The second law of thermodynamics tells us that everything in the universe tends towards
disorder. And in complex systems, chaos is the norm. So you'd naturally expect the universe
to be messy. And yet, we can observe occasions of spontaneous order, the synchronization
of metronomes, the perfectly timed orbits of moons, the simultaneous flashes of fireflies,
and even the regular beating of your heart. What puts these things in order in spite of
nature's tendency for disorder.
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On June 10 2000, the Millennium Bridge, a new footbridge Across the River Thames in
London was opened to much excitement. But as crowds filled the bridge, it began to wobble
back and forth. Police started restricting access to the bridge, but that only resulted
in long lines to get on the wobble was unaffected. Two days later, the bridge which had cost
18 million pounds, was fully closed, and it wouldn't reopen for another two years. So
what went wrong?
Well, it's long been known that armies should break step when crossing bridges. This dates
back to an accident in 1831. When 74 men from the 60 of Rifle Corps were marching across
the Broughton suspension bridge in northern England. It collapsed under their synchronized
footsteps. 60 men fell into the river 20 of whom suffered injuries like broken bones or
concussions. Luckily, no one was killed. But after this, the British Army ordered all troops
to break step when crossing bridges.
Now look at the people walking across the Millennium Bridge. Most of them are walking
in step with each other. But they are not part of an army. They're random members of
the public so why are they walking together? And why couldn't a modern bridge designed
for heavy pedestrian traffic handle this? Well, to understand it, we have to go back
350 years.
In 1656, famous Dutch physicist Christian Huygens created the first working pendulum
clock. The goal was to help sailors figure out where they were on the globe. Latitude
can be judged by measuring the position of the sun or stars. But for longitude you also
need to know the time at some fixed location, say your home port. But clocks at the time
were routinely out by around 15 minutes a day. So they were effectively useless. wagons
pendulum clocks by contrast, were accurate to around 10 to 15 seconds per day. Huygens plan
was to attach his clocks to a heavy hanging mass on the ship, so they wouldn't get tossed
around by the rolling seas. His plan called for two clocks in case one stopped or was
damaged.
But testing out this arrangement while at home sick in February 1665. He made a remarkable
discovery. To have his clocks hung from a wood beam across some chairs. Watching the
pendulums sway back and forth for hours. He noticed after half an hour or so they would
spontaneously synchronize. As one clock swung one way, the second would swing the other
way. As one would tick, the other would talk.
So he tried disturbing the clocks. He set them ticking out of sync but again, within
30 minutes or so they were back to the same lockstep. Wiggins thought this strange sympathy
of clocks must have been caused by air currents between the pendulums, so he placed a large
board in between them, but their clocks continued to sync up. It wasn't the air currents.
When he separated the clocks, the synchrony would disappear, their times drifting apart.
But when he brought them back together, the synchrony returned. Wiggins realized the two
clocks were synchronizing because they were hung from the same wood beam. He transferred
mechanical vibrations from one clock to the other, making the two oscillators coupled.
wegens was the first to observe this kind of spontaneous synchronization in inanimate
objects. And although he qualitatively described what was happening, he was only a few decades
ago that scientists started fleshing out a rigorous theory of synchronization.
You may have seen this demo where you put several metronomes on a light wobbly platform
and start them out of sync.
It's trickier than people make it look.
When you do get it to work, though. It's kind of magical.
These metronomes don't have exactly the same natural frequency, and yet they still beat
in time. To understand how this works, it's easiest to first consider a couple metronomes
oscillating in sync with each other. When the large masses accelerate to the left, they
push the platform to the right. And when they accelerate to the right, they push the platform
to the left. So the center of mass of the system always stays roughly in the same spot.
Now, if you start another metronome completely out of sync with the first two, the motion
of the platform gives it a kick every half swing, speeding it up until it's in time with
the first two.
This works, regardless of the number of metronomes,
you have, the platform just goes whichever
way the majority of metronomes are pushing it.
We can represent the position of a metronome pendulum or any other oscillator as a point
on a circle. This shows its phase that is what part of the cycle it's in. So you could
call the rightmost point of the pendulum zero degrees. And then the leftmost point is 180
degrees. And as the pendulum oscillates back and forth, the point goes around the circle,
the higher the frequency of the oscillator, the faster that point goes around.
So this represents two metronomes with different frequencies.
And this represents two metronomes with the same frequency, but completely out of phase.
