In the seventeenth century, two philosophers built machines that did arithmetic. They proved something that seems obvious now and was radical then: calculation could be delegated to a deterministic mechanism that does not think, only turns.
The idea
Represent numbers as the positions of toothed wheels, and arithmetic becomes the turning of gears. The hard part is the carry, propagating a tens-overflow from one digit to the next, which is exactly the problem a digital adder must solve.
Pascal’s Pascaline
In 1642 Blaise Pascal built an operational mechanical calculator with a reliable tens-carry. Its trick was a weighted mechanism, the sautoir, that stored energy as a wheel turned past nine and released it to nudge the next wheel forward. He built about twenty of the machines.
Leibniz’s Stepped Reckoner
Gottfried Leibniz designed a more capable machine from 1672 and built versions in 1694 and 1706. Its stepped drum let it multiply as well as add, and it introduced a movable carriage of the kind mechanical calculators would use for centuries.
Why the carry matters
The carry is the genuinely hard part of mechanized arithmetic. Adding two digits is easy; handling the overflow that ripples down a row of digits is where the engineering lives. That same carry propagation is the heart of the binary adder inside every modern processor. Pascal and Leibniz were solving, in brass, a problem digital hardware still solves today.
Related Notes
- Leibniz and Binary, the number system Leibniz also gave computing
- The Antikythera Mechanism, an even older computing machine
- Von Neumann Architecture, where arithmetic finally went electronic
- History of Computing, the section index
Sources
- “Mechanical calculator,” Wikipedia. https://en.wikipedia.org/wiki/Mechanical_calculator . Supports Pascal’s 1642 operational calculator with a tens-carry using the weighted sautoir, Leibniz designing the Stepped Reckoner from 1672 and building versions in 1694 and 1706 with a stepped drum that could multiply and a movable carriage, and the use of gears with carry mechanisms to automate arithmetic.