MECHANICAL COMPUTATION, BABBAGE AND HIS ENGINES Janet Delve & David Anderson Taken from A History of Computing Technology by Michael R. Williams, 2000 MECHANICAL CALCULATING MACHINES MECHANICAL CALCULATING MACHINES The development of automatic computation started with the mechanical devices that automatically performed the four standard arithmetic operations: addition, subtraction, multiplication, division. These systems of mechanical levers, gears and wheels replaced human intellect and set the scene for the complete automation of the process of calculation. The great inventors following were polymaths, i.e. brilliant at many things, like Leonardo de Vinci. They all got their knowledge from being allowed to study in vast libraries. Slide 3 Slide 4 MECHANICAL CALCULATING MACHINES There are 6 basic elements common to most calculating machines: A Set-up mechanism to enter a number into the machine; A Selector mechanism to perform addition or subtraction; A Registering mechanism to indicate the value of the number stored within the machine; A Carry mechanism to ensure any carry would be sent to the next digit A Control mechanism to control the gears at the end of each cycle; An Erasing Mechanism to reset the registering mechanism back to zero. Slide 5 LOGARITHMS Log 10 a = b so 10 b = a Log 10 100 = 2 so 10 2 =100 10 2 x 10 5 = 10 7 We add powers so 2 + 5 = 7 1239.5 x 0.3367? Hard??? Take log of each number, add them, then reverse log process (take antilog) to get result. Slide 6 1
Napier s Bones How do Napier s Bones work? The 'bones' consist of a set of rectangular rods, each marked with a counting number at the top, and the multiples of that number down their lengths. When aligned against the row of multiples, any multiple of the top number can be read off from right to left by adding the digits in each parallelogram in the appropriate row. Using the multiplication tables embedded in the rods, multiplication can be reduced to addition operations and division to subtractions. Slide 7 Slide 8 Wilhelm Schickard (1592-1635) Wilhelm Schickard, professor at Tübingen University, now Germany, invented the first really usable adding machine in 1623, using Napier s bones (multiplication tables). It had a working carry function and was able to fully automate multiplication. The machine itself is lost, but a drawing survives. Slide 9 Blaise Pascal (1623-1662) Blaise Pascal came from a wealthy French family and was self-taught. At the age of 19, he was helping his father in a tax office in Normandy. His work led him to develop the first of around 50 machines to help with the boring daily grind of adding up long columns of tax figures. Slide 10 The Pascaline The Pascaline in Paris His adding / subtracting machine, the Pascaline, comprised a small box which sat on a table, and numbers were entered in the same way as an old-fashioned telephone. It was somewhat delicate, and never caught on commercially. Photo David Anderson 2005 Slide 11 Slide 12 2
Gottfried Wilhelm Leibniz (1646-1716) He was born in Leipzig, now Germany, and was also selftaught. He worked as a diplomat, and his most famous machine is his mechanical multiplier, which was lost in a university attic for 200 years! It contained a stepped drum, gear shafts and wheels. This design was in use until 1875. The Arithmometer In 1820 a commercial version, the Arithmometer, was constructed by the Frenchman Charles Xavier Thomas de Colmar. Slide 13 Slide 14 Charles Babbage (1791-1871) Babbage background Charles Babbage Slide 15 Babbage is known as the grandfather of the computer age, or of modern computing. He was about a century ahead of his time in terms of his ideas. He needed to make mathematical tables, and whilst doing this he came up with idea of his Difference Engine to automate the calculation for him. He then had an idea for the Analytical Engine, which is similar in principle to today s computers, and used punched cards. Slide 16 Charles Babbage Chronology I79I Born in London, the son of a wealthy London banker, Childhood in Totnes, poor education, self-taught to high level in mathematics. 1810 Trinity College Cambridge, Analytical Society, talented propagandist when young man. 1814 Left Cambridge, married, gentleman philosopher in London. 1816 Disruptive member of Royal Society. Logarithmic and trigonometric tables first large scale task done by human computers. Logarithmic tables simplified mathematical computation in the 16th and 17th C. Trigonometrical tables -angles and areas -surveying and astronomy. Table Making Slide 17 Slide 18 3
