The Spring Paradox
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- เผยแพร่เมื่อ 28 ก.ค. 2021
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So it turns out Up and Atom made a video about this a while ago( • Braess's Paradox - Equ... )! Thanks for bringing that to my attention commenters! I've just watched it and it's really good! The whole channel is fantastic actually. Check it out!
This spring paradox is actually an analogy for Braess's Paradox which is about traffic. The surprising behaviour of the springs when the blue rope is cut is just like how journey times can actually go down when you close a major road, even with the same number of journeys being made.
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So it turns out Up and Atom made a video about this a while ago! I've just watched it and it's really good! The whole channel is fantastic actually. Here's her video: th-cam.com/video/cALezV_Fwi0/w-d-xo.html. Sorry for copying your idea, Jade!
You can also discuss this video on REDDIT: stvmld.com/ph999g87
Can you please do a video on the particle physics illustrated by cars in a traffic jam? I've always found the traffic flow parallels so interesting. If anyone can convince people to have a 2-3 car length from the car in front of them you can.
My reaction is that the blue string is NOT under tension -- at least no more than the springs are. So the weight should stay at the same level. It moving up was no more surprising than what you expected.
Thanks, I thought I was going crazy... like: I've got a deja vu of exactly this video, but with a female presenter. Turns out I'm not completely off the rails after all (yet)
@@Blackmark52 The blue string is quite clearly under tension; and as you pointed out, so are the springs... they're all in a line (in series) so they all experience tension in that arrangement due to gravity
Pinned by Steve Mould 25 minutes ago (edited), "So it turns out Up and Atom made a video about this a while ago! I've just watched it and it's really good! The whole channel is fantastic actually. Here's her video: th-cam.com/video/cALezV_Fwi0/w-d-xo.html. Sorry for copying your idea, Jade!"
So, Just as in your analogy, here we have two independently created IDEAS, seemingly connected, but each independently carrying full exposure, and so we the viewers(and subscribers) (Jade's 331,000 and Steve's 1000000 subscribers) both receive the benefit. I just subscribed to Jade's Channel as I expect many others will. I say ALL BENEFIT!
"You're NOT stuck in traffic, you ARE traffic!"
This is one of my favourite sayings
I am become traffic, the destroyer of commutes.
I'm stuck on the road being traffic
"It's not about the size of the traffic, but how you use it".
@@SteveMould the way you explain difficult things is the best way.... U R just awesome... supercalifragilisticexpialidocious..
A "Hectocar" is my favourite unit of measure.
Who knows, maybe rich people use it on regular basis.
As long as their speed is measured in Hectofurlong per Hectofortnight, of course.
Fore US viewers: 1 hectocar = 0.69444... grosscar
Yaa that's clever.
An alternate unit could be the Leno, named for the American comedian with at least 100 cars.
I've definitely done this while playing Cities:Skylines. Sometimes the best way to solve a traffic jam isn't by adding, but subtracting.
You end facing this solution in all recent city builders
It's more of an optical illusion.. some of the endpoints and connections weren't realized until after the cut
that's usually because they despawn
how is it ? how to subtract the traffic ?
Just like real life! Induced demand and chaos from lane switching
Came for physics, stayed for game theory
that's how they get ya. I would know well, as I, too, watched the full video.
Xddddd
Ah yes, the Nash equilibrium
I heard from a Google developer at one point that Google maps already is acting as a hive mind in this sense, recommending routes based on what will improve the time for everyone.
Interesting!
Didn’t waze do that first then get bought by google?
Oh! That explains why Maps sometimes recommends a non-optimal route for me personally. When I noticed, have ignorantly chosen to go the way that was fastest for me.
My thoughts at the time were that Maps was routing me around a traffic jam that had already cleared. In reality, it was routing me around a potential traffic jam that hadn't formed.
I will try to follow our well meaning robot overlords more often.
Oh...so all of the times I find a better route, I actually did not outsmart Google?!
@@hamjudo Hey, this just happened to me very recently on some very short distance travels, say few crossings. Google provided me with a clearly "wrong", longer, more turn route instead of a straight (!) route.
Lesson learned: tiny taxi drivers cause the spring to go up when the blue rope is cut. You learn something new every day!
wow!
Luke skywalker to Kylo ren: Amazing! Every word you just said is wrong.
I'll be dang!
they’re electrons
Yes
This is the opposite of click bait. Dragged me in with something simple yet cool, showed me that and then provided something even more complex and cool. Well done!
I, commonly, choose a slightly longer route to avoid traffic. I see quite a few people doing the same on my rush hour commutes. We don't like sitting in heavy traffic. It's just too stressful
First of all, I do that too. Secondly, your sentence works [better] without the two commas. Or switching the two words (and making it one comma) would also work quite well
Agreed. I will do anything to avoid standing still which makes the journey tedious for me.
@@idontwantahandlethoughno, both of those commas are necessary. That is the correct usage of apposition.
