Leibniz wheel

Gottfried Wilhelm Leibniz wanted a machine that could multiply and divide, not merely add and subtract like Pascal's calculator. His Stepped Reckoner, developed between 1673 and 1694, introduced a new mechanism—the stepped drum or Leibniz wheel—that would dominate mechanical calculator design for two centuries.

The stepped drum was a cylinder with teeth of varying lengths along its surface. As the drum rotated, these teeth engaged a counting wheel. The position of the counting wheel along the drum's axis determined how many teeth engaged per rotation—setting the digit to be added. Multiple rotations performed multiplication; division worked through repeated subtraction.

The mechanism was ingenious but the execution was flawed. Leibniz's prototype suffered from the same manufacturing limitations that plagued Pascal's machine. The carry mechanism occasionally failed, producing incorrect results. Leibniz spent decades refining the design without achieving reliability.

Nevertheless, the stepped drum principle proved correct. Thomas de Colmar's Arithmometer of 1820, the first commercially successful mechanical calculator, used Leibniz wheels. So did the Monroe, Friden, and Marchant calculators that equipped 20th-century offices before electronic computers arrived.

Leibniz saw the Stepped Reckoner as part of a larger project: mechanizing reasoning itself. If calculation could be automated, perhaps logic could follow. His work on symbolic logic, though incomplete, planted seeds that Boole, Frege, and eventually Turing would cultivate.

The contrast between Pascal and Leibniz illuminates different approaches to mechanical computation. Pascal automated a specific operation (addition) with a dedicated mechanism. Leibniz sought generality—a machine that could perform multiple operations. This tension between specialized and general-purpose computation persists in computer architecture today.

The Leibniz wheel proved that multiplication could be mechanized. That practical machines took another century to appear reflects manufacturing constraints, not conceptual limitations.