The late 18 th Century Navigational tables for mariners, Star tables for astronomers, Life insurance tables for actuaries, Civil engineering tables for architects All produced without any mechanical aid. Reliable tables vital for GB (ships, economy) and later USA Mechanising the Process (1) Difference Engine used the method of differences that French mathematicians and others used in table-making. Difference Engine very simple concept: It consisted of a set of adding mechanisms for calculations and a printing part. Very expensive to build very advanced engineering needed. Replica in Science Museum, rebuild led by Professor Doron Swade (our visiting professor). Slide 19 Slide 20 The Difference Engine Slide 21 Babbage only built a small prototype of the Difference Engine. He had a new idea - that was capable of performing any calculation that a human could specify for it. In almost all important respects, it had the same logical organisation as the modern electronic computer. Babbage was so taken with the notion of this wonderful machine that he completely forgot the original purpose for making a mechanical calculator: table-making. used punched cards, inspired by French weaving looms invented by Joseph Marie Jacquard that used such devices. Slide 22 Jacquard s Loom Slide 23 Jacquard s Loom Slide 24 4
Silk picture portrait of Jacquard 1839 Original portrait Jacquard Used 2,400 cards! Jacquard s Loom Slide 25 Slide 26 Punched Cards Slide 27 Slide 28 Born December 10 th 1815, daughter of the poet Lord Byron and his wife Anna Isabella (Anabella). Parents separated 4 weeks later, then Byron left England, never to return. Her mother brought her up as a mathematician and a scientist and did not want her to be a poet. Ada hoped to be an analyst. She was highly imaginative and wanted science to be poetical. Lord Byron At the age of 8 Ada showed an interest in mechanical devices and built detailed model boats. (Note most of the people today have been practically-oriented as well as towering intellectuals.) She was tutored in mathematics by a professor at the University of London (now UCL). Slide 29 Slide 30 5
In November 1834, Ada heard about the Analytical Engine at a dinner party. He talked about using his machines to forecast. Ada was impressed by the universality of his ideas and was apparently the only one to understand them and envisage how they might work. Ada and Babbage became good friends and she worked with him helping him with: design documentation translating his writing producing programs for his machines. Slide 31 Slide 32 In 1842 Babbage went to Italy and lectured on the Analytical Engine. An Italian article on the engine was translated by Ada who then added her own notes to form the Sketch of the Analytical Engine (1847), which is the authority on the subject. She married Lord Lovelace in 1843. She had 3 children which her husband brought up while she studied mathematics! Ada was a woman of vision and imagination. She felt mathematics would become a universal system of symbols to represent anything in the world. Title page of Sketch Slide 33 Slide 34 She predicted the Analytical Engine could be capable of almost anything. She thought it could be programmed with rules of harmony and composition and thus produce scientific music. She suggested the first ever program using Bernouilli numbers. The programming language Ada was named in 1979 in her honour. She died in 1852, aged 36. A year later a difference engine was built by the Swedish Scheutz brothers. She also said it would produce graphics, and would have scientific and practical uses. Slide 35 Slide 36 6
The analytical engine was to be powered by a steam engine and would have been over 30 metres long and 10 metres wide. The input (programs and data) was to be provided to the machine via punched cards. For output, the machine would have a printer, a curve plotter and a bell. The machine would also be able to punch numbers onto cards to be read in later. It employed ordinary base-10 fixedpoint arithmetic. There was a store (i.e., a memory) capable of holding 1,000 numbers of 50 digits each. An arithmetical unit (the "mill") would be able to perform all four arithmetical operations. Slide 37 Slide 38 The programming language to be employed was akin to modern day assembly languages. Loops and conditional branching were possible. Hence the language as conceived would have been Turing-complete* long before Alan Turing's concept. *next week Three different types of punched cards were used: one for arithmetical operations, one for numerical constants, and one for load and store operations, transferring numbers from the store to the arithmetical unit or back. There were three separate readers for the three types of cards. Slide 39 Slide 40 7