Braess's Paradox - Equilibria Gone Wild

[@upandatom]

What life lessons can we learn from Braess's paradox?

[@benadians1769]

Humans suck

[@AutoFirePad]

Human societies have limitations.We're not bees nor ants. There is always selfishness.

[@gaurangagarwal3243]

The whole mind of central system of car AI lies in the mind of dog

[@NetAndyCz]

Networks are complicated and unintuitive. Especially when the individual parts are not equal. And that you should be careful how you build your network so you do not inadvertently replace parallel setup with a series with lower throughput.

[@landspide]

A little bit of random goes a long way to shorten the way!

[@ReaperUnreal]

That spring+string demo blew my mind.

[@SomeOtherMikey]

For real! I'm usually a passive viewer of media, but when she released the spring, I was that annoying guy in the theater yelling at the screen, all "WHAAAAAAAAT!?"

[@fzigunov]

Spring theory!

[@SykoSparx]

Given the fact that we saw unnecessary connections burdened the system, I assumed the fact that they were connected meant all the strings were doing was not pulling their weight while adding their weight. It seemed kinda natural that they would rise given all this but I definitely could see how someone would think they would fall and my thought process was likely flawed anyways because it seemed to have more to do with the springs being able to divide the weight and less to do with the strings pulling any weight.

[@skynet4496]

But string theory is just a hypothesis, this is a real theory- testable lol

[@JimGiant]

Intuitively I'd have said it went down but realising it was a trick question guessed up. Took a good 5 minutes to figure out why though.It's amazing that such a simple system is so unintuative.

[@isxiahrxxxxx6725]

it always makes me chuckle when solutions to traffic problems basically end up reinventing some form of public transportation

[@deus_ex_machina_]

😅 I just came from Yet Another Urbanist's video on the Braess Paradox.

[@rawmilkmike]

This is very retarded. Some one must have changed the definition of Braess's Paradox. Someone who clearly doesn't understand traffic engineering.

[@fatsquirrel75]

"No one in New York drove, there was too much traffic" - Fry.

[@harrymills2770]

Nobody goes to that club, any more. It's too crowded.

[@ericbedenbaugh7085]

@@harrymills2770 Yogi Berra !!!! "A nickel aint worth a dime any more."

[@ericbedenbaugh7085]

He's paraphrasing Yogi Berra, when asked about a certain restaurant replied, "No one goes there anymore, it's too crowded."

[@ericbedenbaugh7085]

@Agent J "When you get to the fork in the road, take it."

[@goodchessactor]

I went to a crowded casino. I was lucky to get in.

[@blackboardbits]

I teach this paradox as an introduction to game theory-on the first day of class, I get the students to recreate it (letting them discover the paradox for themselves, arising out of their own decisions!). It works really well, and it's also a nice way to introduce students to one of the fundamental ideas of game theory, namely, making choices in an environment where other people's choices affect you.

[@yongmrchen]

I think the best example to INTRODUCE game theory is always the Prisoner’s Dilemma because it requires the least number of assomptions to obtain the same and most generic conclusion. In Braess’s Paradox, in addition to people behaving independently in a self-interested way, you need to assume the fixed number of drivers and the time spent on each leg of the road network and also the topology of the network, to some extent.

[@GaneshKarthik-j9p]

Teachers like you are the teachers we need.

[@juannarvaez5476]

What kind of class setup do you make that recreates this paradox?

[@abjorndahl]

@@juannarvaez5476 I have the students stand to either side of the room to indicate their choice of which route to take. We do the simple, 2-route game first, and the class always eventually distributes themselves evening (finding a Nash equilibrium). Then I add the shortcut, tell students they can "choose" it by sitting down in their seats, and watch as more and more students sit down. As they do, you can see that they start to get confused/perturbed, because the quicker ones notice their travel time is getting worse and worse. A few might even stand up, briefly, but then quickly sit back down when they realize that the shortcut is still fastest, even if they're worse off than before. After most people have sat down (approaching the new N.E.), I convene the class for a open discussion about what happened and why.

[@ryuheechul]

So many hours that I spent on that Chyung-gye highway in my dad’s car when I was a kid due to the everyday route from my school to his work places and home. After the highway gone, the traffic indeed improved. And thanks to this video now I know why!

[@cuzbo_]

This is probably the most underrated channel. Every video is thought provoking and super well explained.

[@reyadsalahin1101]

Unfortunately, that’s the reason why it’s underrated.

[@hussainismail2080]

Yes, it is entirely scripted like she has written every sentence of this video 😅

[@rjcalara4174]

I find the video very interesting. I learned a lot today.

[@guetali]

absolutely agree ...

[@Frankyboy2424]

Not to forget that amazing work of animation

[@checkm8418]

16:26 "your natural state often isn't your most efficient state" with visual lmao. Nice work miss Up and Atom.

[@greensteve9307]

*Jade

[@Adraria8]

Basically what she’s trying to tell us is to take drugs

[@josephgerman2674]

Technically, the laying down picture is more efficient. She's not wasting any energy. If she gains weight being couch potato, that's because she's conserving energy. Bears waste energy hunting to get fat, then they hibernate and switch to an extremely efficient energy state, where they can survive for long periods of time on less energy.

[@josephgerman2674]

@@_Egon If a car can go longer with less energy, it's necessarily more efficient. Efficiency is just a ratio of useful output divided by total input.

