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On the Teeth of Wheels

Brian Hayes

For many years, the basic raw material of the computer industry was not silicon but brass. The calculators of Wilhelm Schickard, Blaise Pascal and Gottfried Wilhelm Leibniz were all based on the meshing of metal gears. Later, Charles Babbage conceived elaborate fantasies of gearwork for his calculating engines. Later still, Vannevar Bush put gears and other rotating parts at the heart of his differential analyzer. And all of these inventors were foreshadowed by anonymous artisans in the city of Rhodes in the first century B.C., who assembled more than 30 gears in a remarkable calendrical computer known as the Antikythera mechanism.

Figure 1. Antikythera mechanism . . .Click to Enlarge Image

These examples testify to the importance of gears in the history of computing. Less obvious is the importance of computing in the history of gears. I was ignorant of the connection myself until quite recently, when I went looking in the library for a work on number theory and found myself making a detour into the engineering shelves. I learned there that the designers of gear trains have not merely borrowed ideas from mathematics but have also developed some of those ideas on their own and lent them back to the mathematicians. Mechanical engineers doubtless know all about this two-way traffic between math and mechanism, but others may find the computational roots of gear design as surprising as I did.

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