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Babbage's Calculating Wheels
From: Science Museum
| By:
Doron Swade |
EDITOR'S INTRODUCTION |
Charles Babbage's calculating wheels are today considered to be a pioneering design in the creation of mechanical engines. Although only one of the engines, the Difference Engine, was ever physically built, Babbage's designs anticipated the contemporary division between 'processor' and 'memory' which we see in modern electronic computers. |
 harles Babbage (1791-1871) was an English gentleman of science with an impressively wide range of interests. He was an inventor, reformer, mathematician, philosopher, scientist, critic, political economist and a prolific writer. He is nowadays widely known for his pioneering work on vast mechanical calculating engines. The few mechanical assemblies that survive represent the earliest antecedents to the modern computer and are among the most celebrated icons in the prehistory of computing. |
The tedium of doing calculations by hand stimulated attempts to build mechanical calculators well before Babbage's own efforts, and the task had challenged some of the most versatile intellects of all time. Devices were built in the seventeenth century by Blaise Pascal, the French philosopher-mathematician, and by Gottfried Leibniz. Pascal's invention was paraded before the social and intellectual elite of the day (including Lord Byron's daughter, Ada Lovelace) and caused something of a stir. Though these early desk-top devices represent significant steps in the evolution of mechanical calculators, they were more in the nature of ornate curiosities. |
Before the widespread availability in the twentieth century of dependable mechanical and, later, electronic calculators, scientists, astronomers, navigators, actuaries, bankers and the like relied for the most part on printed mathematical tables to perform calculations requiring more than a few figures of accuracy. The repetitive calculations for these tables were performed by hand by people called 'computers', and results were then copied and set in loose type for printing. Inevitably there were mistakes. |
 The task that Babbage set himself in 1821 was to build automatic calculating machines that would eliminate all these sources of inaccuracy at a stroke. The 'unerring certainty of mechanism' would free calculation of human error, and having the machine print the results automatically would eliminate the risk of mistakes in manual transcription and typesetting. Babbage's Difference Engine was conceived to do just this -- to calculate and automatically print error-free mathematical tables. The Difference Engine is so called because of the mathematical principle on which it is based, the method of finite differences. The advantage of the method is that it allows certain complex mathematical expressions to be calculated using simple addition only, without the need for multiplication and division which would ordinarily be required. |
 Work on Difference Engine No.1 started in the early 1820s. The project was abandoned in 1833 after a dispute with the engineer Joseph Clement who had been engaged to build the machine. About one-seventh of the machine had been assembled as a demonstration piece by Clement in 1832. This portion of the engine is the first known automatic calculator, and is one of the finest examples of precision engineering of its day. It is automatic in the sense that, for the first time, mathematical rule was successfully incorporated into the mechanism: the operator did not need to understand the mechanical principles to achieve useful results. All that was required was to turn the handle and the machine did the rest. |
 The Difference Engine is capable of a fixed set of operations determined by its wheel work, i.e. it is not a general-purpose machine and we would nowadays prefer to call it a calculator rather than a computer. Babbage's Analytical Engine, however, conceived by 1834, has features that are startlingly similar to those of a modern electronic computer. The analytical Engine was programmable using punched cards -- a technique used in the Jacquard loom to control patterns woven with thread. The engine had a repertoire of basic operations (multiplication, division, addition and subtraction) and could automatically execute sequences of these operations in any order. The internal organisation of the machine was also surprisingly modern in conception: the 'mill', where information was processed, was physically separate from the 'store' or memory where information was kept. The separation of 'store' and 'mill' (today called the central processor) is a feature that has dominated the design of the electronic computer since the mid-1940s. |
In operation the engine was capable of 'looping' -- repeating the same sequence of operations a specifiable number of times -- and of 'conditional branching' -- choosing one of a number of alternative actions depending on a predetermined condition being met. While we tend to speak of the Analytical Engine as though it was a physical thing, the machine was never actually built, though the designs were highly developed. It would have been the size of a small locomotive. All that Babbage accomplished in the way of hardware was a small, simplified experimental model of a portion of the 'mill' which was under construction at the time of his death in 1871. This assembly does scant justice to the grandeur of his schemes, but remains nonetheless a monument to the earliest attempts to realise an automatic general-purpose machine. |
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