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Stephenson:Neal:Quicksilver:299:…When you turn the crank?(Alan Sinder)

From the Quicksilver Metaweb.

This is a page for gear heads and the Arithmatickal Engine.

Stephensonia

Quote:*“It is unworthy of excellent men to lose hours like slaves in the labor of calculation which could safely be regulated to anyone else if machines were used.” Neal's fictional Leibniz feels Daniel is being too literal minded — but leads us from thinking about cogitation and computation being one and the same (in John Wilkins' Analytical Language), to a philosophical theory on Mind and Matter*. One of them sees the false dichotomy — at least.

Authored entries

Arithmetickal Engine

Gottfried Wilhelm von Leibniz lived in Paris from 1672-6, and while waiting for an opportunity to carry out his diplomatic objectives, set about learning mathematics and getting himself known in intellectual circles. So Leibniz took a trip to London, in January 1673, which enabled him to make personal contact with members of the Royal Society, in particular its secretary, his fellow German Henry Oldenburg.

The Society had given a mixed reception to his treatise, The Theory of Concrete Motion, which he had sent them, but they were very intrigued by another of his projects which he had brought along to show them. This was the prototype of a mechanical calculator he had been working on while still in Germany. It may have been on this trip that he learned of (or heard rumors about, depending on your position in the controversy) Newton's work on the calculus (see The Priority Dispute).

He was very proud of his invention, once thought of commemorating it with a medal bearing the motto SUPERIOR TO MAN, and much later he had a machine made for Peter the Great of Russia to send to the Emperor of China as an example of superior Western technology. Its immediate applications were obvious: it would save considerable labor and improve accuracy in accountancy, administration, surveying, scientific research, production of mathematical tables and so on. This was all more significant than we might now appreciate, since at the time even educated people rarely understood multiplication, let alone division. For example, Samuel Pepys had to learn his multiplication tables when already a senior administrator at the Navy Office.

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**A K A the Leibniz Calculator

"It is unworthy of excellent men to lose hours like slaves

in the labor of calculation which could safely be regulated to

anyone else if machines were used."**

In the long term, this was not necessarily a disaster as there were in existence several calculating aids (eg, abacuses of various flavors, and so on), and calculating shortcuts (eg, casting out nines, successive duplation, etc), which worked well for the sort of unit based accounting needed in commerce before long term capital finance became an issue. It was the calculus and its applications (in industry as well as finance) which required a considerable advance on those existing methods.

Leibnitz envisaged a larger version of his calculator being used to mechanise all reasoning processes, once all possible thoughts had been given a number through his projected ‘Universal Characteristic.’ Instead of fruitless arguing, people would say, ‘Let us calculate’ – and they could do so by setting the dials and cranking the handle of his machine (one of a number of Leibnizian schemes satirised in Jonathan Swift's Voyage to Balnibarbi).

The calculator itself was a considerable advance on most earlier mechanical calculators, for instance Pascal's Pascaline of 1642. No example of an earlier design, Wilhelm Schickard's of 1623, has survived, but it may have been more capable than either, if the partial descriptions surviving have been understood properly. Leibniz designed his specifically as a multiplier and divider, and invented a number of devices which became standard in later technology – in particular the stepped reckoner (or ‘Leibniz wheel’), which had cogs of varying lengths. The Leibniz calculator incorporated a new mechanical feature, the stepped drum — a cylinder bearing nine teeth of different lengths which increase in equal amounts around the drum. This will feature in later calculators for the next 300 years.

However, despite spending a small fortune on the project right up to the end of his life, he never developed a version which could do carrying completely automatically. One of his models still survives, and is now in the Hanover State Library.

Leibniz's trip to London was cut short by the news of the sudden deaths of both his patrons: * of Boineburg in December 1672, * and of the Elector in February 1673.

IBM's Replica

IBM built a replica of the Leibniz Calculating Machine.

Logic Mill

One is also curious about the logic mill of Daniel's. His school's tee-shirt display a portion of the machinery.

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The Curta Calculator