@@idontwantahandlethough both with and without are grammatically correct. They just emphasize different things
I prefer to potentially drive longer in order to gain the benefit of a more reliable eta (by avoiding traffic)
"What'll happen if I cut the blue hope?"
Obviously explode. It's never the blue wire Steve, stay safe
Bro he should've cut the red wire
Cuts blue rope < atmosphere turns to flames
How many batteries are on it?
cut the blue rope? whats next, people are gonna be marrying their dogs????
:D
I would definitely take a longer route if it’s less congested, even if it takes a couple more minutes. It would just “feel” faster & less stressful that being single-file
A driver who want to go fast would take the blue route, but a driver who HATE WAITING like myself would take the longer route, even if I know it is likely to take longer.
3:47 Что за грязные двухцветные тряпки висят на домах?
@@user-ww2lb8di7x, probably the Russia flag
Exactly what I do everyday to college.
@@greymonwar9906 You're also forgetting drivers that care about efficiency. I take the more efficient route, even when it's slower.
There's a related effect called the Downs Thompson paradox. To the effect that the equilibrium speed of road traffic is determined by the average door to door time of the equivalent journey taken by public transport. In other words, if you have a city with a public transport network, speeding up public transport also speeds up the road network. So if you've got a city with congested roads, your best solution might be to speed up the trains, rather than simply widen those roads. (Yes, I'm thinking of you, Sydney).
My experience of NSW Transport planning is that wider and more roads generate more votes than faster trains, another paradix maybe 😂
Never underestimate the power of politics to stuff up transport effectivness.
@@barrieshepherd7694 Never underestimate the banality and shallowness of human minds.. roads get more love because people are more familiar with them and because the roads lobby has had all the resources to promote them. You need to get people to understand that high speed trains are better value - for them personally. Takes time.
That's why it's a problem when buses get stuck in traffic, if the buses are stuck in traffic they will never be faster than cars, leading to longer car times since no one switches to public transport.
@@saumyacow4435better value according to you. To anyone who values privacy, cleanliness, or even basic peace and quiet they do not even remotely offer any better value. Given that's most people, I think the flaw in this logic ought be fairly obvious, but when you decide that your personal value weightings must apply to everyone whether they actually agree with them or not I guess that's easy to miss
@@felixjohnson3874 You should Google 'the tragedy of the commons'
We do have a similar situation in my town. Instead of going through town which is less miles to drive, I take a longer, less traveled outer road north of town and get to work faster than those driving through town. But I know it's not going to last forever.
Years ago there was another route south of town that a few people used to do the same thing to avoid traffic, but as more and more people found out about it, it eventually became as slow as driving through town. It's only a matter of time before the northern route also becomes a traffic hazard.
I know people that still drive on the southside of town but take an outer road that is further south than the previous southern route, and they say that's quicker because it avoids much of the city traffic. And that's about it - our outer roads are just becoming bigger and bigger circles around town.
From an urban planning point of view, main regional roads belong outside of town anyways, as cars shouldn't be going over 30mph inside any city in the first place
"or you could consider that I'm making a video about it so it's probably the counterintuitive answer"
This is why I love this channel
cause you are cringe?
Yea,most of the channel will go ThIs WiiL BLow YoUR MiND
@@citationneeded2093 Why? Seriously, why? And don't answer "it's funny" or "to trigger people". We're not triggered, just wondering.
@@WritersMoment I don’t know why the person is saying that for certain, but I suspect it’s for attention. (And also because this is the internet and whatever you say is basically anonymous)
I’d recommend not responding in the future. Some people feel that they really need the attention, even if it’s negative attention. But that is a very unhealthy way to go about things. So for the sake of your time and this person’s mental health please don’t respond to these sort of comments in the future.
@@sammmmmp1455
Nice paragraph cringelord
If you're trying to look it up, "Bray's" paradox is actually spelled "Braess's" paradox.
So it’s a silent double S? What is the point of letters? May as well throw in a few silent Ns, a silent F and a G that sounds like an L for good measure.
@@orangeapples yes, English Spellings need a reform.
@@AndersJackson Dietrich Braess is German.
At 3:13, with captions on, it says that.
@@AndersJackson That is very obviously not english
I absolutely love this channel. The way you go from springs to routes to a hive mind and self driving cars made my day ❤ thanks!
I saw the thumbnail for this video yesterday and added it to my watch list.
I then started thinking about it in bed a few hours later, and now when I read the comments here it is pretty intriguing that the same analogy that I came up with after having it kept me awake for a while, traffic and a bridge...
Now I want to see a working system representing this in spintronics, a video from Steve I did watch yesterday before bed :)
A hectocar sounds like a really uninspired late generation Pokemon name 😅 Great video, as I highway engineer I am ashamed to say I was completely unaware of this law!
New method to try in Mini Motorways, maybe?
I'm thinking about the game and how I play it "the wrong way"... Wait for new gameplay videos with this knowledge!
oh, hi Matt
Hi Matt, fellow engineer here:) hopefully you use this in mini motor ways lol
Good to see the engineer doing engineering things
"I'm making a video about it, so it's probably the counterintuitive answer."
