Synchronization and feedback

[From Bruce Abbott (960711.1255 EST)]

Bill Powers (960711.0815 MDT) --

I find your description of coupled oscillators lucid and informative --
thanks. However, I remain puzzled as to why you appear to believe that
negative feedback is not involved in the synchronization process. Perhaps
the following passage offers a hint:

A natural oscillator would be some sequence of processes, each one
leading to the next, in a closed circle. Such a process would have a
natural periodicity, not controlled with respect to any particular
frequency but simply occurring at the frequency set by the speed of all
the individual processes in the circle. This process would not be under
feedback control; if anything changed in one or more of the processes,
the frequency would change (which is exactly equivalent to starting a
sudden continuous shift in phase relative to the old phase).

When I suggested that synchronization of menstrual cycles would be achieved
by a process involving negative feedback (and you replied that negative
feedback was not involved), we may have been thinking about different
processes. In the above passage you state that "this process would not be
under feedback CONTROL" (emphasis mine). Perhaps you took me to mean
"feedback CONTROL" when I said that negative feedback was involved. I MEANT
negative feedback, period. The movement of a simple pendulum involves
negative feedback, but no control. And so, I assert, do the synchronization
processes you and I described.

Perhaps I should explain how, for the benefit of other readers. In your
rubber band example, when one pendulum gets ahead of the other, the energy
transferred to the rubber band through stretching generates a force between
the pendulums that acts to retard the lead pendulum and advance the other,
in proportion to their masses. Thus, the phase difference between pendulum
swings brings an increasing force into play whose effect is to limit or
even reduce the separation. This opposing force has (by definition) a
negative feedback relationship to that phase difference.

Regards,

Bruce