[@sdgathman]

​@@josephgerman2674 "There is nothing so useless as doing efficiently that which should not be done at all." - Peter Drucker "I do only what I see my Father in Heaven doing." - Jesus

[@sankalpabanerjee6218]

Your example with the strings and springs and the analogy with the roads was utterly fascinating, such an excellent way to explain the concept.

[@generic_youtube_name3]

8:05 Assuming a linear spring constant and perfectly inelastic ropes with equal amounts of slack, the weight will rise if the system satisfies this equation: s < 4.9 * m / k where s is the slack in each rope, m is the mass of the bottle (in kg), and k is the sprint constant

[@nikilmanu334]

Yeah i found the same. I did the classical physics equations and thought she would say all three are possible and it would depend on the parameters of the system like spring constant and weight and length difference of strings and spring. But i was sad. The same happens in my exams aswell they ask you to assume things.

[@rickebert7548]

Very good explanation/illustration of Braess’ . (i had not know about the Korean highway) - The practical issue for traffic engineers is that the initial west-east road network made things very arduous for the people traveling north-south. That connector made things very nice for people living at midpoint south the get to midpoint north. Also mention that the illustrated road network was simplex (one-way at any given time - often done on bridges tollways). Kudos to you and roborace for raising awareness!

[@kaushikgupta9490]

Kudos for the spring-string anology !

[@Alexa-Raine]

It's a lie.. x/100 road must be equal to or greater than the 45min road NECESSARILY.

[@martiddy]

This is why her videos are so awesome, she always shows simple but effective analogies that are easy to understand the topic.

[@Alexa-Raine]

@@martiddy ineffective and incomparable..

[@jackjohnson493]

The strings were carefully chosen to be just slightly longer than the stretched springs. If the strings were arbitrarily long, this demo would not have worked.

[@metalzonemt-2]

@@jackjohnson493 Why would they pick arbitary long strings, since they are based on the lenght of the roads?

[@cromptank]

Using the spring/string model is an ingenious way to model this phenomenon! Great work on this vid

[@MedlifeCrisis]

The animation is so good! You explain more complicated concepts than any other channel I watch regularly but you do it so well & clearly. I had never heard of Braess. I couldn't tell if the magician's hands were you or a professional, such expert mysterious movements ;p

[@MedlifeCrisis]

Also like 80% sure your backing track has been in a Hindi movie

[@upandatom]

I was practising those hand movements for hours I'm glad it paid off.

[@brentmartin1981]

I absolutely love, love, love your videos!!! Science can sometimes be very confusing to me, but you break it down in easy to digest steps, keep up the wonderful work.

[@Densoro]

Man, I thought the bottle would stay in place, as the strings and springs compensate for each other. Figured the height of the bottle was immutable equilibrium itself. Fascinating twist! I was never great at STEM but I just found your channel and you make it so digestible. Subbed :3

[@Ragnarok540]

The string + spring experiment made me click the notification bell.

[@ethanepperly5645]

Absolutely everything I’ve seen on this channel is absolutely amazing! Keep up the great work!

[@smalin]

For me, a visceral understanding of this paradox came from looking at the center of the string/spring setup at 9:03 and imagining what would happen if a force pulling the two visible center spring ends towards each other were applied. Once I realized that the lower end of the left spring would have to move down, I could see that the weight at the bottom would be free to move down as well (since the left string would be moving down and, because the situation is symmetrical, the right spring would be stretching as much as the left spring).

[@ShayerSUtsho]

Why is this comment so underrated

[@edp7476]

Educational/informative way to present scientific principles and paradoxes. Plus, you made it fun to watch with graphics, demonstrations, and thought provoking questions. Great channel. Will definitely keep watching more.

[@UncleChopChop22]

Found this channel recently and being enjoying content. But gotta admit wasmore excited for a second with this one as read it as the Braless Paradox.

[@JJ-kl7eq]

For those that might not be convinced this video is about an actual paradox, Braess yourself.

[@louisng114]

That spring/string demonstration really raises the bar for the next video.

[@HerbertLandei]

Math puns are the first sine of madness...

[@Alexa-Raine]

It's a lie.. x/100 road must be equal to or greater than the 45min road NECESSARILY.

[@AugustinSteven]

Didn't she say that it wasn't actually a paradox.

[@SykoSparx]

@@AugustinSteven What if that's the paradox?

[@donnie9886]

Thank you for all the effort you put into your videos!! This was amazing, I learnt so much! 💕

[@Alexa-Raine]

It's a lie.. x/100 road must be equal to or greater than the 45min road NECESSARILY.

[@mohitram6922]

@ 10:30 the analogy was amazing and very clear.

[@davidhand9721]

Really? My choices aren't made by massive bodies universally attracting each other with an inverse square law. It's more like weighing the comparative values of outcomes. If I contribute to a Braes paradox, that means I have made the mistake of valuing my own short-term gain greater than others, that I am more important than other people, which is selfish and illogical, and I should feel guilty about it.

[@Alexa-Raine]

It's a lie.. x/100 road must be equal to or greater than the 45min road NECESSARILY. @4:00

[@Alexa-Raine]

Spring analogy was bad... The road doesn't shrink (spring pulling)...

[@deandeann1541]

The analogy wasn't really about springs, it was about equalibrium points.

[@Alexa-Raine]

@@deandeann1541 no it isn't.. equilibrium, yes, points, no.

[@SentinelPrimek]

Smarter every day tweeted your traffic video and now I'm subbed.