Crap, he's onto me. No one tell my high school teachers (and some college professors).
he's making a video about it, holy fuck that's an easy 30 grand for the already rich youtuber fuck.
@@tommytomthms5 wut?
@@tommytomthms5 what do you snort? You need to stop asap.
@@ItsIdaho With the quality he's got I'm sure he can afford it.
It's an interesting concept in relation to city planning - maybe constructing short, fast routes, but reserving them for emergency vehicles only could improve travel times where it matters most.
some places do this, they cut off roads and streets to most cars with the exception of emergency and perhaps delivery vehicles. people end up walking and cycling more through these areas and reduce the overall traffic time (the same effect of the road being so wide that it never gets congested, except its less cars instead of a wider road)
Even better when you reduce the volume of traffic to begin with by providing alternative methods of transportation, like trams or trains.
If you have enough emergencies for that to be worth it, the roads aint your fuckin issue
@@felixjohnson3874 I don't think there should be a prerequisite for the number of emergency vehicles/emergencies; it should just be there, readily available, as an option.
@@regulate.artificer_g23.mdctlsk Give 80% of your annual income over to the government to pay for it then say that sentence again
I deal with this exact traffic paradox daily and can say in practice it literally does play out like this
Something to note to help explain this intuitively, glancing at the initial setup makes your brain equate the red rope with the bottom spring and the green with the top since they are next to each other respectively. However, when you look, the force pulling on the red rope is actually the top spring and the force pulling on the green rope (when the blue is cut, of course). So, the springs can pull the ropes to overlap which helps make the weight rising make sense
Nice!
Yupppzz!
put another way, the springs go from being in series to parallel, where they see 1/2 the weight, and the total stretch is 1/4 since the "stretch" isn't in series anymore, which is significantly more difference than the slop in the strings. edit, yup that is what the video says :)
whats funny - i couldnt figure it out from looking at the configuration, but as soon as he cut it and i saw the result i immediatly exclaimed "its going from serial to parallel!" XD
Thank you budd. You saved my 9 minutes and 30 seconds.
The remaining blue road bit could be used as a public-transit-only road. Having a transit option that is able to take the shortest amount of time (4+1+4) sees more people taking the bus (or a similar option), which frees up more cars to drive on the longer routes (11+4), boosting people throughput through the road system.
Yeah, and those people who live on the houses either side can still walk or cycle across for short journeys. It's a low-tech solution available today, whereas self-driving cars (and all the legal and sociological questions that will need resolving) are potentially still decades away.
Or just reduce the speed limit or make it a toll road.
Yeah public use is a good idea and also emergency vehicles too me thinks, ambulance, police and fire brigade.
Where I live there are a few one-lane roads for buses only (with car traps so private vehicles can't use them), though I don't know if this is the reason for them. The ones I know of are really short, though.
Plus, roads don't maintain a jam-less state on their own! given a high enough population, the number of people using the roads will increase until it's more convenient for people to take public transportation. Making the public transportation better increases the amount of people who don't need to use cars, reducing the number of cars stressing the system and making things even faster for those who do need to use cars.
This was really interesting and enlightening! I didn't think that this would end up with a traffic mgmt equivalent!!! Great video!!!
Wow. That was mind-blowing for sure. _And_ it certainly explains a gazillion things as well. Thanks for doing the video!
A physical analogy for the Nash Equilibrium! The reason that locally optimal systems are not necessarily globally optimal (see also: climate change and many other social problems).
@@2000jago People seem to like his comment. You must go to interesting parties...
Cool. How does Nash Equilibrium explain how solutions are unable to scale? Is it because the personal incentive to break the law for profit on large scales?
@@tonyhinderman Wasn't he saying that optimized local solutions may not exactly mirror the overall global optimized solutions, even while contributing to the global optimization?
@@hattielankford4775 Yes but I'm asking why, it's clear that they don't mirror at scale, but if applied why would local solutions break down?
@@tonyhinderman One silly example: they discover the globally optimized system consists of 32% solar, 33% wind, and 35% duck, but there are no ducks locally.
As someone who lives in a heavily traffic city, I can honestly say that I rather take the longer timed route but be driving without any traffic than take the quicker route but be stuck in bumper to bumper traffic!
I know that's not what this video is about, but since he brought it up, I wanted to chime in my personal preference.
Don't worry, anyone who has ever owned a car with a manual transmission understands completely. I would get off a stop-and-go freeway in favor of even slower surface streets, just because the stop-and-go cycles were longer and I wasn't constantly clutching and shifting. Rally cars can be shitty daily drivers. :)
As someone who drives a manual transmission, my left foot agrees
@@mal2ksc my solution to the problem of a manual transmission in stop-n-go is to make a game of it: how much more smoothly can I drive than the person in front of me? Managing a constant speed is, IMHO, easier with a manual than an automatic.
