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00:00This 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
00:07That's so weird, right?
00:09Here it is under controlled conditions
00:11There's a cup hanging from the mechanism
00:13But now look what happens as you add water to it all of a sudden the cup shoots up
00:18The amount it shoots up is tiny, but the physics behind it is so counterintuitive
00:23Nobody thought it was possible. It feels like it violates physics. That's why it's fun
00:28The paradox that controls this mechanism governs everything from mechanical systems to food chains
00:34From traffic jams to power grids and to understand it. You just need to ask a simple question
00:40What will happen to this weight if you cut the green rope?
00:43Where's this gonna end up is it gonna go up is it good gonna gonna go down or is it gonna stay the same?
00:50Can I touch yeah? Yeah, you can try it nothing you don't think anything's gonna happen in the same place
00:55Wait, it's gonna be right over there, but like it's gonna fly off forward now
01:00No, not too much, but probably it's going to go to this way you cut the green, right?
01:05This is gonna come down if you go down
01:07We go down it drops it'll fall down on it
01:10The first thing that occurs to me is as soon as you cut that the weight is gonna drop
01:14I imagine the weight ends up lower than it started
01:17Here's a closer look at the setup
01:19You have a spring hanging from a hook up here and then by this green rope it's connected to another spring that's carrying this weight below them
01:26There are two extra ropes here as well. So the red one and the black one are slack
01:32They're not under any tension whatsoever. So they're not actually carrying any weight
01:37What's gonna happen if you cut the green rope you can pause the video here and try to figure it out for yourself
01:42Here it is in slow motion
01:52So even though the ropes on the side were slack and we cut the only rope in tension the weight somehow went up
02:00Okay, so if you're unconvinced that cutting the green rope actually makes the weight go up
02:04Here's a huge version of the experiment
02:06So the black and red ropes are still very much slack and it's just held together by this tiny piece of green rope here
02:13So let's see what happens now
02:15Okay, you ready?
02:17Okay, three two one
02:24That's actually insane. That was pretty pretty good, right?
02:27I still don't believe it looking at it
02:30Okay, so why does this actually happen?
02:32Because the springs are contracting back and just pulling it together
02:35Maybe the tension in the, you know, this part is changed
02:39It releases the tension in the springs and only goes to the length of the ropes
02:42Okay, I believe that the molles were rotated for the weight, instead of no
02:47Look at what happens when you remove the slack side ropes from the initial setup
02:50You're left with this
02:52A mass hanging from a spring, hanging from another spring
02:55So these springs are connected in series
02:58Obviously, when you hang a weight from one spring, it extends
03:02Just like you'd expect
03:03And the amount it extends by, call it X
03:06Is proportional to the force exerted by the weight
03:08That's Hooke's law
03:10But if you add another spring in between in series
03:13Now both springs extend roughly the same amount
03:15X
03:16Because both springs feel the same force of the weight pulling from below
03:19So in the case of ideal massless springs
03:23You would end up with exactly 2X of displacement
03:26Now there's another way to connect these two springs to the weight
03:30And that is in parallel
03:31This way, both springs are independently connected to the hook above and to the weight
03:36So each spring is only carrying half the weight of the mass below
03:40Which is why both springs extend only half as far
03:43Or X over 2
03:45If you look at the setup right after the green rope is cut
03:48You'll notice that this is actually exactly how the springs are laid out
03:53So the red rope is connecting the bottom spring directly to the hook above
03:57And the black rope is connecting the top spring to the weight
04:00So these springs are in parallel
04:02So by cutting the green rope, you're actually forcing the springs to go from a series to a parallel
04:08And that change is what causes the contraction to happen
04:11When you cut the rope, each spring only extends by about half as far as before
04:16Which 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
04:22When you cut the rope, you go from series to parallel
04:24And that pushes you up
04:25The slack ropes, that's where I get to cheat
04:27And that's the misleading bit, you know?
