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The term “odd sympathy” was coined by the 17th-century Dutch mathematician and physicist Christiaan Huygens to describe the strange phenonmenon he observed while laying sick in bed and looking up at two of his newly invented pendulum clocks hanging on the wall above him. Inexplicably, the two pendulums always swung in opposite directions even though they were at opposite ends of the wall. Even when he would release them in different positions, they eventually fell back in synch (or antisynch, to be precise). Huygens had discovered the principle of coupled oscillation, but it took a recent study by physicists at Georgia Tech (image above) to prove that it was the miniscule force of the pendulums operating on a beam in the wall that caused them to link up. From American Scientist:

To explain why the pendulums move in opposite directions, the team set up a system of equations that took into account the pertinent properties of the system, including the weights of the various components and friction. The structure of the equations made it clear that friction is the cause of the antisynchronized motion. As Huygens originally postulated, the swinging of the pendulums exerts small forces on the supporting beam. If the pendulums are moving in the same direction, together they nudge the beam the other way, giving rise to frictional forces that naturally put a damper on this kind of motion. If the pendulums are moving in opposite directions, however, the forces they exert on the beam cancel each other, and the beam doesn’t move. So over time, antisynchronized motion wins out over synchronized motion.

The mathematics of “odd sympathy” are explained in this 1993 Scientific American article. The phenomenon is also exhibited by fireflies in Southeast Asia that blink in unison (right), creating vast auras of flashing light:

When the males arrive at dusk, their flickerings are uncoordinated. As the night deepens, pockets of synchrony begin to emerge and grow. Eventually whole trees pulsate in a silent, hypnotic concert that continues for hours.

Have a look at this virtual model of firefly synchronization, and this do-it-yourself plan for building electronic, synchronized fireflies.

Like fireflies, crickets also chirp in a shared, sympathetic chorus. In 1897, a scientist named A.E. Dolbear discovered that the rate of chirping is directly proportional to the outside temperature. Hence Dolbear’s Law:

where N is the number of chirps per minute and T is the temperature in degrees Celsius. (The forumla is applicable only to snowy tree crickets. Field crickets, which are more common, are less reliable thermometers.)

In another example of “odd sympathy,” pacemaker cells in our heart learn to beat at exactly the same instant. And as any sorority sister can attest, menstrual cycles have a habit of aligning. (A study conducted at Radcliffe in the 1960’s found that the average difference in starting dates of menstrual cycles of close friends decreased from 8.5 days to 5 days over the course of a school year).

More recently the phenomenon of “odd sympathy” has been invoked to explain why people clap in unison:

Our results indicate that after an initial asynchronous phase, characterized by high-frequency clapping (mode I), individuals synchronize by eliminating every second beat, suddenly shifting to a clapping mode with a double period (mode II) where dispersion is smaller.

Next time there’s a round of applause, keep your ears peeled for that moment when the clapping slows down by half. That’s the sound of chaos turning into unison.

This entry was posted on Monday, October 23rd, 2006 at 1:05 pm and is filed under clock, science. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.