Charles Babbage's Difference Engine

Early calculating machines, despite their ingenuity, were more like intellectual playthings than essential aids. Most of the functions that had to be calculated for standard tables were far more complicated. Charles Babbage (1791-1871) found a way to simplify these calculations, and in so doing conceived one of the earliest notions of a general-purpose computer. Never completed in his lifetime, a remaining fragment built by his son, Henry, demonstrates the working principles of Babbage's design.

Dr. Louis Auzoux was a French doctor who made papier-mâché models of humans, animals, and plants for use in teaching medicine and anatomy.

'Dissectable' models

Dr. Auzoux's models were designed to be taken apart and put back together. 'Dissecting' the models provided a similar experience to examining real human bodies or animals. The models were known as 'clastic anatomies' (from the Greek word 'to break') because they could be taken apart.

New sciences, new models

Dr. Auzoux originally developed his models of human bodies and body parts for professional medical training. Because they were so useful for general education, they were widely adopted for teaching purposes around the world.

The public also benefited from Dr. Auzoux's knowledge, attending his lecture courses in anatomy and physiology that were specifically designed for a general audience. He even claimed that people could learn anatomy without the aid of an instructor simply by 'dissecting' the models by themselves, as many of the anatomical details were identified by labels in French. Other numbered labels, decorated with a small image of a hand, showed the order in which the models should be taken apart and reassembled by the student.

Dr. Auzoux founded a factory in his hometown in France for producing the models. Responding to changing trends in scientific research and education, the company began producing models of human embryos, animals and plants, as well as continuing to make models of adult humans.

Fame across France and beyond

In the 1820s Auzoux's models gained the approval of scientific and medical academies and he proudly publicised this when advertising his models.

Auzoux himself used his models for demonstrations in his own private lecture courses on anatomy and physiology for general audiences. Auzoux's company exhibited its teaching models at the industrial shows which took place in the second half of the 19th century, such as the Great Exhibition of 1851 in London, where they received much praise and many prizes.

During the 19th century Auzoux models were sold throughout the world, until models in plastic or plaster increasingly replaced them. Auzoux became a household name: in 1844 sculptor Antoine L. Dantan (1798-1878) produced a bronze bust of him. Upon Auzoux's death, his grateful home town erected a monument in memory of its benefactor.

Rival companies

By the end of the 19th century, rival companies emerged and developed other forms of biological teaching models for general audiences, some of them made entirely of plaster.

These models were increasingly simplified and without labels, unlike many of Auzoux's densely labelled examples, as their makers claimed that a large number of details would only confuse an inexperienced student.

Read more:

• Inside Auzoux's models
• Human models
• Animal models
• Plant models
• Foetus models

Life and work

Charles Babbage(Image 1) was born to a wealthy London-area banking family in 1791 and, after being educated in a number of schools and by various tutors, he enrolled at Trinity College, Cambridge in 1810. There, he befriended future Victorian science luminaries John Herschel(polymath astronomer and one of the first inventors of photography) and George Peacock (a noted mathematician), with whom he formed the Analytical Society to support the use of Leibniz's calculus over that of Newton.

Babbage was elected a fellow of the Royal Society in 1816, just two years out of Cambridge, and eventually became Lucasian Professor of Mathematics in 1828, a position held once by Isaac Newton and, more recently, Stephen Hawking.

Babbage's life was typical of the 19th century gentleman scientist. Like many of his peers, inherited wealth allowed him to explore his interests and contribute to research in mathematics, astronomy, and engineering.

Babbage's largest project, the Difference Engine no. 1, was a machine intended to save the government money by preventing critical errors in tables calculated and copied by hand. But after twenty years of costly work on his design - in which time he suffered through personal disputes with his toolmaker Joseph Clement and lost his father, wife, and all but three of their eight children - the Difference Engine no. 1 remained uncompleted.

Difference Engine no. 1

Tables of data generated from polynomial functions were critical for aiding navigation at sea using the lunar distance method of determining longitude. But because such tables had to be calculated by human 'computers', they suffered from errors in both calculation and in transcription and typesetting for the printing process.

Babbage was something of a connoisseur of tables and fastidiously combed through them for errors. During a meeting with Herschel in 1821 to verify calculations made by human computers he lamented,

"I wish to God these calculations had been executed by steam." Babbage in 1821(1)

Babbage's idea, hatched over the following two years, was for a device that would reduce the calculation of polynomial functions to mechanical addition using the method of finite differences. The engine would be 'programmed' with a function and cranked by hand to deliver the result. It would also be equipped with a press that would allow results to be printed as they were calculated in real time and replicated on the spot without error.

In 1822 he received funding for the device, called the 'Difference Engine', and hired a toolmaker, Joseph Clement, to build it. The Difference Engine called for nearly 25,000 parts in total, one of the most complicated engineering feats attempted in its day.

Although the engine would only be able to calculate polynomial functions, these could approximate logarithms and trigonometric functions, which was of much use to scientists and navigators. Babbage often required support for the device from his friends in high scientific society, and John Herschel used a seafaring comparison to great rhetorical effect:

"An undetected error in a logarithmic table is like a sunken rock at sea yet undiscovered, upon which it is impossible to say what wrecks may have taken place." Sir John Herschel, 1842 (2)

Understandably, the government was more interested in reliable tables than the machine in principle. A demonstration model was constructed in 1832, but despite his best efforts Babbage never saw one of his engines put to work in his lifetime.

Funding was officially cut off in 1842 at which time he had spent over £17,000, ten times as much as originally intended. Somewhat embarrassingly, the British government purchased a difference engine based on Babbage's original design made by Swedes Georg and Edvard Schuetz, which they demonstrated at the World's Fair in 1855. Babbage, however, was already preoccupied with bigger problems.

Henry Babbage's fragment

Part of the reason for the failure of the Difference Engine No. 1 was Babbage's growing preoccupation with an even more ambitious project, his Analytical Engine, a machine more revolutionary, yet simpler in design, on which he began work in 1834.

Inspired by the punched cards used to set up the industrial loom of Joseph Marie Jacquard, the Analytical Engine would 'store' numbers and intermediate results, while a separate 'mill' would process them arithmetically. Its architecture and degree of programmability has led many to label it a forerunner to the electronic computer. For her written description of how the Analytical Engine could be used to calculate a series of numbers, Ada King, Countess of Lovelace, has been called the first computer programmer.

Babbage learned much from designing the Analytical Engine and in 1847 began work on his Difference Engine no. 2, which could calculate much larger polynomials than the original engine and would require only one third of the number of parts.

However, the Difference Engine no. 1, even as incomplete, has its own place in computer history. After his death, Babbage's son Henry continued to work out his father's engineering problems, having inherited original components made during the failed construction attempts.

By recombining these components, Henry produced the partial fragment held in the Whipple's collection (Image 2) in 1879, as a means of demonstrating the feasibility of his father's design. This fragment has only two axles, compared to the seven in the original, so it can only perform very simple calculations. Indeed, it was used in the 1950s in Cambridge University's computer laboratories to demonstrate the automation of simple addition.

A similar fragment at Harvard University may have inspired a young Howard Aiken, who developed the Harvard Mark I (or IBM Automatic Sequence Controlled Calculator), the electromechanical calculator used by the U.S. in the Manhattan project.

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