Pascal's machine with the lid removed

Mechanization and automation of computing operations is one of the fundamental technical achievements of the second third of the 20th century. Just as the appearance of the first spinning machines marked the beginning of the great industrial revolution of the 18th and 19th centuries, the creation of electronic computer became a harbinger of a grandiose scientific, technical and information revolution in the second half of the 20th. This important event was preceded by a long backstory. The first attempts to assemble a calculating machine were made back in the 17th century, and the simplest computing devices, such as the abacus and counting, appeared even earlier - in antiquity and the Middle Ages.

Although an automatic computing device is a type of machine, it cannot be put on a par with industrial machines, say, a lathe or a weaving machine, because unlike them, it does not operate with physical material (threads or wooden blanks), but with ideal, non-existent ones. in nature by numbers. Therefore, the creator of any computer (be it the simplest adding machine or the latest supercomputer) faces specific problems that do not arise for inventors in other fields of technology. They can be formulated as follows: 1) how to physically (objectively) represent numbers in a machine? 2) how to enter the initial numerical data? 3) how to simulate the execution of arithmetic operations? 4) how to present the input data and calculation results to the computer?

One of the first to overcome these problems was the famous French scientist and thinker Blaise Pascal. He was 18 years old when he began working on creating a special machine with the help of which a person, even not familiar with the rules of arithmetic, could perform four basic operations. Pascal’s sister, who witnessed his work, wrote later: “This work tired his brother, but not because of the strain of mental activity, and not because of the mechanisms, the invention of which did not cause him much effort, but because the workers had difficulty understanding him." And this is not surprising. Precision mechanics was just being born, and the quality that Pascal demanded exceeded the capabilities of his masters. Therefore, the inventor himself often had to take up a file and a hammer or rack his brains over how to change an interesting but complex design in accordance with the skill of the master. The first working model of the machine was ready in 1642. Pascal was not satisfied with it, and he immediately began to design a new one. “I did not save,” he later wrote about his car, “neither time, nor labor, nor money to bring it to a state of being useful... I had the patience to make up to 50 different models...” Finally, in 1645, his efforts were crowned with complete success success - Pascal assembled a car that satisfied him in every way.

What was this first computer in history and how were the problems listed above solved? The mechanism of the machine was enclosed in a light brass box. On its top cover there were 8 round holes, around each of which there was a circular scale. The scale of the rightmost hole was divided into 12 equal parts, the scale of the hole next to it was divided into 20 parts, the remaining six holes had a decimal division. This graduation corresponded to the division of the livre, the main French monetary unit of that time: 1 sou = 1/20 livre and 1 denier = 1/12 sou. In the holes, geared adjustment wheels were visible, located below the plane of the top cover. The number of teeth of each wheel was equal to the number of scale divisions of the corresponding hole.

The phenomenon of pressure is present almost everywhere in our lives, and we cannot even mention the famous French scientist, Blaise Pascal, who invented the unit for measuring pressure - 1 Pa. In this article we want to talk about the outstanding physicist, mathematician, philosopher and writer, who was born on June 19, 1623 in the French city of Auvergne (in those days Clermont-Ferrand), and died in 1662 - August 19.

Blaise Pascal (1623-1662)

Pascal's discoveries serve humanity in the field of hydraulics and computer technology to this day. Pascal also proved himself in the formation of the literary French language.

Blaise Pascal was born into the family of a hereditary nobleman and from birth had poor health, to which doctors were surprised how he even survived. Due to poor health, his father sometimes forbade him to study geometry, as he was concerned about his health, which could worsen due to mental overstrain. But such restrictions did not force Blaise to abandon science, and already at an early age he proved the first theorems of Euclid. But when the father learned that his son had managed to prove the 32nd theorem, he could not forbid him to study mathematics.

Pascal's adding machine.

At the age of 18, Pascal watched his father prepare a tax report for an entire region (Normandy). It was a very boring and monotonous task, which took a lot of time and effort, since the calculations were carried out in a column. Blaise decided to help his father and worked for about two years on creating a computer. Already in 1642, the first calculator was born.