[@rubiks6]

When the video got to the point of disconnecting the two springs you got a new subscriber :) Excellent job (the whole video, not just the springs) of explaining Braess's paradox. It is very subtle and it will take me time to begin seeing its impact on my daily world. As for traffic, I live near Washington DC. One of the worst traffic areas in the US.

[@jameshelton8311]

One important thing that we can learn is that one choice that gives us a very small gain, such as saving 2-3 minutes on an hour drive can have a larger impact on more people, such as causing 50 people to lose 5 minutes. Also, even before we are in fully autonomous cars, apps like Waze already use collective intelligence to improve the entire system. Even with a small percentage of driver's acting as a sensor network, Waze is pretty good at predicting slowdown and mitigating it by redirecting drivers to alternate routes. It regularly chooses different routes home from work that have similar times and distances. I've noticed that when I ignore the chosen route and choose the more commonly used high efficiency route, I fairly regularly end up in congestion with all of the other drivers who are also choosing the route that is more efficient at times that there are less travelers. Thank you for this video (and all of your videos!) It is very insightful and you always present things in a very interesting and engaging way!

[@Liam-qr7zn]

I was thinking about Waze while watching the video, but I doubt it can be a solution to Braess's paradox since it always tries to determine the fastest route for each user. Therefore the introduction of Waze may even have contributed to Braess's paradox, even if it may have had other effects that have reduced traffic congestion overall. Changing Waze to reduce Braess's paradox by giving users routes that are optimal for the system rather than for the individual user would be a hard sell since then people who don't use Waze would have a comparative advantage, especially if they use a competitor's product that behaves the way Waze does now. Or users will just start using Waze to check alternative routes and select for themselves the fastest route before each drive. Not only will that not effect a reduction in Waze's paradox, it'll only incur hassle for the user which will make competing products more attractive. Even if Waze can reduce Braess's paradox, therefore, it'll be at the cost of a loss of users, while those who are actually following Waze's recommended routes will probably be those who don't realize they are at a comparative disadvantage, even though it is their actions that are improving the system for everyone. The only hope is for Waze to lie about the driving times it displays to users and hope people don't notice that using a competing product gives them faster drives.  All this is a bit of a bummer to me as I thought I was improving traffic for everyone by using Waze since I was reducing traffic on congested roads and making use of underutilized roads, when in fact in some cases I may have been making things worse for everyone.

[@tisajokt7676]

I knew about the phenomenon in traffic but I've never seen a physical example! Very cool!

[@ritchiemx7391]

Your videos continue to be some of the best science content on KZbin. Thank you for sharing your talent for explanations with us.

[@josem138]

8:25 I would say the question is uncomplete. The springs have a force constant that changes depending on the spring constitution. If we imagine a soft spring (low constant force) the example you show will become valid. However if you imagine a spring with very high constant force it would behave as a string. Then, I think four strings in your setup would behave the oppositte way falling instead of rising. When the strings are joined together they form a diagonal, where its length is just the cos(angle). When they are free, they return to their normal length which is higher. Then, depending on the spring constant force you can exhibit three different scenarios in which stays the same, falls or rises. Thats my thought

[@mixednutt42]

I wish I had discovered your channel sooner. Your video's are very brilliant, and you have blown my mind several times. Thank you, and please keep up the good work.

[@Lucaazade]

"catastrophically terrible consequences" switching to happy face was great

[@CaseyRuleMusic]

This is an exceptional educational video-probably the best I've seen on this channel so far! Keep up the great work!

[@Corporis]

Dude! That spring string demo was fascinating!

[@mytheory9701]

Fantastic video in so many ways! including great progression from introducing a new concept to demonstrating to current implications! You're terrific. Thanks!

[@littlebacchus216]

Here from Steve Mould who has also made a video on this and he pointed out you did yours first so thought only fair to check it out.

[@kangkarino]

I think linking the 2 lanes would make sense with ever growing traffic load. After 4500 cars, the equilibrium switches since the fastest route is to take the highway but it's only after 9000 cars that the linked configuration is more interesting than the 2 separate lanes.

[@MakakunaruLoco]

Good catch.

[@NONARCS]

Without a doubt the issue with braess is the ever changing demand. Removing an option creates absolute havoc when their is an accident on any of the two highways. These traffic issues are more complicated, and could be better delay with by looking at the funnels at the start and end, why people are driving at the same time instead of spacing out the time and finally why they need to travel at all. You could end most traffic jams and save the planet by switching to telecommuting. Would cost very little and all the highways could be left where they are

[@sarathpenumuru]

Beautiful filmography and storytelling. You make difficult ideas so interesting and digestible.

[@cesalonsomulder1990]

The springs and strings system was amazing. WE ALL LOVE YOU A LITTLE MORE NOW. THanks !!

[@Alexa-Raine]

Roads don't spring... stupid analogy..

[@cesalonsomulder1990]

@@Alexa-Raine but springs have a recovery force that you can suppose it grows proportional to x like the small road they pretend to mimic

[@Alexa-Raine]

@@cesalonsomulder1990 Ces Alonso Mulder The recovery force of a spring doesn't compare to the x in ×/100.. It's the 100.. The more backed up a road gets, the more tension, the more it stretches a spring. The higher the resistance of the spring means a higher available recovery force and less stretch on the spring, so more cars feasibly. It's wrong.. just pretend it's wrong and prove that, if you can. You can. That's called science.