@@benjaminshropshire2900 The problem I've found when trying to do that is twofold: 1, leaving the appropriate gap to smooth things out either has cars constantly jumping in to fill that gap, or annoys the people behind me (even though we're not actually losing any time), and 2, sometimes the traffic is slow enough that the engine lugs even in first (or the clutch needs to be slipped for far longer than is good for it).
I agree. Similarly, I'd usually rather wait extra time sitting or standing somewhere nearby than spend a shorter overall time waiting in a line.
Just Brilliant! I really am impressed by the extension of the 'rope and spring' puzzle to traffic patterns. Thanks for an informative video and impressive presentation.👍👍
Steve you are a truly great teacher 👏👏👏👏 You make the world a smarter place!
Fascinating! You can also explore the concept of resistance in traffic, via the introduction of nominal congestion charges. By adding a cost to the use of certain roads, you're essentially adding a resistor to a circuit. You're making the route less attractive without removing it, and thus changing the dynamics of the system.
Interesting!
You can also add traffic-calming measures like converting lanes into bike lanes, sidewalks, or medians, reducing speed limits, replacing lights with stop signs or 2-way stops with all-way stops, adding speed bumps or raised intersections, etc. By making a residential through-street less enticing to drivers, you can end up with a situation similar to the one he describes the "hive mind" choosing (a superrational choice).
At that point it's hard to fit to these simple physical models, since it relies on different drivers valuing expence vs time differently.
Each driver had a different "cost function" to use a machine-learning term that values expence and time differently.
Yea that's what I was thinking. By charging prices for the silver+blue+silver route,those that really need to make the quick trip are able to do it. Additionally automatically increasing the price in proportion to the amount of vehicles using the route will in effect increase the "resistance" in the circuit. Of course the price will be premium but "time is money". This will also make it better for the buildings that only use the blue road.
we do the more socially just thing already, its speed limits and other traffic rules for residents 🙄
A sufficient high price such that it would have an effect could actually be problematic because it ties the "privilege" of using the road to money which is unbound.
However enforcing of the traffic rules does need to incur non-monetary penalties eventually to be different. (in Germany that's the temporary or permanent los of your otherwise indefinite drivers license)
"No driver wold take the longer route" You underestimate my desire to maintain velocity vs my desire to be efficient.
Also if you are risk adverse you will take the route that will never be obstructed by an accident thereby causing you to take longer than the longer route.
It's okay to take longer as long as it doesn't _feel_ like you're taking longer.
if we go faster the longer route is shorter!
I will gladly take a 50 minute low traffic route over a 40 minute stop-and-go traffic route almost any day of the week. After work, traffic is much more of a hassle than an extra ten minutes.
I was thinking the same thing. It's the psychological effect of "at least I'm moving".
Excellent demonstration, explanation, and extension to other domains. Triple word score!
To solve this problem you need to count traffic. There is a point cutting the blue route becomes fastest. So if traffic is below that point the route can be open, if it is above it then it closes.
(to solve the House to House route, you can think of a 'blue route' that is really slow. If the main route is 50 km/h and the alternative is 10km/h with obstacles, probably no one will take the shorter route even if it is (slightly) faster, unless you specifically need that route to go from house to house)
this is just really neat, like the kinda thing that interests me the most. A simple and self-evident thing that's still counterintuitive but ends in an "aha" moment
7:58 In that "Utopia" The car would say: I'm sorry Dave, I'm afraid I can't do that...
"Open the garage door, Hal."
Just where do you think you're going, Dave?
"Stop calling me Dave! I told you my name is Allan!"
I'm afraid, Dave.
time for your regurarly scheduled amazon advertisement dave
That's genious. Very well explained and interesting.
When you expressed your "intention" to cut the blue rope, then described the blue rope as being "in tension," it broke my brain for a second.
I feel like I've unlocked a new level of consciousness that I can't even begin to put into words
lol
Word Play is Awesome!
Sometimes it takes a moment to catch it. Other times, it just clicks and I volley another back at 'em. 😂
Super interesting! I was expecting a “eh” video and now I’m showing this to my collegues (I’m a civil engineer and didn’t know this). Truly came looking for copper and found gold
Never look for copper on Steve moulds channel, you'll be hard pressed to spot any.
“Unfortunately, humans don’t form hive minds.”
I’m going to start quoting this when I get annoyed by people.
However, hive minds do form humans
Unfortunately we humans do form hive-minds, they're called reddit, twitter, 4chan, and many others.
Down side of hive minds: no privacy, no freedom of speech, no freedom (period), worst tribal warfare in mankind's history, etc.
Up side of hive minds: SAVED 6 MINUTES ON MY COMMUTE!!! TOTALLY WORTH IT!
Actually in this video's example, they save only 2 minutes. 🤦
are you sure about that? *stares at reddit*
I finally found it! been looking for this for days
Awesome video, that was genuinely interesting and you present it so well
"Unfortunately, humans don't form hive minds." Is my favorite lesson of the day
It's never going to happen, is it?