Pascal's adding machine was created on the principle of the ancient taximeter - a device that was intended to calculate distances, only slightly modified. Instead of 2 wheels, 6 were used, which made it possible to perform calculations with six-digit numbers.

Pascal's adding machine.

In this computer, the wheels could only rotate in one direction. It was easy to perform summing operations on such a machine. For example, we need to calculate the sum 10+15=? To do this, you need to rotate the wheel until the value of the first term is set to 10, then we turn the same wheel to the value 15. In this case, the pointer immediately shows 25. That is, the counting occurs in semi-automatic mode.

Subtraction cannot be performed on such a machine, since the wheels do not rotate in the opposite direction. Pascal's adding machine could not divide and multiply. But even in this form and with such functionality, this machine was useful and Pascal Sr. happily used it. The machine performed quick and error-free mathematical additions. Pascal Sr. even invested money in the production of pascaline. But this only brought disappointment, since most accountants and accountants did not want to accept such a useful invention. They believed that when such machines were put into operation, they would have to look for other work. In the 18th century, Pascal's adding machines were widely used by sailors, artillerymen and scientists for arithmetic addition. This invention was sabotaged by financiers for more than 200 years.

Study of atmospheric pressure.

At one time, Pascal modified the experiment of Evangelista Torricelli and concluded that a void should form above the liquid in the tube. He bought expensive glass tubes and conducted experiments without using mercury. Instead, he used water and wine. During the experiments, it turned out that wine tends to rise higher than water. Decort at one time proved that its vapors should be located above the liquid. If wine evaporates faster than water, then the accumulated wine vapor should prevent the liquid from rising in the tube. But in practice, Descartes' assumptions were refuted. Pascal proposed that atmospheric pressure acts equally on heavy and light liquids. This pressure can force more wine into the tube because it is lighter.

Experiments of Evangelista Torricelli

Pascal, who experimented with water and wine for a long time, found that the height of the rise of liquids varies depending on weather conditions. In 1647, a discovery was made that showed that atmospheric pressure and barometer readings depended on the weather.
To finally prove that the height of the rise of the liquid column in Torricelli's tube depends on changes in atmospheric pressure, Pascal asks his relative to climb Mount Puy de Dome with the tube. The height of this mountain is 1465 meters above sea level and has less pressure at the top than at its foot.

This is how Pascal formulated his law: at the same distance from the center of the Earth - on a mountain, plain or body of water, atmospheric pressure has the same value.

Probability theory.

Since 1650, Pascal had difficulty moving, as he was struck by partial paralysis. Doctors believed that his illness was related to nerves and he needed to shake himself up. Pascal began to visit gambling houses and one of the establishments was called “Pape-Royal”, which was owned by the Duke of Orleans.

In this casino, fate brought Pascal together with the Chevalier de Mere, who had unusual mathematical abilities. He told Pascal that when throwing a dice 4 times in a row, getting a 6 is more than 50%. Whenever I made small bets in the game, I won using my system. This system only worked when throwing one die. When moving to another table, where a pair of dice were thrown, the Mere system did not bring profit, but rather only losses.

This approach gave Pascal an idea in which he wanted to calculate probability with mathematical precision. It was a real challenge to fate. Pascal decided to solve this problem using a mathematical triangle, which was known even in ancient times (for example, Omar Khayyam mentioned it), which later received the name Pascal’s triangle. This is a pyramid consisting of numbers, each of which is equal to the sum of the pair of numbers located above it.

Brilliant people are brilliant in everything. This common statement is fully applicable to the French scientist Blaise Pascal. The inventor's research interests included physics and mathematics, literature and philosophy. It is Pascal who is considered one of the founders of mathematical analysis, the author of the fundamental law of hydrodynamics. He is also known as the first creator of mechanical computers. These devices are prototypes of modern computers.

At that time, the models were unique in many ways. In terms of their technical features, they surpassed many analogues invented before Blaise Pascal. What is the story of "Pascalina"? Where can you find these designs now?

First prototypes

Attempts to automate computing processes have been carried out for a long time. The Arabs and Chinese were the most successful in these matters. They are considered the discoverers of such a device as the abacus. The principle of operation is quite simple. To carry out the calculation, it is necessary to move the bones from one part to another. The products additionally allowed for subtraction operations. The inconveniences of the first Arab and Chinese abaci were associated only with the fact that the stones easily crumbled during transfer. In some shops in the outback you can still find the simplest types of Arabic abacus, although now they are called abacus.