[@cesalonsomulder1990]

@@Alexa-Raine I think that what you say is not very accurate with the model. If you suppose the mass that is hanging proportional to 1/× , I mean , proportional to the inverse of the cars that drive by the narrow and wide roads everyrhing fit. The law of springs is linear and likewise the road's law is as well, but they are not lineal in x

[@tudorburchill8426]

great vid Jade, i work in manual therapy and I use a network of questions for diagnosis and treatment (destination). In this network of Q's many answers provided by clients provide shortcuts to more advanced questioning and getting to the destination quicker as certain answers cuts out swathes of Q's. This is called pattern recognition. Biological systems and manual therapeutics are inherently complicated. For instance roughly every second day I will encounter something new amongst 1 of 16 clients in clinic- effectively growing my Q's network whilst the other 15 clients provide an opportunity to eliminate or tailor existing networks.

[@theultimatereductionist7592]

I love your string-spring setup. That is very cool. Right - the non-stretching string is analogous to the fixed-time number-of-car-independent half of the route from A to B, while the stretchy spring is analogous to the time-varies-with-#-cars half of each route. A+!

[@z-beeblebrox]

Basically, when you're driving on a road, you become a fluid particle

[@Verrisin]

Except, those will just go wherever is the least pressure, I think. Cars can go in any direction they think works...

[@MakakunaruLoco]

@@Verrisin In other words, the perceived least pressure.

[@Verrisin]

@@MakakunaruLoco Well, no. I will not go to some random direction. I travel towards a destination. All fluid particles have the same idea where they want to go. Not the case with cars and people. "direction they think works" - By that I meant, a direction they think is sensible for eventually arriving where they want to. Sometimes you go in the opposite direction for a little bit, hence it's not just always 'in the direction towards destination' ... but yeah.

[@SykoSparx]

@@Verrisin I constantly make wrong turns when I let my directional system go into auto pilot.

[@MakakunaruLoco]

@@Verrisin very true. Particles just go wherever they have less energy or are stabler or something. Sometimes we do that in a total different way.

[@julian_ossuna]

This was so didatic and well researched (and interesting)! Great job Jade 😉

[@attilaborocz5422]

Your natural state :DD That was priceless

[@rayj4722]

I knew the load on springs were going to contract but the strings threw me off I thought it was gonna stay the same at the same time I thought it was going to go up but I voted for stay in the same I keep learning things from your Chanel keep it up this is very educational, key words here are ‘learning’ and ‘educational’, don’t stop for the love of everything good in this mundane existence keep teaching, please and thank you.

[@PoeRacing]

@ 14:25 you manage to very clearly display your passion for advancing technologies and self driving cars in particular. I LOVE your work and very much appreciate the effort that goes into every video!!! Thank you for continually overcoming your "natural state"!!!

[@stevemattero1471]

That moment when your sponsor promotion is as interesting as the rest of the video

[@corbin2169]

Thank you for the awesome video, 17 minutes well spent. Looking forward to the next video.

[@gab.lab.martins]

Didn't even realise it lasted 17min.

[@bagusamartya5325]

Honestly though this Paradox makes me anxious about my life choices lol

[@chrisreynolds6391]

It explains why some cultures have arranged marriages. Many peoples choices are worse than statistical chance.

[@SurajNayak007]

@@chrisreynolds6391 bruh 😆😆😆

[@bored_person]

@@chrisreynolds6391 what a horrible justification.

[@StuartB138]

I came here from Steve Mould’s very short video on the same subject (made in 2021) and found a great video and new channel to subscribe to. Great vid and I really like the cheery yet quite dark not at the end. Brilliant! 😁

[@Lee-qj4hk]

06:00 Two lanes narrow to one ahead. Lane A will cease to exist, lane B will continue. There is a queue in lane B. Do you (a) join the queue only to see some drivers skip around you by joining lane A and inserting themselves back into lane B right before lane A disappears? This may continue to the point where lane B ceases to move. So there's pressure to follow along. Or do you (b) realise that this will happen and behave rationally from the outset by joining lane A and skipping past more considerate drivers? If everyone behaved rationally, everyone would join lane A. Fairness would be reached, everyone would have the same time to reach the narrowing point then offering the option to join lane B to skip around this queue. Perhaps the equilibrium is to join whichever lane is emptiest? Although drivers in lane A depend on drivers in lane B allowing them to rejoin B.

[@JoeBlogster]

Fascinating but I think this is where theory and reality divide. In reality, it wouldn't be that everybody @5:00 would take upper road and then switch to lower road. What would actually happen is 70-80% would start on lower road and switch to upper road where there is maximum throughput at all times. The remaining 20-30% would equalize the upper-to-lower route due to lack of traffic. A theorist might be tempted to say “Let's assume Braess Rd is a one way.” but again, this isn't theory. In reality you'd be a fool to build a one way road in this configuration. Theory is nice but short of going to some extreme like a Tesla Valve (AKA, valvular conduit) I'm struggling to imagine a real-world situation where one could reduce flow by adding more paths for the cars/water/electrons to flow through. I'd be interested in seeing you collaborate with either Physics Girl, Smarter Every Day or King of Random to test a functioning model of this. Say, start with a tub of water with connecting pipes of different diameters. Then throw a valve and see what happens.

[@mack_wei]

My thoughts the same thing why the video didn't trace the maximum throughput path of lower to upper if the travel times are constant? Also, real life applications have car pools and tolls to extract more dollars for high cost areas for elites (private communities) rather than make more sensible urban planning projects to maximize public good.