04:30The key to getting this paradox right comes down to the length of the slack ropes
04:35Each one has to be longer than the length of one of the springs in series plus the green rope
04:40That's what adds the slack
04:41But they also can't be much longer than that
04:43Because too much slack will nullify the contraction you get between series and parallel
04:48And the weight will still fall
04:50Now, you might think that this paradox only really works with the springs in this demo
04:54But the first time it was discovered was actually because of its influence on people
04:58In April of 1990, New York was getting ready for its 20th annual Earth Day
05:04It was going to be Manhattan's biggest celebration of environmentalism to date
05:08STOP THE WAR AGAINST THE EARTH
05:11On the day, Central Park was turned into a massive festival ground
05:14With almost a million people pouring in to see a stacked lineup of performers
05:18Including Hall & Oates and the B-52s
05:23But the boldest stunt of the day was to ban traffic on some of New York's most important streets
05:28Including 42nd Street, one of the busiest streets in Manhattan
05:32It stretches from river to river, connecting Times Square to Grand Central Station
05:37And it's almost always jammed with slow-moving traffic
05:41The only thing that's an hour from 42nd Street is 43rd Street
05:45And maybe not surprisingly, people were really against this idea
05:49Insisting that just a six-hour closure of 42nd Street would mean doomsday
05:54As the commissioner of New York's Department of Transportation put it
05:57You didn't need to be a rocket scientist or have a sophisticated computer queuing model
06:01To see that this could have been a major problem
06:04But the city went ahead with it anyway
06:06And no cars were allowed on 42nd Street for the day
06:11Now, to everyone's surprise
06:13The traffic in the surrounding area actually got better
06:17The number of cars was reduced by 20%
06:20With bystanders claiming the whole area was a ghost town compared to the way it normally is
06:25But one man wasn't surprised by this result
06:28In fact, he predicted it over 20 years earlier
06:32His name was Dietrich Braes, a German mathematician
06:36And back in 1968, Braes was studying road networks
06:40As part of his research, he imagined a scenario
06:43Where drivers from one side of a fictional town were trying to get to the other
06:47But there were only two possible routes the drivers could take
06:51Route 1 starts with a wide highway that takes you halfway across town
06:55The road is so wide that regardless of how many cars are on it
06:59This part of the trip always takes 25 minutes
07:01The second half of this route turns into a narrow city street
07:05And the time to drive through this street depends on how many cars are on it
07:09For every 100 cars on the street, the time to pass through it takes an additional minute
07:14So 100 cars will take 1 minute, 200 cars will take 2 minutes, and so on
07:19The second route through town starts with a similar narrow city street that depends on the number of cars
07:25It takes you halfway across and then turns into another 25 minute highway stretch
07:30Where the transit time doesn't depend on traffic
07:32So which route would you take to get across town?
07:35Well, you can see that the routes are identical but flipped
07:38So it doesn't really matter
07:40Since this is just a mathematical model
07:42Both will get you there at the same time
07:44So say there were 2,000 drivers trying to get across the city
07:48Half of the cars would end up on the first route
07:50And half on the second route
07:52And since there are now 1,000 cars going down each narrow city street
07:56The travel time on these segments increases to 10 minutes
07:59So the total time on both routes is 10 minutes for the narrow street
08:03Plus 25 minutes for the highway
08:05A total of 35 minutes regardless of route
08:08But now say the city decides to connect these two routes at the halfway point
08:12With a small piece of highway to give drivers more options
08:16This piece only takes a minute to travel across
08:19So which roads would you use now to get across town?
08:22Well, as an individual driver, you should just go straight down
08:26It will take you 10 minutes to get through the first city street
08:29One minute on the new connecting road
08:31Another 10 minutes for the second street
08:33So your total journey time would now be only 21 minutes
08:36Compared to the 35 minutes for everyone else on routes 1 and 2
08:40Okay, great, so you minimize your own time and that's that, right?
08:44Well, not really
08:45See, drivers like you are selfish
08:47And everyone wants the shortest possible travel time
08:50Which means everyone starts flooding the narrow city streets
08:53As drivers switch to this new shortcut
08:56The narrow streets become more and more congested
08:58Making the route slower and slower
09:00But this makes the original routes worse too
09:03Because the time to get through the street segments
09:05Keeps increasing for every driver
09:07So everyone decides to switch to the shortcut
09:10And now all 2,000 cars are driving down the city streets
09:14Now the time to traverse each city street jumps to 20 minutes
09:18So the total journey time for everyone increases to a whopping 41 minutes
09:23Compared to the 35 minutes we had before the new road was constructed
09:27So traffic actually got worse for everyone
09:32To fix it, the drivers could simply go back to their original routes, right?