Relevance of the problem

Pascal began designing his car at the age of 17. The teenager’s thoughts about the need to automate routine computing processes were inspired by the experience of his own father. The fact is that the parent of a brilliant scientist worked as a tax collector and spent a long time doing tedious calculations. The design itself took a long time and required large physical, mental and material investments from the scientist. In the latter case, Blaise Pascal was helped by his own father, who quickly realized the advantages of his son's development.

Competitors

Naturally, at that time there was no talk of using any electronic means of computing. Everything was carried out only through mechanics. The use of wheel rotation to carry out the addition operation was proposed long before Pascal. For example, a device created in 1623 was no less popular in its time. However, Pascal’s machine introduced certain technical innovations that significantly simplified the addition process. For example, a French inventor developed a scheme for automatically transferring a unit when a number moves to a higher digit. This made it possible to add multi-digit numbers without human intervention in the counting process, which virtually eliminated the risk of errors and inaccuracies.

Appearance and principle of operation

Visually, Pascal's first adding machine resembled an ordinary metal box in which gears connected to each other were located. The user, by turning the dial wheels, set the values ​​he needed. Each of them was marked with numbers from 0 to 9. When full turn the gear shifted the adjacent one (corresponding to a higher rank) by one unit.

The very first model had only five gears. Subsequently, Blaise Pascal's calculating machine underwent some changes regarding an increase in the number of gears. 6 of them appeared, then this number increased to 8. This innovation made it possible to carry out calculations up to 9,999,999. The answer appeared at the top of the device.

Operations

The wheels in Pascal's calculating machine could only rotate in one direction. As a result, the user was only able to perform addition operations. With some skill, the devices were also adapted for multiplication, but performing calculations in this case was noticeably more difficult. There was a need to add the same numbers several times in a row, which was extremely inconvenient. Inability to rotate the wheel reverse side did not allow calculations with negative numbers.

Spreading

Since the creation of the prototype, the scientist has made about 50 devices. Pascal's mechanical machine aroused unprecedented interest in France. Unfortunately, the product was never able to gain widespread popularity, even despite the resonance among the general public and in scientific circles.

The main problem with the products was their high cost. Production was expensive, and naturally, this had a negative impact on the final price of the entire device. It was the difficulties with the release that led to the fact that the scientist was able to sell no more than 16 models in his entire life. People appreciated all the advantages of automatic calculation, but did not want to take the devices.

Banks

Blaise Pascal's main focus during implementation was on banks. But financial institutions for the most part refused to purchase a machine for automatic calculations. Problems arose due to France's complex monetary policy. At that time, the country had livres, deniers and sous. One livre consisted of 20 sous, and a sous of 12 deniers. That is, there was no decimal number system as such. This is why it was practically impossible to use Pascal's machine in banking in reality. France switched to the number system adopted in other countries only in 1799. However, even after this time, the use of an automated device was noticeably complicated. This already touched on the previously mentioned difficulties in production. Labor was mostly manual, so each machine required painstaking work. As a result, they simply stopped making them altogether.

Government support

Blaise Pascal gave one of the first automatic calculating machines to Chancellor Seguier. This one statesman provided support to the novice scientist in the first stages of creating an automatic device. At the same time, the chancellor managed to obtain from the king privileges to produce this unit specifically for Pascal. Although the invention of the machine belonged entirely to the scientist himself, patent law was not developed in France at that time. The privilege from the royal person was received in 1649.

Sales

As mentioned above, Pascal’s machine did not gain much popularity. The scientist himself was only involved in the manufacture of devices; his friend Roberval was responsible for the sale.

Development

The principle of rotation of mechanical gears, implemented in Pascal's computer, was taken as the basis for the development of other similar devices. The first successful improvement is attributed to the German mathematics professor Leibniz. The creation of the adding machine dates back to 1673. Number additions were also performed in the decimal system, but the device itself was distinguished by greater functionality. The fact is that with its help it was possible not only to perform addition, but also to multiply, subtract, divide and even take the square root. The scientist added a special wheel to the design, which made it possible to speed up repeated addition operations.