[@13ninjapirate]

Thankyou! It was really bugging me that this wasn't addressed.

[@HalfgildWynac]

@@13ninjapirate The analysis is pretty solid. In the setup in the video, if 75% use the lower road first, the travel time on the upper road (its first half) is 10 minutes. Surely the 75% would notice that the people using the other road can drive four time faster, so each of them, rationally, should want to switch roads. It is unrealistic to expect a driver to know the WHOLE picture. Then again, if people drive these roads every day, sometimes the left road, sometimes the right one, they will eventually have the idea of how it works. In reality, I think, the problem is usually the uneven network, the finite reaction time of the system (the jams can spread very far very fast) and how impossible it is to satisfy the demand in a large city. Moscow has its share of 10-lane highways going straight into the centre and also in circles. Somewhere along the way the planners forgot that the end of a highway is not the destination where people are driving to-most will eventually need to use other roads with far less capacity.

[@MijinLaw]

It bugged me too, then I realized it's just a bad diagram. What they should have done is have a straight, narrow section and a curved, wide section to each path. Then it makes more intuitive sense why taking the narrow roads and the connecting highway is the preferred option, and why the wide sections have constant, large time. People take the narrow + connecting route until gridlock happens, and then, when gridlock happens, some people will indeed take the other route but never enough to "fix" the system overall.

[@Argellus]

@@MijinLaw yeah it bugged me too, until I realized that the total travel time for the 2 constant speed sections (bottom left and top right) would be 90 minutes, which is more than the other options. Just a badly scaled diagram that should have been drawn more to scale for better visualization (or maybe there are slower speed limits on the wider sections - either way).

[@mattisback4more]

Expected a great video but surprisingly was still blown away by the incredibly written and visualised content. Thanks so much! To me this is another reason why government must regulate intelligent cars very carefully to ban selfish behaviour. Understanding how computers decide choices for the cars is hard though and will require other ML or quantum computers (if they are ever used). Again, thank you. As somebody who has done physics outreach stuff in the past I think you made this video perfectly. It's also not very often I come across interesting concepts I am unfamiliar with.

[@jursamaj]

Neither installing AI in cars not regulating that AI can defeat selfishness. The driver can always choose the route, if by no other means than directing the car to points *on* the road they want to take.

[@_kopcsi_]

well, nice video. I really enjoyed it, as usual I do when I watch your videos:) however, I think the question you asked in the video is not a well-defined question with an exact answer. the mechanical system shown in the video has some parameters which are unknown for us viewers. actually all three proposed answers could be the right answer depending on the exact parameters. most importantly (and in idealistic case) there are 4 parameters which determine the right answer: constant length of the strings (K), constant length of the unloaded springs (S), the spring constant (k) and the weight of the load (m). using the laws of classical physics (Newton): m*g=k*x, where “x” is the spring’s deviation from its original length. so: x=g/k*m=α*m (g and k are constants, so g/k is also a constant, which is now α). so the length of a loaded spring is S+α*m. using these variables we can figure out in which cases will be the “parallel” (i.e. uncoupled) system the shorter one, longer one or exactly equal to the “serial” (i.e. coupled) system. before this we can also deduct some basic conditions from your system by looking at it: K>S (unloaded case), K>S+α*m (loaded case). actually the former is a weaker condition and the latter is a stronger condition. the stronger condition’s alternative form is: (K-S)/m*α > 1. the “parallel” system has a length of: K+S+1/2m*α [the weight of the load on each spring: 1/2m] the “serial” system has a length of: 2*(S+1m*α) [the weight of the load on each spring: 1m] equating these two terms we can determine the configuration of parameters when the two system has the same length. it turns out that the 4 parameters determine this in the following way: - “parallel” system is the shorter, if: 1 < (K-S)/m*α < 1.5 [the lower limit is from the condition mentioned above] - the lengths of the two systems equal, if: (K-S)/m*α = 1.5 - “serial” system is the shorter, if: 1.5 < (K-S)/m*α so, actually it would have been possible that uncoupling your system its length increases, if the configuration of the above-mentioned 4 parameters had been such that. this means that the question asked in the video cannot really be answered due to the lack of enough information:) so those, who had correct answer, either guessed, or simply picked the most counterintuitive answer considering that this video is about a paradox:D ps: do you think this paradox is somehow related to the Simpson’s paradox? I do think this, even if they are related only on a very deep level. I am curious if you can confirm me:)

[@wacpj1929]

I'd imagine the spring constant, mass of the weight, and the amount of slack in the ropes would yield different results. Minimize the weight and maximize the spring constant, and the springs aren't being pushed down much to begin with. Couple that with the extra amount of slack, and the reduction of the spring extension would pale in comparison to the extra slack, making the weight fall. But if there's hardly any slack, and a very stretchable spring with a very heavy mass attached, and the rise would be dramatic. That would be my guess, anyway - different tweaks in those factors lead to different situations, with certain choices even leading to the weight staying where it is (I understand that the experiment itself wasn't the point of the video though)

[@akshatprakash871]

What you said is accurate, I did the math, assuming both springs have the same constant of elasticity and the string is inelastic, if the difference between the length of the string and the length of the extended spring is greater than mg/2k, the setup falls and vice versa

[@amardeepsinghkushwah3245]

Same here! extension in spring would be the same and independent of string length (considering ideal string ).Tension in spring is the same independent of string length which means same extension every time, we can choose our string length as we please to have final increase or decrease in total length.

