To Converge You Must Diverge


You’ve known each other forever. In the restaurant, the appetizer takes an eternity to come. You sit in front of each other, both staring at the empty plates. You want to break the silence, but every possible topic that comes to your mind seems old. There’s nothing left to say. 

Have you ever felt like this before? "Out of sync” with someone you care about? It may not be caused by your differences—in fact, it could be that you two are becoming too similar. Physicists have found that, contrary to common beliefs, diversity can be essential to synchronization. And understanding complex mechanisms behind synchronization may help solve many challenges, from preventing blackouts to designing next-generation self-driving cars.

Synchronization is a collective, coherent behavior that emerges from the interactions of many otherwise autonomous individuals. For example, give two pendulum clocks suspended from the ceiling enough time, and they will mysteriously synchronize their oscillating motion. No one is trying to control them. No outside force is driving them. How can two perfectly autonomous pendulums spontaneously agree on their movements? The great Dutch scientist Christiaan Huygens discovered in 1660s that this “ghost force” originates in the imperceptible vibration of the beam connecting the two pendulums. His was the first scientific description of autonomous objects synchronizing through interactions. 

The synchronization of two pendulums is relatively easy to model and understand, but what about more complex systems – like the entrainment of pedestrians crossing a wobbly bridge, the spontaneous coordination among power-generators in our electrical grid, or the synchronous flashing of fireflies on a clear summer night? To model the spontaneous emergence of order from the complex interactions of thousands of individuals, we represent each individual – whether that’s a pendulum or a person – as a node. We call the interactions between them links. Then, the system of interacting fireflies/people/pendulums can be visualized as a network of interrelated players.

In any such system, two key factors determine its synchronizability: the structure of the network and the dynamics – or traits and behaviors — of the individual nodes. It is a bit like synchronized swimming or diving: to get a high score, the abilities of individual athletes matter, but the coordination between partners is also essential. 

Individual Differences

Often we think the more similar our nodes, the better they will work as a group. Just like “birds of a feather flock together,” one expects that “pendulums of a weight oscillate together.” But could there be scenarios in which only birds of different feathers flock together? Or in the case of consensus—a special yet ubiquitous form of synchronization—can individuals reach an agreement because of (not despite) their differences?

Imagine you invite a group of friends to your housewarming party and order a strawberry-kiwi fruit cake. Everyone is having fun. The cake arrives on time and looks delicious. Then comes the hard part—dividing the cake. If all your friends have the same preference, say, they are all obsessed with strawberry but hate kiwi, then everyone would be eyeing that corner slice with 3 pieces of strawberry on it. On a good day, people might try to be civil and compromise; on a bad day, a fight could break out and completely ruin your party.

But what if the group has a diverse set of preferences? Some like strawberry and some like kiwi; some love corners, others crave middle slices. Then it is easy to find a way to cut the cake that makes everyone happy. In this sense, having friends with heterogeneous tastes can really help the group reach consensus on how to divide the cake and ensure a fun party.

More generally, any interconnected group of people/pendulums/power-generators must overcome perturbations from all possible directions to synchronize. These perturbations can be any disruption to the group – like a person getting sick, a push to one of our pendulums, or a failed transmission line in the grid. And a synchronized network can be particularly vulnerable to one perturbation while being relatively resistant to others.

To see this, just look at a bag of your favorite potato chips. The top edge is different than the other three – it has these rugged ridges, which makes it easier to tear open (just imagine trying to tear open the other sides with the same amount of force). The differences mean the bag reacts differently to external forces acting on its different sides. Similarly, a group of synchronized individuals can also be easier to tear apart with the right perturbations from the right directions. In fact, if all the individuals are identical, they could all be susceptible to the same disturbance, disrupting the entire network.  This is analogous to the importance of a diverse gene pool. If all people or crops were susceptible to the same disease in the same way, we would be more vulnerable – a robust variety helps the population be resistant to a wider range of perturbations caused by diseases or viruses. The right combination of different individuals could be immune to all possible challenges as a group.

Interaction Differences

So if the differences among individuals can help promote synchronization, what about the differences in the way they interact? To see the benefits of heterogeneity in the interaction pattern, let’s take a look at the two simple networks below.


The first network is a homogeneous one: all nodes are connected identically – each one sending information to the node on its right. Yet it contains a feedback loop. Here, node one is listening to node two, node two to node three, node three to node four – but node four is listening to node one. We’re back where we started.  For one thing, it is not clear who is in charge. This sort of loop can amplify disagreements. When a dispute breaks out, confusion kicks in and things can get ugly.

The second network is heterogeneous: the missing link leaves the two ends unconnected. But it has a nice hierarchical, leader-follower structure. The node at the upper-left corner is clearly in charge. If these nodes are people trying to work together, this makes it easy to settle any dispute. Everyone knows to whom they should listen, and they can work together efficiently.

But synchronicity isn’t just about cutting up cakes and getting high scores on diving. It appears all the time in nature and society – like in power grids, laser arrays, and secure communication networks. Understanding synchronicity better can have far-reaching implications.

Robots, self-driving cars, and humans in large groups all need to reach consensus under various conditions and constraints. When self-driving cars share the road, thereby creating a temporal network, they need to negotiate order, turns, and priorities together. If they do not reach consensus fast enough when they encounter each other, they could crash. When designing systems like these, designating purposeful heterogeneity in the right places can encourage cooperation and facilitate faster convergence.

The effect of heterogeneity on synchronization could be another explanation why diversity is advantageous in our society. Perhaps we should encourage “birds of different feathers” to flock together more often. So next time you want to strike up a conversation and “get in sync” with someone, instead of scrambling for a common topic, try adding something new to the mix. Sharing something the other party doesn’t know might give you a pleasant surprise.



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