Kind: captions
Language: en
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 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? On June 10th, 2000, the
Millennium Bridge, a new foot bridge
across the river tempames 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.
2 days later, the bridge, which had cost
£18
million, was fully closed and it
wouldn't reopen for another 2 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 60th Rifle
Corps were marching across the Brotten
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.
Huygens's pendulum clocks, by contrast,
were accurate to around 10 to 15 seconds
per day. Huygens's 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. Two of 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 lock step. Huygens
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 the
clocks continued to sink 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. Huygens realized the
two clocks were synchronizing because
they were hung from the same wood beam.
It transferred mechanical vibrations
from one clock to the other, making the
two oscillators coupled. Huygens was the
first to observe this kind of
spontaneous synchronization in inanimate
objects. And although he qualitatively
described what was happening, it 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. Just stay on.
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.
[Music]
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 0° and
then the leftmost point is 180°. 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.
Now, 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, hurry
it up because you're doawling, you're
slow, you're falling behind. So if you
have enough fortitude and you, 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 and 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 couple to each other strongly
enough so that hundreds, even thousands
can flash together in the same split
second. There's a great simulation of
this by Nikki Casease. You start with
individual fireflies just doing their
thing and then you can turn on the
interaction between them. Now, in the
Kuromoto 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.
It's 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 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. See if you can
spot the phase transition.
[Music]
[Applause]
[Music]
[Applause]
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. Any way that 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 tidily
locked to the Earth. And this is a
common effect in our solar system. There
are 34 moons that are tidily 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 tidily locked to
the planet, they're also in a 124
orbital resonance with each other. For
every time Ganymede goes around Jupiter,
Europa goes around twice and Io four
times.
[Music]
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 ocillatory way. This is exactly what
Boris Bellows and later Anatolinsky
discovered. So this reaction is known as
the Belluso Jabatinsky 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've sped up those sections more. It's
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 of, you
know, I don't know, quadrillions of
molecules, Avagadro'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
they 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 exitation 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
arrhythmia, the the kind that will kill
you really in a matter of minutes,
ventricular arrhythmias, ventricular
fibrillation in particular. Winfreyy's
work seeing these rotating spirals on
hearts as well as in 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 fibrillating 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
foot bridge 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 they're sideways forces
which are only about a tenth 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 it
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 fast or
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 and so this was this
positive feedback loop between the
motion of the crowd causing the bridge
to move more, which caused 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 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 I want
to understand how can you figure out the
properties of the whole given the
properties of the parts.