Leibniz presented his product in France and England. One of the cars even ended up with the Russian Emperor Peter the Great, who presented it to the Chinese monarch. The product was far from perfect. The wheel that Leibniz invented for subtraction was subsequently used in other adding machines.

The first commercial success of mechanical ones dates back to 1820. The calculator was created by the French inventor Charles Xavier Thomas de Colmar. The principle of operation is in many ways reminiscent of Pascal's machine, but the device itself is smaller in size, a little easier to manufacture and cheaper. This is what predetermined the success of businessmen.

The fate of creation

Throughout his life, the scientist created about 50 machines; only a few have survived to this day. Now it is possible to reliably track the fate of only 6 devices. Four models are in permanent storage at the Paris Museum of Arts and Crafts, and two more at the Clermont Museum. The remaining computing devices found their home in private collections. It is not known for certain who currently owns them. The serviceability of the units is also in question.

Opinions

Some biographers connect the development and creation of Pascal's adding machine with the failing health of the inventor himself. As mentioned above, the scientist began his first works in his youth. They required enormous amounts of mental and physical strength from the author. The work lasted for almost 5 years. As a result of this, Blaise Pascal began to suffer from severe headaches, which then accompanied him for the rest of his life.

Frenchman Blaise Pascal began building the Pascalina adding machine in 1642 at the age of 19, after observing the work of his father, who was a tax collector and often performed long and tedious calculations.

Pascal's machine 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 dials accordingly. 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 excess over the number 9 was transferred to the adjacent digit, shifting the adjacent wheel by 1 position. The first versions of the Pascalina had five gears, later the number increased to six or even eight, which made it possible to work with large numbers, up to 9999999. The answer appeared in the upper part of the metal case. Rotation of the wheels was possible only in one direction, excluding the possibility of directly operating with negative numbers. However, Pascal's machine made it possible to perform not only addition, but also other operations, but it required the use of a rather inconvenient procedure for repeated additions. Subtraction was performed using nine's complements, which, to help the reader, appeared in a window located above the set original value.

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, sous de livre. There were 20 sous in a livre, and 12 denier in a sous. It is clear that the use of the decimal system complicated the already difficult process of calculations.

However, in about 10 years, Pascal built about 50 and even managed to sell about a dozen variants of his car. Despite the general admiration it caused, the machine did not bring wealth to its creator. The complexity and high cost of the machine, combined with poor computing capabilities, served as an obstacle to its widespread use. Nevertheless, the principle of connected wheels underlying Pascalina became the basis for almost three centuries for most of the created computing devices.

Pascal's machine became the second really working computing device after Wilhelm Schickard's Counting Clock (German). Wilhelm Schickard), created in 1623.

In 1799, France's transition to the metric system also affected its monetary system, which finally became decimal. However, almost until the beginning of the 19th century, the creation and use of counting machines remained unprofitable. It was not until 1820 that Charles Xavier Thomas de Colmar Charles Xavier Thomas de Colmar) patented the first mechanical calculator, which became a commercial success.

Leibniz calculator History of creation

The idea of ​​​​creating a machine that performs calculations came from the outstanding German mathematician and philosopher Gottfried Wilhelm Leibniz after he met the Dutch mathematician and astronomer Christian Guynian. The huge number of calculations that the astronomer had to do led Leibniz to the idea of ​​​​creating a mechanical device that could facilitate such calculations (“Since it is unworthy of such wonderful people, like slaves, to waste time on computational work that could be entrusted to anyone at any time.” using the machine").

The mechanical calculator was created by Leibniz in 1673. The addition of numbers was carried out using wheels connected to each other, just like on the computing machine of another outstanding scientist-inventor Blaise Pascal - “Pascaline”. A moving part added to the design (a prototype of the moving carriage of future desktop calculators) and a special handle that made it possible to rotate a stepped wheel (cylinders in subsequent versions of the machine) made it possible to speed up repeated addition operations, with the help of which division and multiplication of numbers were performed. The required number of repeated additions was performed automatically.