@@AndreLuisPorto it's for the best. We're not a drone species.
Despite some people seemingly being part of an hive mind, but that's beside the point.
It's not unfortunate at all. Individual thought is a good thing.
What's a hive mind?
Thats not unfortunate thats indiviualty if you dont like it move to a bee hive
Well I'm a jee aspirant studying fr jee and this exact same question was given in our module just with values and it's truly fascinating thinking abt how physics works
Watched this video about a year ago and I didn’t fully understand it. Now that I’ve taken 2 electronics classes, and a few other engineering classes, this makes perfect sense and is quite fascinating…
really? I was a psych major back in college & I found this video's material to fairly "high school level". It's a well done video for sure, but what technical information did your college enlighten you with that made this video more understandable? I struggle to find anything in here that confusing.
I'd love to see this in slow motion. In the frame after you cut the string, the weight is already moving up, but there is a finite signal travel speed along the springs and strings, so it seems possible that (with the right configuration) the weight might briefly be in free fall before the tension from the top spring "catches up" and pulls the weight upwards. In your setup it seems like the top spring might always bring the red string taught before the lack of tension can propogate down the bottom spring to the weight, but adding additional slack should fix that.
Edit: my explanation is probably wrong, I forgot about the "slinky effect" that would probably see the weight be stationary.
Yeah the solution and state of the spring is time dependent after the cut. The springs very quickly makes the strings taut. Until the red and green strings are taut the weight should be in freefall. Once the strings are taut the momentum of the springs will work in unison to "bounce" the weight upwards, then it will jiggle down and up until it reaches steady state at the higher position per the video.
I believe that's not quite the case, you'll rather see the weight hanging stationary. The reason why the mass flies up is because you've just doubled the spring constant, and so the force has been doubled. I can't think of a good physical explanation for this though
@@luke8324 I believe there's an important caveat there. The bottom spring is under tension and the bottom end of it doesn't "know" it's been dropped until the compression wave from the top of the spring reaches it. So you've essentially got two competeting effects racing each other to reach the weight.
@@jadewhite766 I think Veritassium did a slow-mo analysis of dropping an extended slinky from the top.
Yes, had the lengths of the red and green strings been long enough, the weight would've remained stationary immediately after cutting the blue string and then may have moved up or down depending on whether the strings become taught first or the tension in the spring just above the weight becomes zero.
I love this information… I just told my friend “I’m not sure why I’ll ever need this knowledge on traffic paradox but now I have it!” Lol although it does make me realize that I’ve been having a valid argument with my dad about traffic being a factor in which route we should take regardless of how the freakin crow flies! Lol
Especially with rising gas prices now, a longer route with less traffic may burn less fuel than a shorter one with more traffic that requires frequent breaking and accelerating.
@@thomasbrand2650 This was always true, just most people never think about how much it costs them to drive. They just think about time..
This is a really great demonstration of the difference between things in series vs. parallel. IT would directly apply to any load, i.e. resistance in a circuit.
This is absolutely fascinating! The only time I learned something this counterintuitive was when someone explained to me how sailing ships can sail *into* the wind using tacking.
This perfectly describes Electric Resistors as well! I always had trouble visualizing series and parallel resistors in a circuit but this makes perfect sense. Thank you!
Electron flow is nothing like this example. Electrons always use any available way even if the resistance in one is way more than the others. Here the ropes have no tention at all when the springs are beeing used
@@InstaLabSparti Its reasonable to compare the two, since more electricity would flow through a path of little resistance compared to one of high resistance. Having two resistors of the same value in series would cause a higher equivalent resistance than the same resistors in parallel, which i think is enough to justify a comparison.
It’s actually better to think of it inversely. Springs in parallel are similar to resistors in series and spring in series are similar to resistors in parallel.
You can think of the voltage across the resistors to be comparable to the tension force in the spring. And the current is similar to the speed at which the spring moves (but that’s for dynamic systems and more complicated, here we’re looking at the system at rest).
Say you have two resistors of equal value in series across a 10V source. Each will experience a 5V drop across each one.
Now take two springs of equal value and attach them to the ceiling in series and hang a 10lb weight from them. The top spring has 10lbs of force hanging from it, and the bottom spring also has 10lbs hanging from it. They’re both experiencing 10lbs of force.
But now put those springs in parallel and they’re going to equally share the weight, thus each one is experiencing only 5lbs of force.
Hopefully that makes sense. If you wanna learn more look up Bond Graph theory.
@@Shancyyy That makes perfect sense, cant believe i didnt think of that. Thanks for this!
This concept describes most of the forces in physics
One thing was overlooked here:
Adding weight (or traffic) will eventually stretch the springs (or extend the narrow road travel time) to equal the red and green in length. The red and green will bear all excess weight (or cars) and the blue will become merely a conduit for the excess. At equilibrium, the blue will have no weight load (or traffic load).
He explained that with the movable blue string seeing them equal out.
