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. This video was sponsored by Kiwico more about
them at the end of the video. 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? Hey, this video is sponsored by Kiwico, which
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