by
James Redin
|
||||||
Gottfried Wilhelm Von Leibniz - 1685 |
||||||
Introduction The purpose of this document is to briefly describe the evolution of the calculating devices within an historical context. The journey starts 2500 years ago with the Abacus, and ends 30 years ago with the introduction of the first electronic calculators. The document has been split into three parts: Part I, describes the evolution of the calculating devices up to the invention of the Stepped Wheel by Leibniz. Part II, discusses the main events during the 19th Century, and Part III reviews the development of office machines until the 1960's when the first electronic calculators appeared in the market. |
The Abacus
The Abacus is an ingenious counting device based on the relative positions of two sets of beads moving on parallel strings. The first set contains five beads on each string and allows counting from 1 to 5, while the second set has only two beads per string representing the numbers 5 and 10. The Abacus system seems to be based on a radix of five. Using a radix of five makes sense since humans started counting objects on their fingers. |
The Antikythera
Calculator
The remains, maintained at the National Museum in Athens, include an ancient geared mechanism, now known as the Antikythera Calculator. This interesting device, made up of 32 gear-wheels and measuring about 6.5 inches, resembles the mechanism of an 18th Century clock, and was used to calculate the movements of the Sun and the Moon. |
Napier’s Bones
The bones are a set of vertical rectangular rods, each one divided in 10 squares. The top square contains a digit and the remaining squares contain the first 9 multiples of the digit. Each multiple has its digits separated by a diagonal line. When a number is constructed by arranging side by side the rods with the corresponding digits on the top, then its multiple can be easily obtained by reading the corresponding row of multiples from left to right while adding the digits found in the parallelograms formed by the diagonal lines. No wonder John Napier is also the inventor of the logarithms, a concept used to change multiplication into addition. Napier's bones were very successful and were widely used in Europe until mid 1960's. Logarithms were also the basis for the invention of the slide rule by William Oughtred (1574-1660), of England, in 1633. |
Leonardo da Vinci’s Design
Leonardo da Vinci got many of his ingenious ideas from a careful observation of the mechanics involved in the movements of living organisms. Interestingly enough, nature did not evolve the wheel as a solution to this problem; that solution was left to human ingenuity. It is interesting to note that the wheel has been the base for most of the mechanical devices used to replicate the thought process involved in arithmetic operations. As George Chase [1] said, "The history of mechanical computing machinery in its essence is the story of the numeral wheel and the devices that rotate it to register digital and tens-carry values." |
Schickard’s Machine The first calculating machines were built by gifted mathematicians moved by an intense desire to simplify the repetitive nature of arithmetical operations.
A friend of the great astronomer Johannes Kepler (1571-1630), Schickard sent him several letters in 1623 and 1624 briefly describing his invention. Schickard and his family did not survive the bubonic plague and his detailed notes remained unknown until discovered in 1935 and 1956 by historian Franz Hammer. Mathematician Bruno Von Freytag from the University of Tübingen used them to reconstruct the machine in 1960. One unit is in the Deutsches Museum in München. |
The Pascaline
Pascal was not aware of Schickard’s machine, and his solution was not as elegant and efficient. As Paul E. Dune said "had Schickard’s ideas found a wide audience then Pascal’s machine would not have been invented." It was built on a brass rectangular box, where a set of notched dials moved internal wheels in a way that a full rotation of a wheel caused the wheel at the left to advance one 10th. Although the first prototype contained only 5 wheels, later units were built with 6 and 8 wheels. A pin was used to rotate the dials. As opposed to Schickard’s machine, the wheels moved only clockwise and were designed only to add numbers. Subtraction was done by applying a cumbersome technique based on the addition of the nine’s complement. Although the machine attracted a lot of attention in those days, it did not get wide acceptance because it was expensive, unreliable as well as difficult to use and manufacture. By 1652 about 50 units had been made but less than 15 had been sold. Initially, Pascal got a lot of interest in his invention and he even obtained a "privilege" protection (medieval equivalent of a patent) for his idea in 1649, but his interest in science and "material" pursuits ended when he retreated to a Jansensist convent in 1655 concentrating all his attention on philosophy. He died in 1662. During a period of 30 years after Pascal's invention, several persons built calculating machines based on this design. The most notorious was the adding machine of Sir Samuel Morland (1625-1695), from England. This machine invented in 1666 had a duodecimal scale based on the English currency, and required human intervention to enter the carry displayed in an auxiliary dial. It is interesting to note that even at the beginning of the 20th Century, several companies introduced models based directly on Pascal's design. One example is the Lightning Portable Adder introduced in 1908 by the Lightning Adding Machine Co. of Los Angeles. Another example is the Addometer introduced in 1920 by the Reliable Typewriter and Adding Machine Co. of Chicago. None of them achieved commercial success. |
Leibniz Stepped Drum
Like Pascal, Leibniz was a child prodigy. He learned Latin by the age of 8 and got his second doctorate when he was 19. As soon as he knew about Pascal’s design, he absorbed all its details and improved the design so as to allow for multiplication and division. By 1674 his design was complete and he commissioned the building of a prototype to a craftsman from Paris named Olivier.
|
Calculating devices during the 18th
Century Pascal's and Leibniz’s designs were the basis for most of the mechanical calculators built during the 18th Century. Giovanni Poleni made one in 1709, Lépine in 1725, Antonius Braun in 1725, Jacob Leupold in 1727, Hillerin de Boistissandau in 1730, C.L. Gersten in 1735, Jacob Isaac Pereire in 1750, Phillip Mathieus Hahn in Germany in 1773. Charles, the third Earl Stanhope, of England, in 1775; Johan Helfreich Müller in 1783, Jacob Auch in 1790, and Reichhold in 1792. [4]. Special consideration deserves the Parson Phillip Mathieus Hahn (1730-1790) who developed in 1773 the first functional calculator based on Leibniz's Stepped Drum. Hahn's calculator had a set of 12 drums in a circular arrangement actuated by a crank located in the axis of the arrangement. Hahn made these machines until his death in 1790, however, his two sons and his brother-in-law, Johann Christopher Schuster, continued with the manufacture probably as late as 1820. By the end of the 18th Century, calculating machines were still curiosities used for display purposes, rather than for actual use. The limitations imposed by the technology made it impossible to meet Pascal's dream of making them a practical calculation device. |
Reference Sources Internet Sources Translation to Russian made by Mario Pozner French Translation |