The machine was demonstrated by Leibniz at the French Academy of Sciences and the Royal Society of London. One copy of the calculator came to Peter the Great, who presented it to the Chinese emperor, wanting to surprise the latter with European technical achievements.

Two prototypes were built, to this day only one has survived in the National Library of Lower Saxony (German). Niedersächsische Landesbibliothek) in Hannover, Germany. Several later copies are in museums in Germany, such as one in the Deutsches Museum in Munich.

Pascaline

The first computing device to become famous during the author's lifetime was the Pascaline or, as it is sometimes called, the Pascal Wheel. It was created in 1644 by Blaise Pascal (06/19/1623-08/19/1662) and for centuries took the place of the first calculating machine, since at that time Schiccard’s “Calculating Clock” was known to an extremely narrow circle of people.

The creation of "Pascalina" was caused by Pascal's desire to help his father. The fact is that the father of the great scientist Etienne Pascal in 1638 led a group of rentiers who protested against the government’s decision to cancel the payment of rent, for which he fell out of favor with Cardinal Richelieu, who ordered the arrest of the rebel. Pascal's father had to flee.

On April 4, 1939, thanks to Jacqueline, the youngest daughter of the scientist's father, and the Duchess d'Aiguillon, they managed to obtain the cardinal's forgiveness. Etienne Pascal was appointed to the post of intendant of the Rouen generalship, and on January 2, 1640, the Pascal family arrived in Rouen. Pascal's father immediately plunged to work, sitting day and night calculating tax revenues.In 1642, at the age of 19, Blaise Pascal, wanting to make his father's work easier, began work on a adding machine.

The first model created did not satisfy him, and he immediately began to improve it. In total, about 50 different models of computing devices were created. Pascal wrote about his work like this: “I did not save any time, no labor, no money to bring it to a state of being useful to you... I had the patience to make up to 50 different models: some wooden, others ivory, ebony wood, copper..." The final version of the device was created in 1645.

The description of "Pascalina" first appeared in Diderot's Encyclopedia in the 18th century.

It was a small brass box measuring 36x13x8 cm, containing inside many interconnected gears and having several dial wheels with divisions from 0 to 9, with the help of which control was carried out - entering numbers for operations on them and displaying the results of operations in windows.

Each dial corresponded to one digit of a number. The first versions of the device were five-bit, later Pascal created six- and even eight-bit versions.

The two lowest digits of the eight-bit Pascalina were adapted to operate with denier and sou, i.e. The first digit was decimal, and the second was duodecimal, because in those days the French coinage system was more complex than the modern one. There were 12 deniers in the livre and 20 sous in the denier. When performing normal decimal operations, it was possible to turn off the digits intended for small change. Six- and five-digit versions of the machines could only work with decimal digits.

The dialing wheels were turned manually using a drive pin, which was inserted between the teeth, the number of which was ten for decimal places, twelve for duodecimal places, and twenty for decimal places. For ease of data entry, a fixed stop was used, attached to the bottom of the dial, just to the left of the number 0.

The rotation of the dial wheel was transmitted to the counting drum using a special device shown in the figure on the left. The dial wheel (A) was rigidly connected to the crown wheel (C) using a rod (B). The crown wheel (C) was engaged with a crown wheel (D) positioned at right angles to the crown wheel (C). In this way, the rotation of the dial wheel (A) was transmitted to the crown wheel (D), which was rigidly connected to the rod (E), on which the crown wheel (F) was fixed, used to transfer overflow to the most significant digit using teeth (F1) and to receive overflow from minor digit using teeth (F2). Also attached to the rod (E) was a crown wheel (G), which was used to transmit the rotation of the dial wheel (A) to the counting drum (J) using a gear wheel (H).

When the dial was turned completely, the result of the overflow was transferred to the most significant digit of Pascaline using the mechanism shown in the figures “Mechanism for transferring overflow in Pascaline.”

To transfer the overflow, two crown wheels (B and H) of adjacent digits were used. On the crown wheel (B) of the minor category there were two rods (C) that could engage with a fork (A) mounted on a double-cranked lever D. This lever rotated freely around the axis (E) of the senior category. Also attached to this lever was a spring-loaded pawl (F).

