# Mechanical Computers

In the last class, Dr Luca Di Mare described the origins of computing, going right back to the analogue machines of the ancient and medieval worlds. This time, Dr Di Mare continues the story, recounting the history of mechanical computers from Isaac Newton through to the famous Difference Engine and Analytical Engine developed by Charles Babbage in the nineteenth century.

Two important events that determined the evolution of computing equipment took place several centuries from each other. The first was the introduction in Europe, through the writings of Arab scholars, of the decimal numbering system, an Indian discovery. This is the system we use nowadays and which became universally adopted in the western world from the 13th century onwards. Computing machines that produce results in the form of digits – not necessarily in base 10 – are called digital computers.

The other event was Newton’s publication of the Principia and his (contested) discovery of calculus. Many of the predictions based on Newton’s new theory gave rise not to simple algebraic relations, but rather to differential equations, which express relations between functions and their derivatives. In general, differential equations can only be solved in an approximate manner, i.e. with even larger amounts of computational effort. Unsurprisingly, soon after the publication of Newton’s Principia, computing aids started appearing in increasing numbers, even though they were not always very practical. The first functional mechanical digital calculator was Blaise Pascal’s Pascaline, built in 1642 – admittedly to help with the work of Pascal’s father as a tax collector. The Pascaline, and its derivatives, were the precursors to the mechanical calculators of the late 19th and early 20th century.

Though useful, early mechanical computers lacked the ability to reuse previous results. They were unable to perform repeated operations on a variable like modern computers do. This feature was first introduced by Charles Babbage in his Difference Engine. Babbage graduated from Peterhouse in Cambridge with a degree without examination – possibly because he failed to show up for the defence of his thesis. Eventually, he became Lucasian professor of Mathematics (the same chair held by Newton and recently by the late Stephen Hawking) but attracted his colleagues’ antipathy with his lack of interest in teaching: he never gave a lecture in Cambridge. Babbage’s Difference Engine was a mechanical computer intended to produce tables of logarithms for naval applications. Its design was revolutionary because it featured a printer and a device to store previous results. Its first design was too complicated for the manufacturing techniques of the time and was never completed despite the expenditure of £17,000 (about £2,000,000 in today’s money) granted by the government of the time. Having abandoned the Difference Engine, Babbage moved on the Analytical Engine: the first programmable computer in human history. The Analytical Engine had two separate input streams, one for the data and one for the instructions, a memory and a computing unit: all the main features of modern computer architecture. Babbage didn’t live to see the Analytical Engine completed. His son oversaw the construction of a section, which was competed in 1906.

Dr Luca di Mare is Tutorial Fellow in Engineering Science and Fellow for Graduates at St John’s College, Oxford

Next time, Dr Di Mare will take the story up to the twentieth century, and the remarkable stories of the ‘human computers’ involved in some of the most crucial developments in the history of science and engineering.

## Further Resources

A Babbage difference engine simulator