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230 pointsColinWright41 comments

I have a story seemingly remotely associated with this, but actually very much the same.

Years ago, at highway construction sites, sawhorses would be erected that were equipped with flashing lights for safety after dark. In those days the flashing lights were gas-discharge lamps connected to a simple charging circuit consisting of a capacitor connected across the lamp and charged by way of a resistor -- a very simple arrangement, but one that would reliably flash the light all night long.

It turns out that the specific moment the lamp broke down and flashed could be affected by nearby lights of the same kind. As a result, if a large number of sawhorses were erected in a dark location, eventually all the lights would get into synchronization. I can remember on a number of occasions on long trips through dark countrysides, cresting a hill and seeing a construction site in the distance, with all the lights flashing as one.

As I would approach closer, as my headlights shone more brightly on the construction lights, they would go out of sync.

This is a purely historical note, because modern construction sawhorses use LEDs instead of high-voltage gas-discharge lamps -- cheaper and more reliable. The LED's never become synchronized, of course.

How would your headlight desynchronize the construction lights just by shining on them, if it was powered by a separate source? Did the construction lights have light sensors?

> Did the construction lights have light sensors?

The construction lights were light sensors. The reason they got into synchronization is because they were triggered to break down at a specific time by the flashes of light from the other lamps.

In a system like this, the voltage on all the lamps is increasing because a charging current is applied to a capacitor that'a connected across the lamp. But the specific time of breakdown, the exact voltage at which the lamp breaks down, depends on the ambient light level. And a nearby flash of light is sufficient to trigger the lamp to break down in sync.

This effect washes out in daylight, or in a place with normal background light. Or if a light source interferes with the delicate balancing act responsible for the synchronization -- like the headlights on a passing car.

Can you explain what you mean by "break down" in this context?

Plasma breakdown. The voltage across the gas eventually accelerates electrons fast enough that they can ionize atoms when they collide, and an avalanche occurs creating a plasma and light. Same effect as a neon lamp

As the voltage across the gas increases, at some point it causes electrons to leave their valence orbits and travel through the gas (the gas becomes a plasma). That's a "breakdown" if the threshold-crossing causes a sudden, abrupt increase in overall current in the gas, and if the system has a negative resistance trait (one in which the relationship between voltage and current contradicts the usual expectations).

The idea in this case is that the photoelectric effect (Einstein) also can cause an electron to leave its valence orbit. Therefore if the voltage in the gas is high enough to almost cause a breakdown or "avalanche", any extra electrons released by photon interactions may trigger the avalanche in advance of the time it might otherwise have happened.

So you have the possibility of an avalanche caused by the electric field, and you also have some electrons liberated by the photoelectric effect. The breakdown point is determined by both populations, not just one.

This reminded me of Synchronous fireflies. There are at least 2 kinds on them (Asian and North American).

Here is the night time video: http://www.youtube.com/watch?v=a-Vy7NZTGos

Here is an article on this: http://www.nps.gov/grsm/naturescience/fireflies.htm

There is a place in the UK where this happens with spooky regularity with people walking. There is a covered walk way between Waterloo and Waterloo East railway stations. The mob of people enter it unsynchronised and by the time they leave, they are usually all synchronised. I assume this happens in many other places too, I just haven't been every where else to see!!!!

I always assumed this was because people can hear each other and subliminally fall in to syc, whether this is the same or not, Im already internally debating!!!

> There is a place in the UK where this happens with spooky regularity with people walking.

Sometimes in the military, when crossing a bridge, troops are ordered not to walk in step, because of the stress it places on the bridge.

http://en.wikipedia.org/wiki/Angers_Bridge

A quote: "As usual in crossing that bridge, the soldiers had been ordered to break step and to space themselves farther apart than normal."

More dramatic:

http://en.wikipedia.org/wiki/Broughton_Suspension_Bridge

A quote: "On 12 April 1831, the 60th Rifle Corps carried out an exercise on Kersal Moor under the command of Lieutenant P. S. Fitzgerald, the son of John Fitzgerald. As a detachment of 74 men returned to barracks in Salford by way of the bridge[6] the soldiers, who were marching four abreast, felt it begin to vibrate in time with their footsteps. Finding the vibration a pleasant sensation some of them started to whistle a marching tune, and they began to "humour it by the manner in which they stepped", causing the bridge to vibrate even more.[6] The head of the column had almost reached the Pendleton side when they heard "a sound resembling an irregular discharge of firearms".[6] Immediately, one of the iron columns supporting the suspension chains on the Broughton side of the river fell towards the bridge, carrying with it a large stone from the pier to which it had been bolted. The corner of the bridge, no longer supported, then fell 16 or 18 feet into the river, throwing about 40 of the soldiers into the water or against the chains. As the water was only about two feet (60 cm) deep at that point none of the men were killed, but 20 were injured, including six who suffered severe injuries including broken arms and legs, severe bruising, and contusions to the head."

