Such is the tale as it has come down to us: Sometime around the year 1580, while visiting the cathedral in his hometown of Pisa, Galileo Galilei (1564–1642) noticed a recently lit lamp swinging overhead from a long rope. Curious about its motion, the young man calculated the rate of the lamp’s arc against his pulse and realized that the time it took the lamp to complete its arc remained constant, from the larger swings at the start of its motion to those near the end as the lamp slowed to a stop. In other words, the distance the lamp traveled from its vertical hanging position became gradually smaller but the speed during each swing decreased in just the right proportion to keep the time required of a full cycle constant throughout. It was at this moment that Galileo first conceived of “that very simple and regulated measure of time by way of the pendulum, which nobody had previously noticed.”

Galileo believed he had observed the isochronous—from the Greek iso, or equal, and chronos meaning time—nature of the pendulum: that its period (cycle time) was independent of its amplitude (distance travelled from the vertical). A pendulum operates something along the lines of a rollercoaster, converting potential energy at its highest point to kinetic energy as it accelerates toward its lowest point, before heading back the opposite direction, again storing potential energy and repeating the process. As we know, gravity is the force causing the pendulum’s natural swing, a back-and-forth motion that would continue indefinitely in the absence of any other forces. In reality, pendulums are subject to the additional force of air resistance, along with friction at the pivot, which causes the oscillations to slowly decay until eventually the bob hangs at rest. Galileo would have understood the effects of gravity and realized how the duration of the swing depended on the length of the line, and in his world the pendulum’s period remained constant as the amplitude decreased. To be sure, this observation was accurate only for pendulums swinging in a limited arc and others soon discovered that the pendulum’s period actually did increase somewhat at larger amplitudes.