to take part in meetings of the mathematical circle - “Mersenne Thursdays”, where he became better acquainted with prominent mathematicians of the time. There, for the first time, he gave a report on the theorem named after Pascal. It is still an integral part of all geometry courses today.
Already at the age of sixteen, Pascal formulated a theorem about a hexagon inscribed in a conic section (Pascal's theorem). It is known that he later obtained about 400 corollaries from his theorem.
A few years later, Blaise Pascal created a mechanical computing device - a summing machine that made it possible to add numbers in the decimal number system. The son of a tax collector, Pascal conceived the idea of building a computing device after observing his father's endless tedious calculations. In 1642, when Pascal was 19 years old, he began working on a adding machine. Believing that this invention would bring good luck, father and son invested a lot of money in the creation of their device. But Pascal’s calculating device was opposed by clerks - they were afraid of losing their jobs because of it, as well as employers, who believed that it was better to hire cheap bookkeepers than to buy an expensive machine.
In this machine, the digits of a six-digit number were set by corresponding turns of disks (wheels) with digital divisions, and the result of the operation could be read in six windows - one for each digit. The disks were mechanically connected; when adding, the transfer of a unit to the next digit was taken into account. The units disk was connected to the tens disk, the tens disk to the hundreds disk, etc. If, when turning, the disk passed through zero, then the next disk turned one forward. Other operations were carried out using a rather inconvenient procedure of repeated additions, and this was the main drawback of the machine. However, the principle of connected wheels invented by Pascal was the basis on which most computing devices were built over the next three centuries.
Pascal continued to work on improving the machine, in particular, he tried to design a device for extracting square roots. Work continued until 1652. In a few more months, he would send his machine to the young Swedish Queen Christina, famous for her intelligence, eccentricity and learning, and then retire from computing forever.
"Arithmometer" by Blaise Pascal
Pascal presented one of the first successful models of his machine to Chancellor Seguier. The patronage of Pierre Seguier helped the scientist receive a royal privilege on May 22, 1649, which established his priority in the invention and assigned him the right to produce and sell machines. From 1646 to 1649, Pascal produced a number of machines, and sold some of them.
Seven arithmetic machines have survived, four of which are in the Paris Museum of Arts and Crafts, one in the Clermont Museum, two in private collections. One of the machines of the Paris Museum is certified by Pascal’s handwritten note and the date of manufacture (1652): “Esto probati instrumenti sumboium hoc: Blasius Pascai aguenus, inventor, 20 May 1652.”
Pascal's machine was widely used: in France it remained in use until 1799, and in England even until 1971.
Subsequently, calculating (computing) machines were created that were incomparably more expensive and more complex than Blaise Pascal’s machine; machines, the benefits of which for humanity are difficult to overestimate... However, their beginning should be sought in the modest Pascal wheel.
At 24, Blaise Pascal became paralyzed. He could hardly walk on crutches, but continued to work. Oh, how these crutches bothered him! After all, now he decided to completely solve the mystery of atmospheric pressure and finally put an end to the many years of work of Galileo, Torricelli and Ray. At first he agreed with the ancient scholastic axiom: “Yes, obviously, nature really does not tolerate a vacuum.” But, having got to the bottom of it, the scientist realized that “nature’s aversion to emptiness” is an empty set of words. If this is true, the “disgust” at the top of the mountain and at its foot should be the same, if it is different, then it’s a matter of atmospheric pressure. But how to carry out such an experiment if his legs refused to serve him?!
In November 1647, Pascal wrote a detailed letter to his sister's husband, in which he asked him to stage the experiment he had planned on Mount Puy de Dome (altitude 1467 meters). Only in September of the following year, Blaise, burning with curiosity, received the exact answer: the pressure at the top of the mountain is less than at its foot. In Paris, he himself repeats this experiment in a tower on the Rue de Rivoli. Pascal outlined the results of his research in the book “New Experiments Concerning Emptiness” and henceforth went down in the history of physics, establishing the basic law of hydrostatics and confirming Torricelli’s assumption about the existence of atmospheric pressure.
It would seem that the spirit of this extraordinary man defeated his weak flesh, but suddenly a sharp change occurred in 25-year-old Blaise Pascal. He abandons all his studies in mathematics and physics, reads only theological books, and becomes gloomy and withdrawn.
How can we explain the reasons for such a drastic change? Perhaps a shaken nervous system, frequent severe headaches, and the fashionable teaching of the Jansenists, who convinced him that abandoning science would be a sacrifice to God, who sent him physical suffering, played a role here. He was also influenced by the death of his father in 1651 and the tonsure of his beloved younger sister Jacqueline as a nun.
In 1655, Pascal settled next to his sister in a monastery, where he wrote “Letters to a Provincial” - a brilliant example of French literature, containing fierce criticism of the Jesuits and propaganda of true moral values.
From 1658 Blaise Pascal's health rapidly deteriorated. Christian Huygens, who visited Pascal in 1660, saw a very old man in front of him, although he was only 37 years old. Doctors forbade him from any mental stress, but the patient managed to write down everything that came to his mind, literally on any material at hand.
Blaise Pascal died on August 19, 1662, having confessed to a priest before his death. His last words were: “May God never leave me!” The great scientist is buried in the Parisian church of Saint-Etienne-du-Mont.
An autopsy was unable to establish the exact cause of Blaise Pascal's death, but obvious lesions in the abdominal organs pointed to pulmonary tuberculosis and stomach cancer. The headaches that plagued Pascal all his life were caused by organic lesions in certain areas of the brain.
After Blaise's death, Jansenist friends found whole stacks of such notes, tied with twine, which they deciphered and published in a book called “Thoughts.” The main theme of these notes is the relationship between God and man, as well as the apologetics of Christianity in the Jansenist understanding. “Thoughts” became a classic of French literature, and Pascal became the only great writer and great mathematician in modern history at the same time.
A crater on the Moon, the SI unit of pressure, and the Pascal programming language are named after Blaise Pascal.