> troops are ordered not to walk in step, because of the stress it places on the bridge

Not really, not because of the "stress." The walking rhythm may match the natural oscillation of the bridge thus resulting in a resonance effect. At least that's what they taught us in high school.

I've always been told this, and it's always seemed plausible, but it was declared busted by Mythbusters.

Having said that, as quoted elsewhere, the Millennium Bridge across the Thames in London did exhibit resonant swaying as pedestrians crossed it, and extra dampers needed to be added.

Added in edit ...

Auto-hoist, petard-wise. It seems some people have assumed that I meant that this never happens, and cannot ever happen, simply because it was the subject of a Mythbusters episode in which they declared it busted, even though I then added that something similar has in fact happened in real life.

I thought the implication was clear, but obviously not. So let me say more explicitly ...

It is clear that people walking on a bridge can cause resonance, it has been seen in real life.

http://en.wikipedia.org/wiki/Millennium_Bridge_%28London%29#...

http://www.youtube.com/watch?v=eiaM_LZUsqM

Further, that was a non-extreme case, so it is totally plausible that more vigorous marching, more definite synchronisation, and closer matching to the structure's resonant frequency is not only possibly going to cause problems, but likely to cause problems.

It is, however, unlikely that marching will match the resonant frequency. Structures these days don't resonate at 2 Hz. Football stadiums are designed to resonate at above 12 Hz. Further, structures often have explicit energy dissipation system built in to them. Taipei 101, for example, has a tuned mass damper to change the resonant frequencies and help absorb, then dissipate energy (yes, I'm speaking loosely here):

http://en.wikipedia.org/wiki/Taipei_101#Structural_design

So yes, I knew all that, and yes, a single Mythbusters episode is not proof of anything, but it does provide a collection of data from which to start forming your own hypotheses, designing your own experiments, and understanding that things aren't necessarily as simple as you thought.

> but it was declared busted by Mythbusters

That episode seemed particular weak to me. The "myth" is that this can happen under particular circumstances - but they seemed to test the hypothesis that marching in lock step will determinedly bring down any bridge.

Another famous example would be the collapse of the Tacoma Narrows Bridge in 1940, widely believed to have been caused by forced resonance. However, as per Wikipedia, the real cause of the collpase was aeroelastic flutter.

Video of bridge collapse : http://www.youtube.com/watch?v=xox9BVSu7Ok Wikipedia: http://en.wikipedia.org/wiki/Tacoma_Narrows_Bridge#cite_note...

The pneumatic "marching" rig they used was anything but synchronized or controlled. I would put little faith in that particular Mythbust.

> declared busted by Mythbusters

Oh, goodie, case closed then. Mythbusters have this tendency to "bust" stories that revolve around rare and unique circumstances by running just few experiments. Obviously that's a flawed approach.

And then there was the time they tested shock absorbers on a car's bumper exploding in a fire and sending the bumper flying away. They couldn't replicate it.

They spoke to a woman with scars on her legs from a bumper that hit her after shock absorbers on a burning car exploded and sent the bumper flying away.

So they called it confirmed, since it could happen, they just couldn't get everything right in the lab.

I know it's entertainment first and science second, but a complete reversal of policy just because there is someone you're not willing to look at and call a liar? Weak.

> The walking rhythm may match the natural oscillation of the bridge thus resulting in a resonance effect.

Yes, and that stresses the bridge. If it didn't, there would be no reason to avoid it.

london's "millennium bridge" mentioned briefly in the first article.. http://www.youtube.com/watch?v=eiaM_LZUsqM

It was the London Millennium Bridge. Here is a video of the effect in action: https://www.youtube.com/watch?v=gQK21572oSU

Here the problem is attributed to the peoples reaction. The evidence from the metronomes might suggest that it has nothing to do with people.

The fix involves changing the natural frequency of the bridge.

I think your assumption is right on. Just try to listen to music when you walk and not end up lock-step with the beat.

