Explaining the mysteries of synchronization, from swinging pendulums to chirping crickets

birds do. bugs do. Even the audience at a play does. The cells in your body are doing it right now, and it’s pretty amazing.

What they all do is sync. From lightning bugs flashing to the rhythm of a summer field to the thunderous applause of an audience that somehow melds into a beat, life and the universe offer several notable examples of spontaneous synchronization between populations. While there are still deep mysteries as to how this happens, scientists have already grasped the basic mechanism that not only explains spontaneous synchronization, but may also provide some fundamental clues about life and its use of information.

Science of Synchronization

Scientists have grappled with the mystery of synchronization since the birth of science. In 1665, Christiaan Huygens, the inventor of pendulum clocks, wrote of a strange kind of sympathy shared by pendulums positioned side by side. After each began out of phase – in other words, swinging to its own rhythm – the two pendulums soon engaged in a perfect dance. The brilliant physicist that he was, Huygens concluded that there must be some subtle and imperceptible movements in the material supporting both pendulums that drove them to synchronize.

The subject was later expanded beyond mechanical phenomena. In 1948 Norbert Weiner wrote a book entitled cybernetics which focused on the twin problems of control and communication in systems. In his book, Weiner asked how large populations of crickets or neurons manage to synchronize their behavior so that their chirps or neural fires end up moving in lockstep.

So if both the living and non-living worlds exhibit spontaneous synchronization, what are the key elements needed to capture their essence?

clutches and oscillators

The crucial advance in this field came with the realization that all cases of synchronization can be mathematically captured with two components. First, there is a population of oscillators – a fancy mathematical way of saying anything that repeats. A pendulum is a mechanical oscillator. A neuron firing repeatedly in a brain is a cellular oscillator. Lightning bugs that flash in a field are animal oscillators.

The next step is to enable some kind of coupling between all individuals. The pendulums rest on a table. The neurons have connections to other neurons. The fireflies can see each other light up. These are all examples of pairings.

With these two components, the entire problem can be neatly captured in mathematics using what are called dynamical systems, which are basically differential equations for steroids. Yoshiki Kuramoto did just that in two works written in 1975 and 1982. The so-called Kuramoto model has become the gold standard basis for studying spontaneous synchronization. The Kuramoto model showed the balance between the strength of the coupling between oscillators and the variety of frequencies contained in each of them.

What’s the frequency, Kuramoto?

If each cricket chirps on its own pulse—a pulse that is completely random compared to all other crickets—then only very strong coupling results in beautiful synchronization of the chirps. “Strong coupling” here means that the crickets are really looking out for each other. Weak coupling would mean the crickets hear each other, but they’re not motivated to pay much attention. Only when all crickets have innate chirping frequencies that are relatively close together can they become synchronized, even with weak coupling.

A wide range of natural frequencies requires strong couplings for synchronization. A small range of natural frequencies requires only weak couplings for synchronization.

However, the most important feature that the Kuramoto model revealed was the pronounced phase transition in these types of systems. A phase change is a relatively abrupt change from one mode of behavior (no synchronization) to another (full synchronization). Scientists found that the Kuramoto model showed a clear onset of synchronization, which is the hallmark of a phase shift. As the coupling strength between a population of oscillators increases, they make the sudden transition from chaos to chorus.

The Kuramoto model is a nice example of a simple mathematical system capable of capturing complicated behavior in a complex system. Therefore my colleagues and I use it as a first step in trying to develop a theory of semantic information. We recently received a Templeton Foundation grant to understand how life uses information to create meaning – something that normal information theory doesn’t really address. Because the Kuramoto model is both simple and reflects life’s remarkable behaviors, we plan to examine whether we can transform it into an information-theoretic framework. If it works, then perhaps we will see a little deeper how life and the universe make sense out of harmony.