Kind: captions
Language: en
This little mechanism shrinks when you
try to stretch it. You try to pull it
apart and all of a sudden it pulls back
on you. That's so weird, right? Here it
is under controlled conditions. There's
a cup hanging from the mechanism. But
now look what happens as you add water
to it. All of a sudden, the cup shoots
up. The amount it shoots up is tiny. But
the physics behind it is so
counterintuitive, nobody thought it was
possible. It feels like it violates
physics. That's why it's fun. The
paradox that controls this mechanism
governs everything from mechanical
systems to food chains, from traffic
jams to power grids. And to understand
it, you just need to ask a simple
question. What will happen to this
weight if you cut the green rope? Where
is this going to end up? Is it going to
go up? Is it going to going to go down?
Or is it going to stay the same?
Can I touch? Yeah. Yeah. Yeah, you can
try it. Nothing. You don't think
anything's going to happen? In the same
place. Uh, weight is going to be right
over there. Like it's going to fly off
or what? No, not not too much, but
probably it's going to go to this way.
If you cut the green rope, this is going
to come down. It will go down. It will
go down. It drops. It'll fall down. The
first thing that occurs to me is as soon
as you cut that, the weight is going to
drop. I imagine the weight ends up lower
than it started. Here's a closer look at
the setup. You have a spring hanging
from a hookup here. And then via this
green rope, it's connected to another
spring that's carrying this weight below
them. There are two extra ropes here as
well. So the red one and the black one
are slack. They're not under any tension
whatsoever. So they're not actually
carrying any weight. What's going to
happen if you cut the green rope? You
can pause the video here and try to
figure it out for yourself.
Wait, what? Here it is in slow motion.
So, even though the ropes on the side
were slack and we cut the only rope in
tension, the weight somehow went up.
Okay, so if you're unconvinced that
cutting the green rope actually makes
the weight go up, here's a huge version
of the experiment. So, the black and red
ropes are still very much slack and it's
just held together by this tiny piece of
green rope here. So, let's see what
happens now. Okay, you ready?
[Music]
Okay. Three, two, one.
[Music]
That was actually insane. That was
pretty pretty good, right? I still don't
believe it looking at it. Okay, so why
does this actually happen? Cuz the
springs are contracting back and just
pulling it together. Maybe the tension
in the, you know, this part is changed.
It releases the tension in the springs
and only goes to the length of the
ropes.
Look at what happens when you remove the
slack side ropes from the initial setup.
You're left with this a mass hanging
from a spring hanging from another
spring. So these springs are connected
in series. Obviously when you hang a
weight from one spring, it extends just
like you'd expect. And the amount it
extends by, call it X, is proportional
to the force exerted by the weight.
That's Hook's law. But if you add
another spring in between in series, now
both springs extend roughly the same
amount, X, because both springs feel the
same force of the weight pulling from
below. So in the case of ideal massless
springs, you would end up with exactly
2x of displacement. Now there's another
way to connect these two springs to the
weight, and that is in parallel. This
way, both springs are independently
connected to the hook above and to the
weight. So, each spring is only carrying
half the weight of the mass below, which
is why both springs extend only half as
far or x over two. If you look at the
setup right after the green rope is cut,
you'll notice that this is actually
exactly how the springs are laid out.
So, the red rope is connecting the
bottom spring directly to the hook
above, and the black rope is connecting
the top spring to the weight. So these
springs are in parallel.
So by cutting the green rope, you're
actually forcing the springs to go from
a series to a parallel. And that change
is what causes the contraction to
happen. When you cut the rope, each
spring only extends by about half as far
as before, which is why you can add so
much slack on these black and red ropes
to give the impression that the weight
is going to fall down. When you cut the
rope, you go from series to parallel and
that pushes you up. The slack ropes,
that's where I get to cheat. And that
that's that's the misleading bit, you
know. Yeah,
the key to getting this paradox right
comes down to the length of the slack
ropes. Each one has to be longer than
the length of one of the springs in
series plus the green rope. That's what
adds the slack. But they also can't be
much longer than that because too much
slack will nullify the contraction you
get between series and parallel and the
weight will still fall.
Now, you might think that this paradox
only really works with the springs in
this demo, but the first time it was
discovered was actually because of its
influence on people.
In April of 1990, New York was getting
ready for its 20th annual Earth Day. It
was going to be Manhattan's biggest
celebration of environmentalism to date.
Stop the war against the Earth. On the
day, Central Park was turned into a
massive festival ground with almost a
million people pouring in to see a
stacked lineup of performers, including
Hallen Oats and the B-52s.