[@monteparnas]

I've been recently starting to champion the implementation of Game Theory in my corporation, for HR and some other areas. I'll use this video to do so, as I think it would be relatively simple to translate a lot of corporate stuff, like organization, procedures and personal management into networks and network assembly. Overall this has been an excellent channel, good work!

[@WayOfTheCode]

That's monkey was so lit. Also such an novel and awesome video. Also the idea of using network theory to road is so compelling and those happen now.

[@JeffSchwarz]

I come for the science, I stay for the quirky animations.

[@animistchannel2983]

Great episode! I enjoyed the various animations and experiments, and I thought they added clarity as well as entertainment, as well as regulating the flow rate of information so that it was easier to follow along as the audience. I think it would be more accurate to say not that people are acting selfishly, but to say they are acting in accordance with their own experience. As an emergence of this, if everyone got where they are going sooner, there would be fewer cars on the road altogether at any time, and so everyone's travel time and conditions would get better. This is how raising the speed limit on interstate highways in the USA actually reduced accidents and fatalities. The 55 mph "safety" speed limit that was imposed for many years was actually killing more people every day. What has already started providing collective intelligence in driving is the cars and cell phones getting traffic updates to inform drivers to take alternate routes before they get snarled in traffic in the first place. It's a good example of how a person can "think with the system" without requiring additional regulatory machinery to be in place. By hooking them into the hive mind, their experience reaches into the potential futures and far from direct view. Many plants engage in this kind of widespread communication naturally.

[@therayven3147]

Ok, I know this was an old comment, but, I had to put my thoughts on your speed limit theory... My theory is, traveling at a higher rate of speed causes the individual to focus more on what's around them, seeing as there is a much less time to react... Calculate a static object... Calculate forward velocity vs distance traveled vs distance to said static object... A driver traveling at 55 mph would be more inclined to become distracted as he has much more time to react... Where as a driver traveling at 80 mph is less likely to become distracted because he has less than half the time to react... This is why Indycar drivers are better at reading crashes than NASCAR drivers... NASCAR drivers train themselves to react at roughly 190mph, whereas an Indycar driver trains himself to react at over 210mph at times... So, more speed does *NOT* nessisarily mean more efficiency, it means better focus, in theory, leading to less incidents...

[@animistchannel2983]

@@therayven3147 Hey, thanks, that's an interesting thought. Maybe next time some back-seat driver asks us how fast we are going, we should answer, "Fast enough that I'd better pay attention to the road and not to you." :)

[@therayven3147]

@@animistchannel2983 lol, good point... Shoot, I remember back in the day when we had an American "Autobahn" up in Montana... I drove roughly 120mph the whole way through and my eyes were glued to the road ahead... And occasionally to the fuel gauge... The only other time such high speeds become dangerous is mechanical failures, such as tyre failures, etc... But distraction is usually not an issue...

[@vedantneema]

3:49 Well, I went and did some math and turns out that in the optimal solution for all the cars, the average time is 64.6875 or just 1035/16. So for people wondering if the highway could actually reduce commute time, there's not a big difference.

[@mosab643]

9:23 Yeh, but it depends on the length of the strings you choose. If the slack in the ropes in the first setup corresponded to a length greater than the length by which the springs contracted in the second setup, the weight would've dropped in that case. So, it was sort of a trick question without knowing the length of the ropes you had chosen.

[@mishaerementchouk]

It does depend on the lengths of the ropes and the strings but this is relevant to the paradox itself. The weight goes up only when it’s not too light and not too heavy. The same with the illustration of the paradox: the middle connection increases the travel time only when the number of cars is not too small (more than 1500) and not too large (less than 4500). The paradox is subtle: it is not particularly difficult to construct a network where it shows up but whether it takes place in a given realistic large network may be quite tough to figure out.

[@baldeagle5297]

Not gonna lie, I thought the title was Braless paradox. Good video though.😉

[@alquinn8576]

is there a patreon or something where we could support this other topic of discussion?

[@kyledailey]

@@alquinn8576 *Just your local strip bar.*

[@mikestevens8012]

A pair of docs. Goes into a Hooters . ...with a comb of honey and an ass...

[@absofjelly]

Here was I thinking I was the only one.

[@brian.willett]

You and me both friend

[@snipersquad100]

I think grannies shouldn't drive when they high on coke.

[@Rygir]

*cake

[@jeremyrixon150]

Super interesting! Another way for people to cooperate and reduce overall traffic is to use public transport. Centrally controlled and more efficient!

[@Dixavd]

Minor feedback, could try to keep contrast levels high when you put text on the screen? 3:25 is difficult to read for me, for instance. A good rule of thumb is to make sure the brightness of the text and background are far apart (i.e. not relying on hue for contrast) and then using complementary colours. Still: Great video, Jade! (although I do fear your fairy lights are going to get knocked inside the power socket behind you....)

