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Leibniz and the Stepped Reckoner

Definition

Leibniz's stepped reckoner was a mechanical calculating machine intended to automate addition, subtraction, multiplication and division, extending earlier mechanical arithmetic devices.

What was the stepped reckoner?

The stepped reckoner was a mechanical calculator developed by Gottfried Wilhelm Leibniz. Work began in the 1670s, and a completed machine dates from the 1690s. It used a mechanism now called the Leibniz wheel or stepped drum. Unlike Pascal's machine, Leibniz aimed to mechanize all four basic arithmetic operations: addition, subtraction, multiplication and division.

How did the mechanism work?

A stepped drum has teeth of increasing length around its circumference. By changing the position at which a gear engages the drum, the machine can transfer different numbers of teeth during a turn. That lets one rotating mechanism represent different decimal digits. The surviving stepped reckoner was ingenious but mechanically unreliable, partly because precision manufacturing of the period was not adequate for all of its moving parts.

Its influence

The design was important even though the original machines were imperfect. Variants of the Leibniz wheel were used in commercial mechanical calculators for roughly two centuries. The story is an early example of a recurring computing pattern: an abstract mathematical operation may be understood long before engineering can implement it cheaply, reliably and at scale.

Related terms, defined

History & Foundations The Jacquard Loom and Programmable Patterns The Jacquard loom used punched cards to control textile patterns. It was not a general-purpose computer, but it demonstrated that external encoded instructions could control a machine's behavior. History & Foundations Charles Babbage and the Analytical Engine Babbage's Analytical Engine was a nineteenth-century design for a general-purpose mechanical computer with concepts resembling a processor, memory and program control. History & Foundations Ada Lovelace and the First Published Algorithm Ada Lovelace's notes on Babbage's Analytical Engine included a procedure for calculating Bernoulli numbers and are widely described as containing the first published algorithm intended for machine execution. History & Foundations Boolean Algebra and Machine Logic Boolean algebra formalizes logical operations with values such as true and false. Its application to switching circuits made it foundational to digital logic. History & Foundations Punched Cards and Automated Data Processing Punched cards encode information through the presence or absence of holes. They were widely used for automated tabulation, data input and early computer programming.

Reference guide and primary sources

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