Network protocols with periodic updates will do the same thing; it used to be a problem, so much so that designers would add noise to timing in implementations. Here's a great paper from Sally Floyd and Van Jacobsen on it:

http://ee.lbl.gov/papers/sync_94.pdf

Here is an example for multicast dns (used in bonjour etc):

http://files.multicastdns.org/draft-cheshire-dnsext-multicas... (page 9)

That is a fascinating paper. Very cool.

After looking at various papers on the topic I found some equations of motion, did some algebra and wrote some python code. Here is the result

video of simulation results animated: http://www.youtube.com/watch?v=U1QqYBOrYjA

python code: git://github.com/paulgribble/metronomes.git

This looks like a scaled up version of this experiment that has been on youtube for about 5 years: https://www.youtube.com/watch?v=W1TMZASCR-I (only 5 metronomes in that one, but I remember being fascinated when I first saw the effect)

The linked article claims that metronomes start 'pairing up' with their nearest neighbors saying that "strongest forces on a metronome will initially be from its nearest neighbors." But if the forces are spread by the string-suspended table swaying back and forth, I wouldn't expect adjacent metronomes to be significantly more connected than further away ones. Instead, I wonder if we just happen to be better at noticing metronome synchronicity when the metronomes are adjacent. Any pairs that formed several steps away would escape our notice.

Probably the initial synchronization happens due to vibration, which would be felt by the closest neighbor. Then the macro synchronization happens due to the table swaying.

Order from chaos! And without any external source of energy.

I wonder what other physical phenomena emerge this way. Magnetic fields, I bet.

> Order from chaos! And without any external source of energy.

It's important to understand that a physical system will seek its lowest energy level, and in this experiment, all pendulums synchronized is a lower kinetic energy level than unsynchronized.

> I wonder what other physical phenomena emerge this way.

There are many. A classic example is a phase-locked loop, in which a local oscillator will fall naturally into synchronization with a remote signal source. Again, the synchronized energy level is lower than unsynchronized.

http://arachnoid.com/phase_locked_loop

It's important to say that, if it went the other way, if unsynchronized represented a lower energy level, getting synchronization would be very difficult.

Feynman started by investigating the wobbles of a spinning plate, and ended up with Quantum Electrodynamics. Looking at the metronome video, I found myself thinking, "There's got to be something deep there".

It'd be really cool if the metronomes turned out to be a model of the quantum vacuum, and the patterns running though the array of oscillators turned out to be virtual particles winking into and out of existence. (Hey, I can dream, can't I?)

---

edit: spelling

I think you're right about the magnetic fields. I'm pretty sure the interactions between the metronomes in the video can be modelled as message passing between nodes in a square lattice of variables, with stronger association potentials in the direction of the swing than in the direction perpendicular to it.

As far as I understand it, this is similar to the Ising model of ferro-magnetism [1], where magnetism arises from the interactions of neighbouring atoms.

For more on this kind of stuff, look into graphical models. Coursera has a Stanford course with Daphne Koller on it.

1: http://en.wikipedia.org/wiki/Ising_model

Uh, no. The article points out the metronomes are on a suspended table. Each metronome adds energy to the table in phase with its cycle, as more metronomes get into phase, their summed energy edition begins to push back on other metronomes bringing them all into alignment. By the end of the video you can see the table is oscillating exactly out of phase with the metronomes as expected by that point.

What difference does that make? The metronomes and table are a closed system, so the fact that energy is transferred between them is moot.

I think lutusp's explanation makes a lot more sense: that when the metronomes sync up, they're at a lower energy level. They spend energy to decrease entropy.

Ordine dal caos, as they say in Italian.

Steven Strogatz has done a lot of work on things like this in the past - including this experiment.

http://www.ted.com/talks/steven_strogatz_on_sync.html

In the simple case of just two metronomes on a single moving plane, the tendency for sync is governed by a non linear differential equation. The math gets rather complicated: http://salt.uaa.alaska.edu/dept/metro.pdf

Wow, we can certainly conclude that conformity is the lowest acute energy state of this system in motion. An apt metaphor for mass social behavior; it eventually sounds frighteningly like soldiers marching.

I have a feeling a similar phenomenon was responsible for the Millennium Bridge being closed:

http://en.wikipedia.org/wiki/Millennium_Bridge_%28London%29#...

Cool! This was first observed by Huygens on two pendulum clocks.

I'm surprised nobody picked up on the seemingly obvious metaphor these metronomes are for people and behavior.

Does this violate the second law of thermodynamics?

Of course not. Nothing does, that's why it's a law!

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