But the boldest stunt of the day was to
ban traffic on some of New York's most
important streets, including 42nd
Street, one of the busiest streets in
Manhattan. It stretches from river to
river connecting Time Square to Grand
Central Station and it's almost always
jammed with slowmoving traffic. The only
thing that's an hour from 42nd Street is
43rd Street. And maybe not surprisingly,
people were really against this idea,
insisting that just a 6-hour closure of
42nd Street would mean doomsday. As the
commissioner of New York's Department of
Transportation put it, you didn't need
to be a rocket scientist or have a
sophisticated computer queuing model to
see that this could have been a major
problem. But the city went ahead with it
anyway, and no cars were allowed on 42nd
Street for the day.
Now, to everyone's surprise, the traffic
in the surrounding area actually got
better. The number of cars was reduced
by 20% with bystanders claiming the
whole area was a ghost town compared to
the way it normally is. But one man
wasn't surprised by this result. In
fact, he predicted it over 20 years
earlier.
His name was Dietrich Braze, a German
mathematician. And back in 1968, Braze
was studying road networks. As part of
his research, he imagined a scenario
where drivers from one side of a
fictional town were trying to get to the
other. But there were only two possible
routes the drivers could take. Route one
starts with a wide highway that takes
you halfway across town. The road is so
wide that regardless of how many cars
are on it, this part of the trip always
takes 25 minutes. The second half of
this route turns into a narrow city
street, and the time to drive through
this street depends on how many cars are
on it. For every 100 cars on the street,
the time to pass through it takes an
additional minute. So 100 cars will take
1 minute, 200 cars will take 2 minutes,
and so on. The second route through town
starts with a similar narrow city street
that depends on the number of cars. It
takes you halfway across and then turns
into another 25-minute highway stretch
where the transit time doesn't depend on
traffic. So which route would you take
to get across town? Well, you can see
that the routes are identical but
flipped. So, it doesn't really matter.
Since this is just a mathematical model,
both will get you there at the same
time. So, say there were 2,000 drivers
trying to get across the city. Half of
the cars would end up on the first route
and half on the second route. And since
there are now 1,000 cars going down each
narrow city street, the travel time on
these segments increases to 10 minutes.
So, the total time on both routes is 10
minutes for the narrow street plus 25
minutes for the highway. A total of 35
minutes regardless of route. But now,
say the city decides to connect these
two routes at the halfway point with a
small piece of highway to give drivers
more options. This piece only takes a
minute to travel across. So, which roads
would you use now to get across town?
Well, as an individual driver, you
should just go straight down. It will
take you 10 minutes to get through the
first city street, 1 minute on the new
connecting road, and another 10 minutes
for the second street. So your total
journey time would now be only 21
minutes compared to the 35 minutes for
everyone else on routes 1 and two. Okay,
great. So you minimize your own time and
that's that, right? Well, not really.
See, drivers like you are selfish and
everyone wants the shortest possible
travel time, which means everyone starts
flooding the narrow city streets. As
drivers switch to this new shortcut, the
narrow streets become more and more
congested, making the route slower and
slower. But this makes the original
routes worse, too. Because the time to
get through the street segments keeps
increasing for every driver. So,
everyone decides to switch to the
shortcut. And now all 2,000 cars are
driving down the city streets. Now, the
time to traverse each city street jumps
to 20 minutes. So, the total journey
time for everyone increases to a
whopping 41 minutes compared to the 35
minutes we had before the new road was
constructed. So traffic actually got
worse for everyone.
To fix it, the drivers could simply go
back to their original routes, right?
Well, who's going to be the first to
switch back? If any one driver goes back
to Route 1 or two, their journey time
will be the 25 minutes on the highway
plus 20 minutes on the now congested
city streets, or 45 minutes in total,
which is even worse than the now
congested streets. So, no single driver
would ever want to go back to the
original route. And because humans are
humans, it's not like we could all just
agree to ignore this new road. So, even
though every driver was making a
rational decision to try to minimize
their own travel time by just using the
city streets, collectively, this made
the situation worse for everyone, and
there's no way out. But if the city were
to destroy this new connecting road,
everyone's journey time would drop from
41 minutes back to the original 35
minutes on route 1 and two. So removing
the road would actually make the traffic
better. It's just like cutting the green
rope from before. That's because both of
these are examples of the same paradox.
The springs are like the narrow city
roads. The more weight or cars you add,
the longer they get. And the ropes are
like the highways. It doesn't matter how
much weight is on them, they don't
change. That is unless you don't know
how to tie them properly.
