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F.P. Journe

Some real food for thought here!

 

It will probably take a few days to digest and comment more fully, but I wanted to note that in the PurstS discussion you linked there is a further link to a 2002 article on the watch (search for "LINK" in the discussion).  That paper notes the behaviour of each of the escapements when connected to a timing machine that can track each vibration.  As "resonance" is achieved, the two patterns are said to merge into one much like the oscillation video you posted (excellent video!) of the metronomes.  The latter seem highly relevant to the mechanism in the resonance, although I would have thought at first guess that the mechanism in the watch is less dramatic since momentum is not likely conserved (i.e. the cans on which the oscillators are allowed to sit can move freely back and forth while the escapements can "interact" in a more constrained way - probably much like Huygens clocks.  In any case, probably wise not to speculate ahead of more thought and reading.

Thanks very much for doing this research and making it easily accessible - no doubt this will provide for a few days of thought and hopefully some insight.  All the best.

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