Odd sympathy

The phrase odd sympathy (the actual phrase used was odd kind of sympathy) was used by Dutch mathematician and physicist Christiaan Huygens (1629-95) in a letter to the Royal Society of London pertaining to the tendency of two pendulums to synchronize, or asynchronize, when mounted together on the same beam. Huygens, the inventor of the pendulum clock, noticed the effect while lying in bed. Two pendulums, mounted together, will always end up swinging in exactly opposite directions, regardless of their respective individual motion.

Huygens originally believed the synchronization was due to air currents shared between the two pendulums, but he dismissed the hypothesis himself after several tests. Huygens would later attribute sympathetic motion of pendulums to imperceptible movement in the beam from which both pendulums are suspended. This idea was later validated by researchers from the Georgia Institute of Technology who tested Huygens' idea.

Using instruments capable of registering movement too small to have been measured in Huygens' time, the Georgia Tech researchers chronicled the nature of the forces at work on the supporting beam. They found that if the pendulums are moving in the same direction, together they tend to move the beam the opposite direction, giving rise to frictional forces that resist motion in the same direction. If however, the pendulums are moving in opposite directions, these forces cancel each other out, causing the beam to remain motionless. Thus, motion, in this example, tends to be perfectly asynchronous.

The Georgia Tech researchers (Bennett and co-workers) refer to odd sympathy as an example (possibly the first observed examples) of the principle of coupled oscillation, which generally addresses the pervasiveness of synchronicity in nature.

Huygens observed anti-phase synchronization of pendulum clocks. Bennett and co-workers from the Georgia Institute of Technology reported also anti-phase synchronization of pendulum clocks in 2002. However, in-phase synchronization of pendulum clocks has also been observed. This was discussed by a book written by I.I. Blekhman. This was also mentioned in the book by Pikovsky and co-workers. A detailed analysis was provided by Fradkov and Andrievsky from Russia in 2007 regarding the conditions for in-phase or anti-phase synchronization of a 2-pendulum system. (Please see reference.)


  • I.I. Blekhman, "Synchronization in science and technology", ASME Press, New York, 1988. (Translated from Russian into English.)
  • Pikovsky, A.; Rosemblum, M.; Kurths, J. (2001). Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge University Press.
  • A.L. Fradkov and B. Andrievsky, "Synchronization and phase relations in the motion of two-pendulum system", International Journal of Non-linear Mechanics, vol. 42 (2007), pp. 895-901.

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