My god. This is the paradox Dietrich
Braze discovered in 1968. It's now known
as Brazy's paradox, and it is the reason
why New York traffic got better after
42nd Street was closed on Earth Day.
Now, sure, you'd be right to argue that
the reason the traffic decreased on
Earth Day in New York was simply because
people decided to walk or cycle more
that day, but it turns out
mathematicians actually modeled the
whole city in 2008. And they found 12
roads that were redundant and could be
cut to actually reduce traffic. And it's
not only New York. The paradox showed up
in Boston, London, Seoul. In fact, if
you were to randomly add a new road to
just about any city, you'd have an equal
chance of making the traffic better as
worse.
But there's nothing special about the
flow of cars. Say instead you want to
send electricity from one station to
another. Well, now you're looking at the
flow of electrons in a power grid. And
just as before, you could try to improve
the grid by increasing the capacity of
existing lines or by adding new lines.
But it turns out that this can actually
destabilize the grid or even cause a
blackout. And virtually any other
network, anytime you're sending things
from one place to another, it can fall
prey to Brazy's paradox. Be it a food
chain, blockchain, or even the internet.
Adding elements to the network can make
it worse.
So less can actually be more. And that
kind of got me thinking. It's the same
with your data on the internet. The less
of your private info is on the web, the
better. See, I got an email from someone
a couple of months ago suggesting that
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then I got a couple of emails and I felt
bad and I thought, okay, I'd be nice and
actually respond. I drafted up a little
email, but once I hit send, suddenly my
inbox flooded with spam emails.
Grace and Jenny offering price lists for
well, I don't really know what. Oh, and
the best email actually suggested we
should turn Veritassium's existing
content into high performing YouTube
videos to increase our audience and
extend the brand's reach. That's a
genius idea. But unfortunately, most of
these emails are spam and I'd very much
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or also there's a link in the
description. Get your data off the
internet. Go get it off. What are you
doing here? Braz's paradox doesn't occur
every time you modify a network. You
need a very specific set of conditions
for it to occur. But if you can make it
work consistently, you get this. So,
we're here at the Amolf Institute where
they actually figured out how to make
something shrink when you pull it. So,
let's go check it out. Is it here? Yeah,
I made all these samples.
That's so weird.
Yeah, right. I guess you never expect
things to yank back on you so
unexpectedly cuz a rubber band, you're
stretching it and you feel it wants to
pull back on you more and more, but here
it just you're never ready for freezing
suddenly, which it's a weird feeling.
There's something almost like human
about it where it starts tugging back on
you when it gets bad. What's special
about this mechanism is that everything
else around us works in the complete
opposite way. Try to press one of your
keyboard buttons slowly so that it
steadily goes down into place. You can't
do it. No matter how slowly you go,
there is some point at which it just
gives way and clicks through. The same
happens if you try to stretch a bendy
straw. You can pull on it as slowly as
you like, but at some point the
individual straw joints are going to
expand suddenly. light switches,
eyeglasses, grasshopper legs, these all
have a failure point beyond which they
give way and quickly snap into a
different position. And this is called
well snapping. Here it is mapped to a
force displacement graph. As you'd
expect, the more force you apply, the
more the material bends or displaces.
But eventually you reach a tipping point
and beyond it, the force required to
bend the material further actually
drops. So if you apply a force higher
than that peak, the displacement has to
rush to the next corresponding value to
match the force which is all the way on
the other side of this dip. And as a
result, you get a huge amount of
displacement for that tiny increase in
force. That's what creates the sudden
snap. It's very intuitive. I mean,
you've all experienced it, at least if
you're in the Netherlands, with your
umbrella. There's a gust of wind
underneath your umbrella. It pops to the
other side. So you sort of go over a
peak in energy or in force and it
suddenly snaps and typically it becomes
softer. And this is the way all things
snap. Everything used to fail in the
direction of the applied force until
this mechanism came about doing the
exact opposite of snapping. Call it
counter snapping. Imagine that gust of
wind blows under your umbrella but
instead of flipping out your umbrella
suddenly closes in. Or you try to pull
apart a straw and the joints suddenly
contract. The wind is pushing on my
umbrella, but instead of it folding out,
it would push itself against the wind to
close itself, right? But it feels like
it violates physics. It It's just so so
counterintuitive that the displacement
is in in the other direction to the
force. That's why it's fun. So, how does
this thing work? Well, the mechanism
itself is built out of three different
components, and on their own, they all
stretch normally when you try to pull
them apart. Individually, they behave
like springs in the sense that they
extend when you pull on them, but then
you combine them together, and then
suddenly they shrink. Exactly. If you
draw the system as a set of springs, it
looks something like this. The long and
lanky components represent the two
springs on the sides, but they actually
don't feel like springs at all. You can
easily pull them apart until they
suddenly get very stiff. Meanwhile,
these pieces represent the top and
bottom springs, and they feel a lot more
springy. So, the more you pull them, the
more they pull back. And finally, the
central piece. It looks very similar to
the previous one, but pulling it apart
feels very snappy. In fact, you can even
hear it snap out.