@Edwin Thomas make sense, thank you
@Edwin Thomas That's already illustrated in the road paradox. When the number of car is 7 or less, the blue route will have 15 minutes travel time (the same as the red/green route). *THAT* is the point where the weight switches from the blue route to the red/green route a.k.a. the moment the strings become taut. Any more car/weight after that point and the string/road will automatically switch the load/traffic to the red/green strings/roads.
The red/green strings/roads will get more weight/car until their length/traffic starts being more than the blue route/string and at that point new weight/cars will go through the blue string/route once again. In the road version this traffic balancing between red and green and blue route doesn't have a hard limit, so the cars will distribute evenly forever. In the string version the length balancing has a hard limit, which is the red and green string's elasticity. Once their elasticity is reached, the red/green string can't get longer than the blue string, so the weight can't distribute evenly forever. They can only get more taut until their tensile strength limit is reached (all the while the blue string doesn't bear any weight), snap, and the weight will all return to the blue string.
@Edwin Thomas
I think you also left out one aspect there. The springs will not just stretch until they're as long as red and green, but rather as long as red, green, and blue combined.
Transferred to the traffic illustration, additional cars will then start to take the blue road again, but in the opposite direction (route: green>blue>red).
The blue road should only be closed in a specific range of traffic volume. On low as well as high volume, it will decrease travel time.
The length of the rope defines minimum trip time at low traffic volume (with the springs assumed at a length of zero).
The length of red / green determines the lower limit when blue is locked.
The sum of red, blue and green determines the upper limit with blue being open.
Whereas with blue being closed, there is no upper limit.
Beautiful explanation of the traffic analogy.
This would make an excellent visual explanation of how resistors work, too!
"Robert, it goes down."
"It don't. It don't go down."
"Robert, _it goes down."_
"No, it don't."
"IT DO GO DOWN."
"OHH"
It does go down until the ropes have load on them.
yeah, I don't get where the paradox is. It would be if it went up without the red and green ropes.
@@vanoscrap6296 not a paradox, just a local maximum
@@vanoscrap6296 its not an actual paradox, its only a paradox in the sense that it acts antithetical to human intuition.
The road example is a demonstration of a solution to the classical tragedy of the commons in game theory. Great video, thank you very much, Steve!
This was awesome, a little physics then surprise detour into traffic, game theory and defection problems.
So glad I found your channel, your videos are going to make their way into my daughter's 'homework'.
You could allow the blue road for only public transportation and emergency services.
Also maybe a subset of the blue road can be used by local residents only traveling inside it, with no access to the grey road outside.
In real life is you have a good, ambitious traffic engineer, not the most common kind who does not care, he'll try to make blue road undesirable for long rang traffic, usually by putting limits, eg. speed limit, weight limits and such. Then nine times out of ten, local politicians will overrule this. Sometimes it can cost an engineer his job. That's why most of them choose not to care.
I prefer the human hivemind idea
You can't make a road only for public transportation if my tax dollars go towards its upkeep. For that matter, the shipping industry can have all of its own delivery highway system too and keep the big trucks off mass transit lanes. I mean hey since we are pretending anyway we might as well dream big.
@@dominodoggy1 what you got there are dedicated freight rail tracks.
@@magic_cfw haha wouldn't that be a lovely invention! EVERYTHING needs to be rail except last mile. Call me crazy.
7:25 Actually, in The Netherlands we have this. Certain faster roads are blocked for normal traffic. Only busses, emergency vehicles, and permit holders (people living in the vicinity of the road) can use the road which is enforced using cameras that function like speed trap cameras.
Classic Netherlands.
"If only humans understood that working cooperatively in this scenario would improve the whole system. Alas, it will never happen"
Netherlands: *coughs*
@@seann4678 well in America it'd probably be seen as "racist" or some other "ism" to not allow X or Y person to use that road whenever they want lol. So I don't see that happening here anytime soon.
We have many roads that could be used to cut down travel time, but have sign Not for motor vehicles, and text sign "Driving on the plot allowed". But if people started to use it as shortcut, people living there could call police about that, and nobody wants to get a ticket
It exists in the UK too, roads meant only for buses. It causes an issue sometimes with sat nav that thinks the road is accessible but isn't.
@@RamAurelius which is incredibly ironic because poor non-white neighbourhoods are commonly bulldozed to make space for roads in america
As I guessed the spring-theory right at the beginning, I thought there isn’t more interesting things to come up. But I was so wrong! Great video and the comparison to traffic was a real mind blower for me. Thank you!
Very interesting! Learned a lot from this 👍🏻
The actual solution in this case specifically, as well as many similar real world cases is to close the road and build a through footpath. It's OK to have routes that are faster to walk or cycle than drive, in fact it's one of the best things you can do to improve traffic.
It's reasonable to ask people to take a 3 minute walk rather than a 1 minute drive.
Or just put a toll on the blue road and give the locals a free pass. The few who are willing to pay to get from A to B won't change the big picture too much if the toll is high enough.