09:37Well, who's going to be the first to switch back?
09:40If any one driver goes back to Route 1 or 2
09:43Their journey time will be the 25 minutes on the highway
09:45Plus 20 minutes on the now congested city streets
09:48Or 45 minutes in total
09:50Which is even worse than the now congested streets
09:53So no single driver would ever want to go back to the original route
09:58And because humans are humans
10:00It's not like we could all just agree to ignore this new road
10:04So even though every driver was making a rational decision
10:07To try to minimize their own travel time by just using the city streets
10:11Collectively this made the situation worse for everyone
10:15And there's no way out
10:17But if the city were to destroy this new connecting road
10:21Everyone's journey time would drop from 41 minutes
10:24Back to the original 35 minutes on Route 1 and 2
10:28So removing the road would actually make the traffic better
10:32It's just like cutting the green rope from before
10:35That's because both of these are examples of the same paradox
10:39The springs are like the narrow city roads
10:42The more weight or cars you add, the longer they get
10:46And the ropes are like the highways
10:48It doesn't matter how much weight is on them
10:50They don't change
10:51That is, unless you don't know how to tie them properly
10:57This is the paradox Dietrich Braes discovered in 1968
11:01It's now known as Braes' paradox
11:04And it is the reason why New York traffic got better
11:07After 42nd Street was closed on Earth Day
11:10Now sure, you'd be right to argue that the reason the traffic decreased on Earth Day in New York
11:14Was simply because people decided to walk or cycle more that day
11:17But it turns out mathematicians actually modeled the whole city in 2008
11:21And they found 12 roads that were redundant and could be cut to actually reduce traffic
11:27And it's not only New York
11:29The paradox showed up in Boston, London, Seoul
11:33In fact, if you were to randomly add a new road to just about any city
11:37You'd have an equal chance of making the traffic better as worse
11:41But there's nothing special about the flow of cars
11:44Say instead you want to send electricity from one station to another
11:48Well, now you're looking at the flow of electrons in a power grid
11:51And just as before, you could try to improve the grid by increasing the capacity of existing lines
11:56Or by adding new lines
11:58But it turns out that this can actually destabilize the grid or even cause a blackout
12:04And virtually any other network
12:06Any time you're sending things from one place to another
12:09It can fall prey to Braise's paradox
12:11Be it a food chain, blockchain, or even the internet
12:15Adding elements to the network can make it worse
12:17So less can actually be more
12:20And that kind of got me thinking
12:21It's the same with your data on the internet
12:23The less of your private info is on the web, the better
12:26See, I got an email from someone a couple of months ago
12:28Suggesting that they can create tailored solutions to accelerate growth
12:32Okay, I thought it was spam so I didn't reply
12:34And then I got a couple of emails and I felt bad
12:36And I thought, okay, I'd be nice and actually respond
12:39I drafted up a little email
12:41But once I hit send, suddenly my inbox flooded with spam from me
12:46Grace and Jenny offering price lists for, well, I don't really know what
12:53Oh, and the best email actually suggested we should turn Veritasian's existing content
12:57Into high-performing YouTube videos to increase our audience
13:01And extend the brand's reach
13:03That's a genius idea
13:04But unfortunately, most of these emails are spam
13:06And I'd very much like them to stop
13:08And I can with the help of today's sponsor, Incogni
13:10So I only signed up to Incogni about six days ago
13:13They already sent out 49 requests to get my data out of Data Brokers' hands
13:18And as of today, 33 of those requests have been completed
13:22Saving me 24 hours of time
13:24Precious time I can spend tying springs to strings
13:28And asking strangers what happens when you cut the green one
13:31Incogni tracks down the Data Brokers holding your information
13:34And starts cutting those connections
13:36With the new Unlimited plan, you can use their custom removals feature
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13:44Where your info pops up
13:45And Incogni's privacy agents will take care of it for you
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13:53Especially those who might be a little too polite when replying to spam emails
13:59What was that?
