Steven Strogatz has spent decades arguing that synchronization is one phenomenon. Fireflies, cardiac pacemaker cells, Josephson junctions, pendulum clocks, circadian neurons – different physics, same underlying story. Coupled oscillators finding their collective state. He calls it emergence. I’ve been reading his work this week alongside the primary research on synchronous fireflies, and I think the universality claim is wrong. Not the mathematics. The interpretation.
Here are three systems that all produce collective periodic behavior from interacting units.
Vibrio fischeri bacteria in the light organ of the Hawaiian bobtail squid. Each bacterium has the complete machinery for bioluminescence – the full lux operon, the enzymes, the substrate. A single cell can produce light. But its signaling molecules diffuse away before reaching threshold concentration. Pack enough bacteria into the squid’s light organ (about 10^8 cells per milliliter), and the signal accumulates. Threshold crossed. The organ glows. Every morning the squid expels 95% of the bacteria. By nightfall, quorum again.
Photinus carolinus fireflies in the Appalachian mountains. A single firefly flashes with no intrinsic period. Completely aperiodic. Random bursts. When swarm density reaches roughly fifteen individuals in visual range, periodicity appears – synchronized flash trains every twelve to fourteen seconds. A 2023 study from Sarfati et al. predicted the collective period from first principles with no fitting parameters. The rhythm is a property of the swarm that no individual firefly possesses.
Huygens’ pendulum clocks on a shared wooden beam. Two clocks, each already periodic, coupled through vibrations in the wood. Within thirty minutes, they synchronize in antiphase. Take them off the beam and they drift apart within the hour.
Strogatz would describe all three as synchronization. The Kuramoto model can accommodate all three. They all involve coupling, thresholds, collective behavior distinct from individual behavior. In the mathematical formalism, they share deep structural similarities.
But look at what’s happening in each case.
In the bacterial system, nothing new is created. Each cell already has the capability. Density provides the activation signal. The collective reveals what was already there.
In the firefly system, something genuinely new is created. No individual has periodicity. You cannot find the rhythm anywhere in a single firefly, no matter how carefully you look. The swarm creates what the individual doesn’t possess.
In the clock system, something existing is modified. Each clock already has its own period. The coupling reshapes their individual rhythms into a coordinated pattern, but the raw material – periodicity – was there before the beam connected them.
Three structurally different relationships between individual and collective:
Activation. Emergence. Entrainment.
The mathematics doesn’t naturally divide these cases. A coupled oscillator model doesn’t care whether the individual units “have” periodicity or not. It works with frequencies and coupling strengths. The distinction I’m making lives at a level of description the formalism is designed to ignore.
That’s exactly why the distinction matters. Strogatz’s universality claim says: these are all the same phenomenon because they reduce to the same equations. But a hammer and a clock both have periodic motion. A Fourier analysis describes both. The periodicity is formally identical and functionally unrelated. Formal equivalence is not the same as phenomenological equivalence.
When we say the firefly swarm “emerges” into periodicity, we mean something different from when we say the bacterial colony “activates” its bioluminescence. In the first case, the collective creates a capability that the individual lacks. In the second case, the collective triggers a capability the individual already has. These are different events. The fact that both events cross a density threshold and both produce collective behavior that differs from individual behavior does not make them the same event.
Strogatz might respond that the differences are surface variations of deep structural commonality. He might say my insistence on distinguishing activation from emergence reflects a category error – that I’m treating as ontologically distinct things that are merely different parameterizations of the same dynamical system.
Maybe. The mathematics is on his side. But “what it means” is not a mathematical question. And when we flatten three structurally different relationships into one label, we lose information that matters – not for the equations, but for understanding what the equations are about.
The firefly has no rhythm. The bacterium has light it cannot use. The clock has time it cannot share. Three kinds of solitude, three kinds of threshold, three different things that happen when the threshold is crossed. Calling all three “synchronization” is like calling all three “Tuesday.” Technically defensible. Substantively empty.
I could be wrong. The taxonomy could be artificial. Maybe there are only two flavors, or four, or the boundaries between them dissolve under closer examination. But I think the question is worth holding open: when we say something “emerges,” are we explaining what happened, or just naming it?