@@pRahvi0 I think the toll should go on the grey roads. Those are the ones where driving on them generates a negative externality for other drivers.
@@OscarCunningham
You are wrong. Those Grey roads are the roads that need to be used to keep things efficient. You need to disincentivize the blue road only. The goal would be to encourage use of the parallel roads and not the blue, so the toll goes on the blue only. The toll would be such that it’s cost would be less than that of a round trip if the road were removed and you just had to get across the blue road, but high enough to dissuade normal use.
@@OscarCunningham That doesn’t make sense. EVERYONE is driving on a grey road no matter their route. That would mean that EVERYONE would need to pay a toll.
@@rebchizelbeak5392 On second thoughts they're actually equivalent solutions. Everyone has to travel on at least one grey road. And they travel on the blue road if and only if they travel on both grey roads. So the two tolling schemes are the same, except that mine charges a fixed amount extra to everyone.
I still think that a toll on the grey roads is the best way to think about it though, since it's the grey roads where travelling on them slows down other drivers. I expect that on more complicated networks that kind of toll would still give the correct solution.
My guess: at the moment the weight is suspended by one line with two springs so each spring is suspending the entire weight with no assistance from the other spring, with the center line cut it will be held by two lines with one spring each. So effectively halving the weight on each spring so it will move up due to the springs contracting even though the strings will no longer be slack.
Tension downward will become zero instantaneously . But spring force still acts upwards, so both spring will compress by moving up
The upper spring is holding the weight and the other spring as well (just a detail)
@@Ryuk-apples if they are of equal length then yes. Mg/2 each
@@harshlodha2056 the upper spring is holding the weight of the blue line, the second spring and the metal weight.
The length of both springs has no effect on what I said.
Please spare me the trouble of coming back to explain my statement further
@@Ryuk-apples I didn't consider the extra weight on the top spring. I guess the effect of this would be that when the centre line is cut the springs contract slightly differently, I will have to rewatch to see if I can notice what effect this has on the movement of the weight, I'm going to guess it is a factor in the weight wobbling sideways slightly and not just directly up and down.
This is one of my favorites ive seen so far.
I’m fairly certain the top spring is shooting up faster than the weight is able to start dropping. If the spring was stronger and had very little load on it then we would likely see a drop.
Make the blue road a cycle route. Happy days!
Yes, but maybe allow cars but drastically lower the speed limit, so people who only have to travel that short bit can take it, but it's slower than red/green is for the on going traffic
let's call this the "Dutch solution " :-)
or more helpfully a bus-only route. which will mean fewer people drive, speeding it up for everyone. .. i mean it's a massive highway, we can do both.
@@mralistair737 yes, there should be sufficient space for both a bus route *and* a "bicycle highway" .... and maybe additionally an electric tram (or a suspended monorail above it, like the "Schwebebahn" in Wuppertal (Germany) ) ... :-)
This is a great analogy, could be applied to electrical, mechanical/ structural, and even fluid movement to explain the series/ parallel relationship.
I love this channel. I learn so much to teach the kids at the library.
Keep it up! It's lovely to see people teaching others.
this hits especially hard when one of your main congested commuter roads every morning is called “the Blue Route” (476 in PA)
I think there's an allegory for our reliance on Amazon and big box stores/super markets over regular stores. Like the number of choices at Walmart are much higher than any other individual store, making them more convenient for shopping, but since they kill off all the smaller, mores specialized stores the total number and quality of choices available in the town are much lower.
Not really the same as you are only getting one of each of those choices. Like if my local store closed and that’s where I got my milk, I’d just get milk from the super store. You can say the number of choices decreases but I only wanted on milk regardless of who sells me it.
@@MysteriousStranger50 OK, but you're thinking of a commodity. The original comment's point was probably more to the line of clothes, tools, furniture, etc., for which choice is relatively more important.
The illusion of choice
The “Blue Route” analogy means so much more for anyone who lives in Delco, PA.
explain
Blue ruote is what locals call the one highway there. Can't remember which one tho. Also Delco is short for Delaware county jsyk
@@benf262 476
@@NotRJPrince You mean the turnpike?
was gonna say something like this but i knew someone else had to already lmao
This has become an annual watch for me... whoever I forget the reasoning for the spring to go up, I check it again.
Very nice video. You get a thumbs up from me for getting ro the point and not making the video 10 minutes longer than it needed to be
1:00 You should make a video where are the puzzle solutions are completely intuitive, which will make us guess wrong every time :)
happened in my country, just exactly as you explained it here. years of having one congested route then gov decides to put concretes jerseys (cut the route) and reflow the traffic through another exits to main streets which were parallel to each others. now there is no more heavy traffic after years of being stuck streets.
I'm going to bet people complained, a lot
I think my head just exploded. love me some paradoxes!
Now when I tell my friends "I know a shortcut" and wander for about an hour, I will refer to this paradox)
Steve, I just want to take a minute and thank you. You videos inspire me, constantly, to investigate the world around me and to continue the pursuit of knowledge. Thanks, and great video!