When the metronomes are synchronized in phase, their dots go around the circle together,
we can use this depiction to illustrate a mathematical model for the synchronizing behavior
we've been looking at. It's called the Kuramoto model. It says the rate each dot goes around
the circle equals its natural frequency, plus some amount related to how far it is from
all the other dots. And the size of this term is determined by the coupling strength. I
like to think of it actually visually by thinking about people that are running around a track,
like suppose you're running with your friend, and maybe your friend is faster than you,
your friend says, you know, come on, move it or hurry it up. Because you're dawdling,
you're slow, you're falling behind. So if you have enough fortitude, and you know, you
try hard enough, and if the friend is sympathetic enough to slow down, then the coupling between
you is strong enough to overcome that inherent difference in your natural running speeds.
But if you're not very good friends, or, you know, if you can't quite suck it up to move
yourself faster, then the coupling will not be strong enough to overcome that difference
in one person will start lapping the other, the fireflies of Southeast Asia are apparently
good enough friends, because they synchronize their flashes. Even though each one has its
own particular frequency at which it likes to flash, they coupled to each other strongly
enough so that hundreds, even 1000s can flash together in the same split second. There's
a great simulation of this by Nicky Case, you start with individual fireflies just doing
their thing. And then you can turn on the interaction between them. Now in the Kuramoto
model, this would mean every Firefly has an effect on every other one. But in this simulation,
a firefly is only affected by its neighbors. If it sees a flash close by it nudges its
internal clock forward a little bit, so it'll flash sooner than it would have otherwise.
Now, what's remarkable about this is even though the interactions are small and close
range, over time, you can see waves traveling through all the fireflies, and eventually,
they're all flashing at once.
Like you might think if you increase the coupling, you just sort of gradually get a system more
and more synchronized. That's not what happens. It's sort of like the way water doesn't gradually
freeze as you lower the temperature, its water, water water as you're lowering the temperature.
And then at a critical temperature, the molecules suddenly start to change their state and become
solid instead of liquid. And this is a sort of time rather than space version of the same
thing. They sort of lock their phases in time, once you pass a critical level of coupling.
And at that point, the sort of crystallization
in time is the phenomenon that we call synchronization.
This is an audience in Budapest applauding after a performance. But what happens next
is completely spontaneous. They're not being instructed by anyone to see if you can spot
the phase transition.
this phenomenon of synchronization that we've been talking about one of the things that
i find most appealing about it is how universal it is that it occurs at every scale of nature
from subatomic to cosmic it uses every communication
channel that nature has ever devised from
gravitational interactions electrical interactions chemical mechanical i mean you name it anyway
the two things can influence each other nature uses that to get things in sync
take our own moon for example we only ever see one side of it because it rotates on its
axis exactly once for every time it goes around the earth we say it is tidally locked to the
earth and this is a common effect in our solar system there are 34 moons that are tidally
locked to their planet the way this happens goes something like this a moon starts out
with its own rotational frequency but the gravitational attraction to the planet is
stronger on the side closer to the planet and so it distorts the moon into an egg shape
which is greatly exaggerated here as the moon continues to orbit and rotate on its axis
those bulges swing out of alignment with the planet and so the gravitational force on them
is constantly pulling them back into alignment and this slows the rotation of the moon until
it is locked to the planet if the moon is initially rotating too slowly this same mechanism
can speed it up until it's locked there are all kinds of other beautiful synchronization
phenomena in our solar system the three innermost moons of jupiter io europa and ganymede are
not only tidally locked to the planet they're also in a one to four orbital resonance with
each other for every time ganymede goes around jupiter europa goes around twice and io four
times
in the 1950s some russian chemists went looking for a chemical reaction that would oscillate
like a chemical analog of a pendulum like could you get something going back and forth
say between blue and orange over and over again and naively you might say that's impossible
because there's principles of thermodynamics which say that closed systems just increase
their entropy over time that they're just going to come to equilibrium but there's no
principle in chemistry or thermodynamics that says you have to go monotonically to equilibrium
you are allowed to oscillate and damp out to equilibrium in an facilitatory way this
is exactly what Boris Belousov off and later Anatol Zhabotinsky discovered so this reaction
is known as the Belousov Zhabotinsky or BZ reaction i've sped it up because it can continue
for half an hour or more oscillating between these colors now it spends more time on the
burnt orange color so i sped up those sections more it's very spectacular and it's kind of
shocking to see a chemical reaction doing these periodic changes in color like chemicals
acting like a clock like a pendulum so the stirred reaction has the advantage that you
you really get a sense of the collectivity of you know i don't know quadrillions of molecules
avogadro's number of molecules all doing the same thing at the same time on the other hand
