Resonance: The Greatest Story Never Written

This is taking a minute.

A couple of months ago, I had a thought which in retrospect I sort of wish I hadn’t had, although that’s not to say I’m actually sorry I had it. The thought was this:

Everyone in the watch world argues about what resonance is and whether or not any so-called resonance watch actually exhibits sympathetic resonance between two balances, but there seems to be very little in writing about watches that addresses the basic physics underlying the phenomenon. Surely there must be at least some research on the subject? And then, if there is some sort of actual, mathematical analysis of coupled mechanical oscillators, surely it can be applied to watches with two balances and you could say for real, whether or not resonance was actually occurring in the watch?

In retrospect, it probably should have been more obvious to me than it was, that I had opened a can of worms. I thought at first about publishing the story over on WatchBox, but it seemed too long, too technical, and above all, far too niche (objections which would apply no matter where I tried to publish it; we’re talking about a long, probably kind of windy story on one of the most niche, if not downright obscure, subjects in horology). It seemed on the whole to be a better fit, as a sort of excrescence of a personal obsession, for Substack.

Anyway, that was the basic idea. What I’ve found out over the last two months (it has never, in my entire life as a watch writer, typically taken me more than two days to write a story, much less two weeks or two months, for crying out loud) is that the subject is a lot more complicated than I thought. First of all not only is there research literature on the subject, there is quite a lot of it – it took a while for researchers to begin to look into the subject, but by 2017 when one of the more recent papers was published, the authors had over fifty citations in their bibliography – and those were just articles on couple mechanical oscillators, largely in the specific context of coupled pendulums.

It probably should have also been more than obvious to me that the subject of coupled oscillators was going to turn out to be bigger than just coupled pendulums. Harmonic oscillators can be found – well, everywhere. They show up in any major branch of science you care to name, including biology, classical mechanics (natch) and even quantum mechanics. A search on Google Scholar for articles on coupled oscillators produces 1.4 million hits (and no, I’m not going to read them all, not unless some rich patron wants to set me up with an annual stipend – a fat one, mind you, I like high living – to spend the rest of my life figuring out how resonance watches work, or if they work.)

All this because twenty years ago, an irascible Frenchman put a bug in my brain about resonance. I thought the story would run to a word count of maybe a grand and a half, but the various drafts are now into thousands of words and source material has gotten out of control as well – if I had nothing to do but work on the story it’d be a full-time job, and I have plenty of other things to do. I’m still going to finish some version of the story, but the subject of coupled oscillators is far, far too large and complicated for a Substack post and it’s much, much bigger than watches and clocks (albeit a lot of the literature in other scientific fields still explicitly mentions Huygens as the father of the science of the behavior of coupled harmonic oscillators). At some point and that right soon, I’m going to have to decide where the story has to end in order for it to be meaningful to its intended audience of watch enthusiasts who, like myself, aren’t necessarily averse to working a little to understand some math but who aren’t actually specialists in the intricacies of classical mechanics and quantitative analysis.

I wouldn’t say that the subject has exactly been a waste of time to research, though. What started with Huygens lying in bed and literally staring at the ceiling – or at least, a couple of pendulum clocks hanging from the ceiling, and fortuitously close to each other in construction and serendipitously close to each other in proximity – has become a field of fundamental, fascinating, and in many cases, highly unpredictable interest in any area of science where there are harmonic oscillators and some mechanism for coupling them (which is, basically, every area of science).

Really, someone should write a book.