Put them all together and you get the
mechanism. If you stretch it slowly,
you'll see how tension builds up in the
three middle pieces with the sides
staying mostly relaxed. But if you keep
stretching, the centerpiece will
suddenly snap out and transfer most of
its tension to the side springs. This
causes the system to stiffen and shrink.
If you now let go, the system resets, so
the mechanism can flip between a set of
springs in series to one in parallel.
It's a reversible case of Brazy's
paradox. The network is basically the
same as the brush paradox. So the the
way they connected, the topology of the
connection is exactly the same. The
force displacement graph you get for the
mechanism is one that loops in on itself
with two distinct curves. One for the
system in series and the other for the
system in parallel. And this leads to
some pretty remarkable properties. If
you slowly control the stretching force
by adding water to a cup below the
mechanism, the mechanism first slightly
sags like you'd expect. But when you
reach the tipping point at the end of
this curve, the displacement has to
quickly reduce to keep following the
force along the graph. And this jump
back is why the mechanism shrinks. Now
you can also control displacement
instead of force and measure how much
force it takes to stretch the mechanism
at any point. This time when you reach
the tipping point, it's the force that
has to follow displacement along the
graph. So you get a sudden jump up in
force showing that the material has
stiffened. Oh, this little force jump is
enough to make it slip out of your
hands. If example, I mean it even though
you said it is a small jump, it's like
this is the only thing that does this
anywhere probably on Earth. Uh yeah, as
far as we know, the force jumping like
this, it was not reported. It is pretty
insane. So what is counter snapping
actually useful for? Well, notice that
there is a force at which the series and
parallel curves of the system overlap.
Which means that at this force, the
mechanism will actually be the same
length in both states. So if you exert
that exact force on the structure by for
example hanging a weight from it, you
can flip between the two states by
giving the mechanism a little tug. And
although that will change whether the
springs are in series or parallel, it
won't change how long the system
actually is. So you can change the
stiffness without changing the length.
Now look at what happens if you give the
mechanism a nudge in its original series
state. If you poke it, you it's
basically a way to measure the natural
frequency. Oh yeah. When the mechanism
is in series, the natural frequency is
3.7 hertz. But if you switch to a
parallel setup, the natural frequency
increases to 6.4. 4 hertz. We switch it
and we look at the natural frequency.
Now we can see it's much higher.
What's unique here is that you're able
to almost double the natural frequency
of the material without changing its
length. I'm going to move the robot
robotic arm very slightly just up and
down. Yeah. Okay. And I put a frequency
of 3.5 hertz. So it's close to the
natural frequency of this system. This
is going to drive the structure into
resonance. But once the vibrations get
big enough, the mechanism is actually
going to switch states on its own,
change its natural frequency, and
thereby reduce the vibrations. Like it
gets stronger and stronger, and then it
just locks it out. Yeah. Yeah. That's
cool. The same happens in reverse. If
you vibrate the robot hand at 6.4 hertz,
the mechanism is quickly going to switch
back to its original state and minimize
the vibrations.
It's interesting uh the way that you say
it. We're moving the point at which
resonance happens. And that's what stops
excessive vibrations. Yeah. Interesting.
Yeah. Other snapping structures could
also switch upon resonance. But the
problem that once they switch, they're
much more elongated, much more
contracted. So they don't, let's say,
they wouldn't provide the same function.
You could use this effect to keep
structures from vibrating or reaching
resonance. Could it be easier to install
a system like this where you're actually
moving the resonance instead of like a
whole tune mass damper or or something
like that? Yeah, I think this solution
is still very complex. It's very
complicated design, but I think the
principle could be used. I know it's
still super early, but I'm really
excited to see like it pop up somewhere,
you know, in a couple of years or
decades. It's more about the concept and
showing what it can do. We're going to
try to see if we can maybe make contra
snapping also maybe with different type
of variables. It's going to be like a
balloon that deflates when you inflate
it.
You increase the pressure and the volume
would decrease. Wait, really? That's
crazy. That would be the equivalent, but
we it's not there yet, but
we'll see. That's so cool. In principle,
it should be possible. Yeah.