[@quirly4648]

came here from Steve Mould's recommendation and now I'm hooked....thanks for your great work

[@TeslaFactory]

Brilliant analogies in the second half, very insightful, I was super impressed 😊

[@cooperbailey5291]

Good video, but your spring demo question was ambiguous. You did not provided enough information to narrow down to one answer. You left out the spring constant and the length of the slack in the string (till after uncoupling the spring). The problem is apparent when looking at Hooke's Law F = -k* x x = -F / k Because the length is proportional to the inverse of the spring constant (k), the length contracted when the force is halved is dependent on the constant and the overall length of the spring. Meaning it is impossible to know how much the spring will contract by. When combined with the unknown length of the slack in the string, there is a ratio between them that would provided any of the options you gave. Eg. Given that the two spring contracts 5cm when the load is split. Then if the slack in the string is greater then 5 cm the load will fall, if the slack equals 5cm then the load would appear have a constant hight, and lastly, your case if the string is less then 5cm then it would rise. Note: providing the clarity to your demo would over complicate things and may subtract from the maim topic, but the ambiguity you created is falsely leading people to your idea, even though you have a good valid argument.

[@jase1911]

@ cooper Bailey Although I somehow agree with you.... you don't get out much do you?🤣🤣

[@felipec06]

That happens in Maximum Flow Problems too (finding a feaseble flow in a flow network that is maximum), where not all the blocking flows that you may find have the maximum flow value for the net (Dinitz algorithm). :)

[@fstemarie]

That kind of reminds me of how, in electronics, putting two resistances in parallel gives you an overall resistance that is lower than the lowest of those resistances which sounds counter-intuitive.

[@crinolynneendymion8755]

That's 'cos your misled by the word "Resistance"; if you were to call it "Conductance", it's straightforward.

[@sleepjamal]

Important life lesson: we blame ourselves for stuff when sometimes it's just physics at play

[@purbeshmitra9704]

And people thought it was about Fullerene :P. Great video btw.

[@FatihKarakurt]

Impressive modeling with the strings/springs example, thx.

[@macdjord]

For highways, there's a solution: controlled access. The way to measure how efficient a road is is by measuring how many cars per hour pass through it. You can calculate this by multiplying the traffic density (cars per kilometre of road) by the traffic speed (kilometres per hour). Now, every road has a certain optimal traffic density which maximized the cars per hour. Imagine a highway that's almost empty. Everyone's zipping along at 120 km/h, but there's almost no one there. If you doubled the number of cars, everyone would have to slow down a bit, but not by half, so it's an improvement. Now imagine a highway that's totally packed - stop-and-go traffic. If you removed half the cars, the speed everyone goes would *more* than double, so that's an improvement too. Now, somewhere in the middle, there's an optimum point which gets the maximum number of cars through per hour. So what you do is you put automatic gates on the on-ramps, connected to cameras which monitor traffic conditions. As long as the traffic density is below the optimal point, the gates stay open. But once you reach the optimum, the gates close, and start letting people on only as fast as they get off. This ensures the traffic is always flowing at a good speed, no matter how many people *want* to use the road at any given time. Now, this doesn't apply directly to the model from the video; because the small roads have travel times proportional to traffic density, all densities are equally optimal for them, and because the large roads have constant travel times, their optimal densities are infinite. But those are unrealistic modelling assumptions.

[@gafoora564]

The whole focus on Paradox is just a cool-set up for Roborace Ad. An intelligent 17 min advertisement. Good job!

[@fauzirahman3285]

This has been mind blowing. The only thing I can think of right now is if a quantum computer can handle that complex road network calculation. Oh, and nice ending theme credit song.

[@Quroxify]

FINALLY.... String Theory that is relevant.. Thanks. :-)

[@acobolew1]

Lol. Supersprings

[@DeclanMBrennan]

Lovely explanation. Cool illustrations; Even cooler demo. Wish I could give you more than one thumbs up.

[@frankribery3362]

Honestly I love how interesting you make your videos...Anybody can watch your videos

[@maggie_sh]

Great explanation, the experiment with the water bottle connected to the spring was really clever!

[@nobiggeridiot]

On top of everything else to be thankful for in your great vids, thanks for the metric love.

[@gaurangagarwal3243]

In top 100 viewers yay! Your animation style is competing Ted ed day by day

[@garret1930]

My solution is just make Braess road a toll road with a ridiculous price.

[@HassanSelim0]

now the cost parameter in the equation wont just be the time taken to drive to the other side, but also the amount of the toll fee. This not only complicates your simulations, but also has side effects of rich people would be more likely to get the two short roads. Now you'll have to think of things like the percentage of people who are rich enough to not mind the toll fee, and if they all take the two quick routes how much would they slow down the poorer people. Your solution is typical capitalism, the country benefits from people's need to go faster, you create a new point of equilibrium, but this new equilibrium might be unfair for some people 😅 Removing the road is a slightly socialist/communist solution in comparison, in that it prevented all people from taking two short roads, each person has to take one short and one long. We all share the average (not-so-good and not-so-bad) timing. I think this area would deserve it's own video, but I don't know if Jade would be interested to cover something a bit political like this.

[@garret1930]

@@HassanSelim0 there are good and bad arguments for both sides of the toll road debate in general. My comment is meant as a lighthearted joke but I can conceive of situations where they make sense, and ones where they don't. If you wish to continue examining it through this paradox then one could argue that the extra revenue from the rich people on that one road could help maintain the entire network and thus actually increase the poor person's experience.

[@ChasmChaos]

@@HassanSelim0 Life is inherently unfair. Without the toll, the situation is biased towards those people who must travel during rush hour (maybe they can't travel earlier since they have kids who must be sent to school or later, since their employer doesn't allow flex work timing). In the absence of a toll, the costs of the road network is obtained via taxes. With a toll system in place, the burden of taxes is reduced on the general populace (who may not use the road) and is shifted on a per-usage basis to the people who do use the toll road.

