Pre-history of computing

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 Pre-history of computing
Thursday, 01 July 2010
Article Index
Pre-history of computing
Logs, bones and the slide rule
Mechanical calculators
Leibniz introduces multiplication

## Leibniz and the multiplier wheel

The next step on the road to workable calculator was made by another mathematician, the German, Gottfried Leibniz.

Gottfried Leibniz (1646-1716)

Leibniz is best known for the co-invention of calculus along with Newton and the acrimonious rows that ensued between them. He knew about the Pascaline and recognized its real weakness, the fact that multiplication had to be done by repeated addition. He solved the problem by inventing a new multiplier wheel.

This was a brilliant invention and it not only worked it formed the basis of all of the mechanical calculators that followed right up to the point where they were made obsolete by the electronic computer.

Two were built around 1673 but only one survives today. It could have changed the world but Leibniz lost interest and indeed grew bored with it. He moved on to consider more challenging problems like how to reunite the Protestant and Catholic Churches.

Leibniz also continued with his work on pure mathematics. In particular he started to think about the number base used to represent numbers. Mathematicians of the time understood the idea of using different bases but the general opinion was that base ten was the best. Leibniz on the other hand became convinced that binary was to be preferred.

From our viewpoint the reason is that binary arithmetic is simple and at the time building a binary calculator would have been easier than building a decimal one. But the reason that Leibniz was so keen on binary was that he thought it would be possible to use it to prove the existence of God. In his logic one symbolized God and zero the empty universe.

No one was very impressed by this mixture of philosophy and mysticism but he did convert the Emperor of China using the argument. What would have happened if instead of going off into the realms of the ridiculous Leibniz had managed to make the connection between his mechanical calculator and binary? Perhaps the information age would have been introduced along with steam engines.

## Colmar and the arithmometer

After Pascal and Leibniz nothing much happened in the mechanical calculator world for 100 years or so. The reason wasn't that the machines didn't work or weren't needed; it was just that the mechanical precision that they demanded wasn't readily available.

Charles Xavier Thomas de Colmar (1785-1870)

In 1820 the first calculator manufacturer, Thomas de Colmar, started building machines of the Leibniz type. He was comissioned to build an "arithmometer" for the 1855 Paris Exposition. It has 15 keys for input and allowed for 30 places of results and was housed in a cabinet that resembled a piano

The Colmar "Piano" Arithmometer

To put this in context Babbage thought of the difference engine in 1812 and the analytical engine, a true mechanical computer, in 1830. Of course, neither was actually completed.

After this point the rate of development increased. In 1870 the Baldwin company manufactured the first rotary drum machines.

Rotary drum calculator

The Baldwin company eventually became the Monroe Calculator Company. Other famous names include Friden, Selling and Burroughs. What is surprising is that so few of these companies made it through to the era of electronic computers. Most of them only went as far as making electromechanical peripherals such as paper tape readers. The only conclusion that you can draw from this is that extreme technological change really is about revolution rather than evolution. If what you are good at is precision metal work then you go out of business when electronics becomes the new medium.

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