if you don't stir if you just put like a petri dish of the bz reaction you can see something
even more amazing i think which is that you can see spiral waves of color or target patterns
expanding circles of color moving through the liquid maybe i should emphasize the liquid
itself is not moving it's not like we're seeing ripples on a pond but what's not still is
chemical concentrations you can see these blue waves in the bz reaction that are chemical
waves not not water waves and that will just propagate and they move at a constant speed
and or they can look like a spiral that just grows and grows and spins around and what's
really spooky and uncanny about this is that the same phenomenon is seen in the heart you
can see spiral waves of electrical excitation in a heart that look exactly like the spiral
waves in chemical oscillations and chemical waves in the bz reaction and this was the
sort of thing that inspired my mentor a guy named art winfrey who used chemical reaction
waves to give himself insight into cardiac arrhythmias you know you may have heard the
most deadly kind of a arrhythmia that the kind that will kill you it really in a matter
of minutes ventricular arrhythmias ventricular fibrillation in particular winfrey's work
seeing these rotating spirals on hearts as well as in chemistry led him to a theory about
what's really causing ventricular fibrillation and how could we design for example better
defibrillators
That are gentler, that could be a good outcome
of this theory. You know, the lack of synchronization
in a fibrillation heart is what causes no blood to be pumped, and then sudden death
ensues. So too little synchronization is obviously a problem. But too much synchronization can
also cause trouble. Remember, the wobbly Millennium
Bridge, it was all apparently down to something
called crowd synchrony Was it the people walking in step that caused it to oscillate? Actually,
kind of the opposite. The Millennium Bridge was designed to look like a ribbon of light.
So its construction is unique. Unlike a typical suspension bridge, its supporting cables run
alongside it stretched taut, like guitar strings. In the civil engineering literature, all designers
know that you do not build a footbridge with a resonant frequency equal to the frequency
of human walking. So we take about two strides per second one with your left foot one with
your right foot. So everybody who takes civil engineering knows if people are going to walk
on the bridge, It better not have a resonant frequency in the vertical direction of two
hertz. Okay, everybody knows that, including the people who, who built the Millennium Bridge.
But what they didn't know. And what was new that day is that half the frequency is also
important, a frequency of one cycle a second, which is the frequency with which you put
down, say, your left foot, half the time you're doing your left foot. So why does that matter?
Because when you're walking across a bridge, and you put your left foot down, you put a
tiny force sideways on the bridge. And normally, that wouldn't matter because people are all
walking at their own pace, they're not synchronized,
so their sideways forces which are only about
a 10th, as big as their downward forces that
they impart on the bridge, that would be negligible,
and it wouldn't do anything to the bridge. But if the bridge happens to have a sideways
frequency of one cycle a second, which the Millennium Bridge had happened did, then people
can actually start to get the bridge moving a little bit. After the bridge was closed,
engineers got their colleagues to walk across it in increasing numbers, while they measured
its acceleration. With 50 people on the bridge, there was very little motion. At 100, the
vibrations had barely increased at 156, there was still no wobble, but with just 10 more
people 166 the acceleration grew dramatically. The bridge swayed, just like it had on opening
day, the system had undergone a phase transition. If people can get the bridge moving a little.
It turns out, people don't like to walk on a platform that's moving a little bit sideways.
If you've ever been in a train, that's kind of going faster, if you stand up in a rowboat,
and it starts moving sideways, people spread their legs apart, to try to stabilize themselves.
And they will actually start to walk in step. With the sideways motion of the bridge, you
can see footage from the BBC, of people doing that. It's spectacular and crazy. So it wasn't
people walking in sync that got the bridge to wobble. It was the wobbling bridge that
got people to walk in sync. And so as the people got in step with the motion of the
bridge, by adopting this weird kind of penguin gate, they ended up inadvertently pumping
more energy into the bridge and making its motion worse. And so this was this positive
feedback loop between the motion of the crowd, causing the bridge to move more, which causes
more people to get in step with the bridge, which made more people you know, drive the
bridge. Once the problem was identified, they could solve it by decreasing the coupling
strength. They installed energy dissipating dampers all along the bridge. It was a tremendous
embarrassment, and it cost several million pounds to repair the bridge.
In science, we do reductionism, all of our science courses tell us the way to solve a
problem is to break it into smaller parts
and analyze the parts. And that has been phenomenally
successful for every branch of science. But the great frontier in science today is what
happens when you try to go back to put the parts together to understand the whole. That's
the field of complex systems. That's why we don't understand the immune system very well.
We don't understand consciousness very well or the economy. It seems like the whole is
more than the sum of the parts. That's the cliche that has entranced me for my whole
research career. I want to understand how can you figure out the properties of the whole
given the properties of the parts?
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