[@HassanSelim0]

I like these arguments 😁

[@tears_of_asariel3198]

@@HassanSelim0 if only people argued politics this calmly and rationally.. but alas, i think its simply not to be..

[@ghollisjr]

This is a beautiful graphical representation of the Prisoner's Dilemma.

[@clockworkkirlia7475]

I do love that Braess' Monkey. The spring-string demo thing was a great way to explain it too! Also the terrifying yet endearing confrontation of life's catastrophic ineptitudes! :D

[@LieseFury]

i'm here from steve mould, awesome video 😊

[@SanPendro]

Awesome animations.. I immediately had to think of our finance system

[@Sciencedoneright]

Came from Steve Mould's Apology!

[@seany.1216]

Great video, and an interesting take on this phenomenon. However, I don't believe that the spring analogy holds in general, does it? Particularly so if the springs were much stiffer, or the strings longer. For the first case, with stiffer springs, detaching the springs would cause them to contract less, thus reducing the rise in height of the weight. In the latter scenario, the increase in the length of the strings would also minimise the contractive effects of the springs, which could result in an overall drop in height as well. Perhaps this could have been clarified in the video? But then again, maybe similar cases also hold for the road example, as varying speed limits on each road give rise to different outcomes, some of which might also not showcase the paradox in question.

[@dubberj2847]

I love your video's! They are so well explained and thought out. Really awesome!

[@johannbauer2863]

Wow, I really like those animations and graphics! :D

[@x_x3171]

I'm here from Steve Mould's channel.

[@alveolate]

why am i so hyped about roborace after watching this???

[@NONARCS]

Looks slow and boring so not sure, maybe you are a nerd?

[@seiji168]

This reminds me of my commute to work. I have two main routes: Route A and Route B. Route A is a straight motorway that on a good day, gets me to work in 35 mins. Route B is a winding back street that runs parallel to route A that no matter the conditions, gets me to work at a consistent 1 hour. Route A has a catch. On a bad day, (weather, congestion, incidents) which is approx 15-20% chance within a 7 day period causes a delay of 1.5-2 hours.

[@OlivierNovel]

I don't know why the AL-Google or Googlerithm I'm not sold on a name for the recommendation engine took so long to recommend me this channel, but I am glad it finally gave up such a gem. Congratulations and thanks to the author, you're a great teacher and are making the world a better place with your work.

[@richardsilva-spokane3436]

Can Braess’ Paradox be “reverse engineered” to manipulate and enhance traffic and other similar systems/networks?

[@Rygir]

If it's possible to avoid Braess's paradox, shouldn't we be able to find examples of it? If an hive mind is a solution, perhaps we might be able to find ant colony behaviour that if they acted selfishly would have led to Braess's paradox, but because of their coördination, doesn't?

[@taragnor]

The thing is that a hive mind isn't really a true "hive mind" as you'd think in sci-fi. Ant colonies can only act based on what they see from other ants, and while that does lead to a lot of cooperation, it's not the same as a computer set up where cars can instantly send in their positions to a central computer that can optimize them. Ants do have some fascinating properties, but with long range communications, humans can do far better with an optimized system, because unlike the ants we actually know what's going on in the opposite end of the colony and thus can make more informed decisions. With AI systems, it's a lot easier to have them signal each other using conventional networking than going with close sensory signals like ants do.

[@jpe1]

taragnor simple example of ants having a harder time optimizing is in route selection. Say an ant wandering around finds a new food source for the colony. She goes back by following her own chemical trail that she left as she went out foraging, so it won’t be optimized at all, but with each successive ant traveling the path it will over time get more and more optimized, but only slowly, in small increments. In contrast, a central intelligence would create an optimized route to the destination and send it out to everyone immediately. Ants are amazing, but still limited.

[@Rygir]

@@jpe1 there's nothing stopping us from using intelligent traffic lights and signage to use the power of computers and sensors right now to break the paradox. We don't need self driving cars to follow the computed advice. The end result of using self driving cars with AI is that traffic routes are designed on the fly, after all. Conversely we don't know if telepathy or fast long range communication is a prerequisite to avoiding the paradox. Perhaps nature has examples on how to avoid it using different methods altogether.

[@jpe1]

Rygir the “paradox” isn’t really a paradox at all, it’s simply a counterintuitive result that individuals optimizing for their own local “best result” can find a stable equilibrium that is worse than what can be found by changing the parameters of the system. I agree with you that self driving cars aren’t needed for improving traffic flow, just networked intelligent signage and signals.

[@Rygir]

@@jpe1 I know. I watched the video ;)

[@tomaszsasiak2026]

Please, give back doggy brain to his owner :( Don't be so cruel! :)

[@C.I...]

Too late. Dog is cars now.

[@ethanpoole3443]

Where do you think we got KITT from? (Although those who didn’t grow up in the 80s May miss this reference.)

[@gnpahdc]

"...one interesting avenue researchers are exploring..." CLEVER. I see what you did there. 14:09. LOL!

[@Faro1]

Hi Jade, nice job on the video. The issue of network efficiency also has to do with one way streets pointing in the wrong direction, two way streets that should become one way in the right direction and one way streets that should become two way streets. I have developed a scientific model that determines which is which. this is the first tier of analysis that needs to take place to inform more complex concepts.