14:00To try Incogni, you can go to incogni.com slash Veritasium
14:03Or also scan this QR code
14:04And if you use our code Veritasium, you get an exclusive 60% off
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14:12Or also there's a link in the description
14:14Get your data off the internet
14:15Go
14:16Go get it off
14:17What are you doing here?
14:18Braze's paradox doesn't occur every time you modify a network
14:22You need a very specific set of conditions for it to occur
14:25But if you can make it work consistently, you get this
14:29So we're here at the Amalf Institute
14:31Where they actually figured out how to make something shrink when you pull it
14:35So let's go check it out
14:36Is it here?
14:37Yeah, I made all the samples
14:41That's so weird
14:45Yeah
14:46Right?
14:47I guess you never expect things to yank back on you so unexpectedly
14:49Because a rubber band, you're stretching it and you feel it wants to pull back on you more and more
14:54But here just you're never ready for it
14:56The force is increasing suddenly, which is a weird feeling
14:58There's something almost like human about it where it starts tugging back on you when it gets bad
15:04What's special about this mechanism is that everything else around us works in the complete opposite way
15:10Try to press one of your keyboard buttons slowly so that it steadily goes down into place
15:16You can't do it
15:18No matter how slowly you go, there is some point at which it just gives way and clicks through
15:23The same happens if you try to stretch a bendy straw
15:27You can pull on it as slowly as you like
15:29But at some point the individual straw joints are going to expand suddenly
15:34Light switches, eyeglasses, grasshopper legs
15:37These all have a failure point beyond which they give way and quickly snap into a different position
15:43And this is called, well, snapping
15:46Here it is mapped to a force displacement graph
15:49As you'd expect, the more force you apply, the more the material bends or displaces
15:54But eventually you reach a tipping point
15:56And beyond it, the force required to bend the material further actually drops
16:01So if you apply a force higher than that peak
16:04The displacement has to rush to the next corresponding value to match the force
16:08Which is all the way on the other side of this dip
16:10And as a result, you get a huge amount of displacement for that tiny increase in force
16:16That's what creates the sudden snap
16:18It's very intuitive, I mean, you've all experienced it
16:21At least if you're in the Netherlands with your umbrella
16:23There's a gust of wind underneath your umbrella
16:26It pops to the other side
16:27So you sort of go over a peak in energy or in force
16:31And it suddenly snaps and typically becomes softer
16:34And this is the way all things snap
16:37Everything used to fail in the direction of the applied force
16:40Until this mechanism came about
16:43Doing the exact opposite of snapping
16:46Call it counter snapping
16:48Imagine that gust of wind blows under your umbrella
16:51But instead of flipping out, your umbrella suddenly closes in
16:55Or you try to pull apart a straw and the joints suddenly contract
16:59The wind is pushing on my umbrella, but instead of it folding out
17:02It would push itself against the wind to close itself
17:06But it feels like it violates physics
17:08It's just so counterintuitive that the displacement is in the other direction
17:13To the force
17:14Yeah, that's why it's fun
17:15So, how does this thing work?