When the minor dial reached the number 6, the rods (C) engaged with the fork (A). At the moment when the dial moved from the number 9 to the number 0, the fork disengaged with the rods (C) and fell down under the influence of its own weight, while the pawl engaged with the rods (G) of the crown wheel (E) of the highest category and moved him one step forward.

The principle of operation of the overflow transfer mechanism in Pascaline is illustrated in the animation below.

The main purpose of the device was addition. To add, you had to do a number of simple operations:

1. Reset the previous result by rotating the dials, starting with the least significant digit, until zeros appear in each of the windows.

2. Using the same wheels, the first term is entered, starting from the least significant digit.

The animation below illustrates how Pascalina works using the example of adding 121 and 32.

Subtraction was a little more complicated, since the transfer of overflow bits occurred only when the dials were rotated clockwise. A locking lever (I) was used to prevent the dial wheels from rotating counterclockwise.

This overflow transfer device led to a problem in implementing subtraction on Pascaline by rotating the dials in the opposite direction, as was done in Schickard's Counting Clock. Therefore, Pascal replaced the operation of subtraction with addition with nine's complement.

Let me explain the method used by Pascal with an example. Let's say you need to solve the equation Y=64-37=27. Using the addition method, we represent the number 64 as the difference between the numbers 99 and 35 (64=99-35), thus our equation is reduced to the following form: Y=64-37=99-35-37=99-(35+37)= 27. As can be seen from the transformation, subtraction has been partially replaced by addition and subtraction of the result of addition from 99, which is the inverse transformation of addition. Consequently, Pascal had to solve the problem of automatic addition to nine, for which he entered two rows of numbers on the counting drum so that the sum of two numbers located one below the other was always equal to 9. Thus, the number displayed in the top row of the calculation result window is represented the addition of the number in the bottom row to 9.

In expanded form, the rows applied to the cylinder are shown in the figure on the left.

The bottom row was used for addition, and the top row for subtraction. To ensure that the unused row does not distract from calculations, it is covered with a bar.

Let's look at Pascalina's work using the example of subtracting 132 from 7896 (7896-132=7764):

1. Close the bottom row of windows used for addition.

2. Turn the dial wheels so that the number 7896 is displayed in the top row, while the number 992103 is displayed in the bottom closed row.

3. Enter the subtrahend in the same way as we enter the terms in addition. For the number 132 this is done like this:

The pin is installed opposite the number 2 of the lowest digit of the “Pascalina”, and the dial is turned clockwise until the pin rests against the stop.

The pin is installed opposite the number 3 of the second digit of the “Pascalina”, and the dial is turned clockwise until the pin rests against the stop.

The pin is installed opposite the number 1 of the third digit of the “Pascalina”, and the dial is turned clockwise until the pin rests against the stop.

The remaining digits do not change.

4. The result of the subtraction 7896-132=7764 will be displayed in the top row of windows.

Multiplication in the device was performed in the form of repeated addition, and multiple subtraction could be used to divide a number.

When developing a calculating machine, Pascal faced many problems, the most pressing of which was the manufacture of components and gears. The workers did not understand the scientist's ideas well, and the instrument-making technology was low. Sometimes Pascal himself had to pick up the tools and polish certain parts of the machine, or simplify their configuration so that the craftsmen could make them.

The inventor presented one of the first successful models of the Pascalina to Chancellor Seguier, which helped him receive a royal privilege on May 22, 1649, which confirmed the authorship of the invention and assigned Pascal the right to manufacture and sell the machine. Over the course of 10 years, approximately 50 models of the computer were created and about a dozen were sold. 8 samples have survived to this day.

Although the machine was revolutionary for its time and caused universal admiration, it did not bring wealth to its creator, since practical application I didn’t receive it, although a lot was said and written about them. Perhaps because the clerks to whom the machine was intended were afraid of losing their jobs because of it, and employers were stingy to buy an expensive device, preferring cheap labor.

Nevertheless, the ideas underlying the construction of Pascalina became the basis for the development of computer technology. Pascal also had immediate successors. Thus, Rodriguez Pereira, known for his system of teaching the deaf and dumb, designed two calculating machines based on the principles of the Pascalina, but as a result of a number of modifications, they turned out to be more advanced.