Steven Strogatz is a great popularizer of maths and science in general: he’s a good story teller and can relate rather abstract mathematical concepts in simple words and captivating stories. I’ve most often come across him in RadioLab; he’s appeared in a number of episodes over the years. What intrigued me about his book Sync (apart from interviews where he mentioned it) was the book The Drunkard’s walk by Leonard Mlodinow I read last fall; I’m not completely sure Strogatz was mentioned in the book itself, but at least reviews and the theme bring them somewhat close together.

Strogatz’ book is dedicated to the discussion of spontaneous synchronization in physics, in nature and in society: in each case he follows the key points in the history of a field and how it viewed this phenomenon, discuses some of the concerns and ideas in the field, presents practical implications and eventually brings many disciplines into one. The book is intended for general public, so he never goes into too much depth - the coverage is not uniform, it is apparent which topics are of more interest to him and how easily can they be related to a layperson.

How exactly do coupled oscillators synchronize themselves, and under what conditions? When is sync impossible and when is it inevitable? What other modes of organization are to be expected when sync breaks down? And what are the practical implications of all that we’re trying to learn?

Steven Strogatz: Sync

First section of the book focuses on sync in living things, starting with the fireflies flashing. This visual and very relatable instance of sync is used as a touch stone throughout the book. The fireflies are summoned again and again, which becomes rather annoying and condescending. What surprised me quite a lot was the research about synchronization of menstrual cycles which I took as an urban myth (apparently not every woman influences others with the same intensity, sometimes a stale mate can occur etc.). The first section also contained the most interesting topic: sleep and circadian rhythms. I was fascinated by the development and the experiments conducted; multiple cycles (melatonin, body temperature) each averaging out around 24 hours were identified and possible relative shifts enabled to explain many parasomnias.

With the evening zone so close to habitual bedtime, even people without sleep disorders may sometimes find themselves trying to fall asleep when it’s most difficult. If you’ve ever gone to bed a few hours early, perhaps because you need to wake up early to catch a plane, you may have noticed how hard it is to fall asleep. The problem is not only that you’re excited about the upcoming trip; you’re also trying to sleep at the worst time in your circadian cycle. The same thing explains why Sunday night is the worst for insomnia. By staying up late and sleeping in on the weekend, you may have inadvertently allowed your circadian pacemaker and its evening forbidden zone to drift later and possibly intrude on your regular weekday bedtime.

Steven Strogatz: Sync

The middle part of the book recapitulates sync in physics and engineering. It starts with Huygen’s two connected pendulums and localization of ships at seas and ends with quantum mechanics (as every book does). Quite a lot of space is dedicated to documentation of the mathematical analysis of self-organisation, but also practical examples are listed (GPS, electrical grid).

A technical difficulty with interconnecting was that all the generators had to be synchronized to spin at exactly the same rate, even though they might be separated by hundreds of miles. Synchrony was crucial. Without it, power would slosh back and forth through the grid, causing tremendous current surges in the transmission lines. In the worst case, a generator might draw so much power that it could explode or be severely damaged. (Today, special protective equipment disconnects any generator that falls out of step.) Part of the solution came from the laws of physics. Electrical engineers found that generators connected in parallel had inherent tendencies to synchronize their rates of rotation. In other words, a parallel grid tends to be self-synchronizing: a beautiful instance of spontaneous sync, in the spirit of Huygens’s sympathy of clocks.

Steven Strogatz: Sync

The last section of the book covers the hardest topics of the book. Personally, I found it a little confusing, often had to re-read few pages to grasp the meaning for at least a few minutes to be able to follow the text. One review I read complained about too few images and this is the part of the book which would benefit from them the most: neither cryptography nor topology are easy to relate by word only. What kept me going was the personal aspect of these two chapters. The last chapter of the section about small-world and scale-free networks was the least revealing for me. It covered all the points common for this topic: Kevin Bacon number, Erdős number, Milgram’s experiment and six degrees of separation, epidemics analysis, power of weak connections in the job market etc. It’s a nice read for someone who has managed to not hear about it ten times over already.

In the very last chapter, Strogatz dives into the implications of sync for human societies. He’s reasonably cautious and doesn’t claim that what holds for crickets has to hold for humans and luckily doesn’t let any more telepathy mumbo-jumbo loose (which unfortunately occurs in this book). The examples he brings forward are the popularity of fads, traffic congestion without any apparent reason or the binding problem of human consciousness.

I found the book interesting, but not as interesting as I expected. That’s partially because of my previous familiarity with some of the concepts presented, but the book was a collection of angles which are only now being bound together and I didn’t feel a clear thread throughout the book. That’s not to say, that it’s uninteresting or boring. For example the chapter about sleep and circadian rhythms was fascinating and I would recommend it to anyone. In any case, Sync is worth reading for anyone who’s interesting in the world around.