A living experiment in synchronization

The Clockmaker's
Wave.

Eighteen pendulums. Eighteen different rhythms. No leader, no communication—and yet they have agreed to meet at precisely the same instant. Watch them keep their promise.

01 / THE ORCHESTRA OF CLOCKS18 instruments · ideal tuning
✧ Tap any pendulum to disturb its rhythm; tap again to change it.
02 / THE SECRET SCOREA whole minute at once

Each row is a pendulum; each column is a moment. Turquoise means moving right, amber moving left. The converging pattern is the clockmaker's signature. Drag on the score to travel through time.

rightleftcenterPerfect alignment at 60 s
Transport / the minute
00:00 / 01:00
At the beginning
0 s15 s30 s45 s60 s
Collective agreement
100 %
Phase coherence · R(t)
Together
An average of eighteen unit arrows. 100% means every oscillator has precisely the same phase; 0% means their arrows cancel.
Phase constellation

All eighteen arrows point together.

Each dot is one clock, viewed on the unit circle. The long green arrow is their average.

Clockmaker's imprecision0.00 cycles
Mathematically exactHuman-made
Observation speed2×
½×1×2×4×8×
No pendulums have been disturbed by hand.
Three experiments

Try the final second with each setting. What matters more—the clocks being individually accurate, or the differences between their frequencies being exactly right?

THE OBSERVER'S NOTE

An appointment with the future

At the start, every pendulum points in the same direction. Then their individual clocks begin pulling them apart. But each is scheduled to complete a whole number of turns in exactly sixty seconds.

THE SMALL PIECE OF MATHEMATICS

Not synchrony. Recurrence.

fj = (43 + j + εj) / 60 Hz,   j = 0,…,17.

With εⱼ = 0, the phase at sixty seconds is 2π(43+j)—an integer number of turns. All phases agree again, although no pendulum ever changed its speed. Add a small εⱼ or disturb a phase and the reunion can fail. These are ideal harmonic oscillators; the hanging strings are a visual metaphor, not a full model of a gravitational pendulum.