17:17Well, the mechanism itself is built out of three different components
17:20And on their own, they all stretch normally when you try to pull them apart
17:25Individually, they behave like springs in the sense that they extend when you pull on them
17:29But then you combine them together and then suddenly they shrink
17:32Exactly
17:33If you draw the system as a set of springs, it looks something like this
17:37The long and lanky components represent the two springs on the sides
17:41But they actually don't feel like springs at all
17:44You can easily pull them apart until they suddenly get very stiff
17:48Meanwhile, these pieces represent the top and bottom springs
17:52And they feel a lot more springy
17:54So the more you pull them, the more they pull back
17:57And finally, the central piece
17:59It looks very similar to the previous one
18:01But pulling it apart feels very snappy
18:03In fact, you can even hear it snap out
18:08Put them all together and you get the mechanism
18:11If you stretch it slowly, you'll see how tension builds up in the three middle pieces
18:15With the sides staying mostly relaxed
18:17But if you keep stretching, the centerpiece will suddenly snap out
18:21And transfer most of its tension to the side springs
18:24This causes the system to stiffen and shrink
18:27If you now let go, the system resets
18:30So the mechanism can flip between a set of springs in series to one in parallel
18:35It's a reversible case of Braze's paradox
18:39The network is basically the same as the Braze paradox
18:42Yeah
18:43So the way they are connected, the topology of the connection is exactly the same
18:46The force displacement graph you get for the mechanism is one that loops in on itself
18:51With two distinct curves
18:53One for the system in series and the other for the system in parallel
18:57And this leads to some pretty remarkable properties
19:00If you slowly control the stretching force by adding water to a cup below the mechanism
19:05The mechanism first slightly sags like you'd expect
19:09But when you reach the tipping point at the end of this curve
19:12The displacement has to quickly reduce to keep following the force along the graph
19:17And this jump back is why the mechanism shrinks
19:20Now you can also control displacement instead of force
19:23And measure how much force it takes to stretch the mechanism at any point
19:28This time, when you reach the tipping point
19:30It's the force that has to follow displacement along the graph
19:33So you get a sudden jump up in force showing that the material has stiffened
19:38Oh
19:39This little force jump is enough to make it slip out of your hands
19:42Yeah, yeah, yeah
19:43I mean, even though you said it is a small jump
19:45It's like this is the only thing that does this anywhere probably on Earth
19:50Uh, yeah, as far as you know
19:52The force jump thing like this is not reported
19:55It is pretty insane
19:57So what is countersnapping actually useful for?
20:00Well, notice that there is a force at which the series and parallel curves of the system overlap
20:06Which means that at this force the mechanism will actually be the same length in both states
20:11So if you exert that exact force on the structure by, for example, hanging a weight from it
20:16You can flip between the two states by giving the mechanism a little tug
20:20And although that will change whether the springs are in series or parallel
20:24It won't change how long the system actually is
20:27So you can change the stiffness without changing the length
20:31Now, look at what happens if you give the mechanism a nudge in its original series state
20:37If you poke it, it's basically a way to measure the natural frequency
20:40Oh, yeah
20:41When the mechanism is in series, the natural frequency is 3.7 Hz
20:45But if you switch to a parallel setup, the natural frequency increases to 6.4 Hz
20:51You switch it and we look at the natural frequency now, you can see it's much higher
20:56What's unique here is that you're able to almost double the natural frequency of the material without changing its length
21:02I'm gonna move the robotic arm very slightly, just up and down
21:07Yeah, okay
21:08And I put a frequency of 3.5 Hz, so it's close to the natural frequency of this system
21:14This is going to drive the structure into resonance
21:16But once the vibrations get big enough, the mechanism is actually going to switch states on its own
21:22Change its natural frequency and thereby reduce the vibrations
21:26Like it gets stronger and stronger and then it just locks it out
21:29Yeah
21:30Yeah, that's cool
21:31The same happens in reverse
21:33If you vibrate the robot hand at 6.4 Hz, the mechanism is quickly going to switch back to its original state and minimize the vibrations
21:41It's interesting, the way that you say it, we're moving the point at which resonance happens
21:46And that's what stops excessive vibrations
21:48Yeah
21:49Interesting, yeah
21:50Other snapping structures could also switch upon resonance
21:53But the problem is that once they switch, they're much more elongated
21:56Yeah
21:57Much more contracted, so they wouldn't provide the same function
22:00You could use this effect to keep structures from vibrating or reaching resonance
22:04Could 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 something like that?
22:12Yeah, I think this solution is still very complex
22:16It's a very complicated design, but I think the principle could be used
22:19I know it's still super early, but I'm really excited to see it pop up somewhere in a couple of years or decades
22:26It's more about the concept than showing what it can do
22:29We're gonna try to see if we can maybe make counter snapping also
22:32Maybe with different type of variables
22:34It's gonna be like a balloon that deflates when you inflate it
22:37Yeah, you increase the pressure and the volume will decrease
22:41Wait, really? That's crazy
22:42That would be the equivalent
22:44But it's not there yet, but
22:46We'll see if
22:49That's so cool
22:50In principle, it should be possible
22:51Yeah
22:52Adrienne
22:54Adrienne
22:57Hey
22:58Bye
22:59Bye
23:00Bye
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