"Broad and easy is the blue road that leads to destruction."
Best & cleverest comment I've seen in a week.
Props, and you have your first subscriber, Erik D.
Made sense that I rewatched twice in a bit of few minutes to see the two strings and the parallel string. I don’t want to say it because I already have the answer in my head
These videos actually makes me doubt my paradigms and helps me become more openminded.
I appreciate that, got my sub.
7:17 in a urban planning setting couldn't the blue road be a footpath/bicycle path? It wont let cars through, optimizing the system, whist also encouraging people who live around the area to walk/cycle there.
Oooh! I love this.
I was picturing this as 2 major Cities and a small town inbetween. They put in a larger section of Highway to alleviate cars going through the town during rush hour.
Yup, and this is exactly how the netherlands does it.
Or a dedicated bus route!
If it was a bike path it would defeat the entire purpose. The model is meant to illustrate how different routes changes efficiency when transporting a variable number of *cars,* so of course you'd have to compare *cars to cars* to actually have the efficiency comparison meaningful.
The point is, when two equal human being is going from the same place to the same destination, their greed will undo each other. They need to be deprived of the best route altogether for them to ever benefit. If you're having problem with the best route going to waste, you can make it an exclusive route for buses or ambulances. That way those vehicles that actually *need* the best route can still benefit without other human's greed undermining them.
I am impressed with myself for keeping up with this video. I didn’t have to play it back once. 😂
what did you do with the almost 10 minutes of life time?
Mommy is proud
@@ypey1 Thank you for your insightful response.
@@CM-mo7mv I ate some Mac and cheese
I'm a little suspicious. I mean, there's no way a science video can be _this_ easy to understand, right?
My favorite video of this channel so far.
The traffic puzzle in interesting. I've often wondered why traffic on busy roads often comes to a complete stop due to a restriction, such as a lane closure, which does not require traffic to stop, but only slow down a little to make space for merging traffic.
Self driving networked cars is a tech solution to something you can already solve by actually making a livable city with public transport and pedestrian/cycle infrastructure. Glad you added the "that'll never work" caveat to the end of that little tidbit.
Great ideas to implement in their own right. But the same paradox applies to them as well.
You are wrong. Self-driving networked cars is a tech solution that doesn't actually solve the problem, because it fails to address the thing that makes the problem in the first place - cars. Cars are the least space and energy efficient way to transport stuff. That's the actual problem.
Yeah exactly, like a hivemind of cars is just public transport with extra steps
The best solution would be to get rid of all the long roads and replace them with trains, much more efficient
Thanos: "This is too complicated, I just cut the population in half."
That was so much more interesting than I expected 🤯
I saw another version of this in electrostatics. The charges (electrons) in a charged body made of a conducting material always reside on the surface alone. This is because the equilibrium state is the state at which every little charge is at an equal distance from its neighbour. This can't happen if you occupy the interior portion of the material, as the radius of interior and exterior portions are different. You can try doing it by fitting 1D points on a 2D paper, and you'll not be able to find any arrangement that satisfies the equidistance criteria if you place points on the interior portion of the paper. Yet, the average distance between two charges will increase (which is what repulsion desires) if they somehow agree to occupy the interior portions also. But all the charges act as individuals and will not get satisfied by anything less than equality throughout the body
😂 I love how he just gave up on the hope for humanity at the end
We never had it.
If we would think like a hive mind we would all now be on the field farming potatoes. Having a margin of error for individuals is pushing the limits and stress testing reality to find better solutions like this blue line removal.
This is where "local traffic only" roads come into play, and where navigation services need to actually avoid them properly.
Nav systems are a special kind of hell. Yes, they definitely help, but they make things worse by helping. Plus the more you use one, the more dependent you get on having that little moving map.
@@dominodoggy1 it's good to use them when going somewhere new, it's also good to look at the general way it's taking you, and if you know a way with fewer back roads to get to a particular arterial road, to go that way instead. Once you've gone somewhere a few times, you shouldn't need it any more, and once you've been enough places you shouldn't need it for as many things
@@Cheesus-Sliced I use it almost everywhere I go, but not for the actual directions. I do it for traffic.
In Austria they forbid some local routes for long route travelling tourists. The Nav-Programmer after a short time adopted that in their programs. So you can do so but should communicate to Nav-Providers in advance so they can put it in their software. Was a total chaos for some weeks.
Bit there's always going to be an option to turn off avoid local roads because, well, there are certain users that would want that. And the propensity for humans to be a dick is surely going to override the benefit.
I guessed it based off the thumbnail before I clicked the vid.
Not sure why, but I did. Nailed it.
The traffic optimization does (or can) happen to some extent already. It's why I always use Google Maps even when I know the route-Google gets a constant stream of traffic patterns via cell data, so it'll show me if a road is congested and send me a different way. If we all used a navigation app while driving our regular routes we'd all be seeing in real time whether we can take silver or if we should take red or green instead.
Thank you for brining back realism back again at the end.
I've seen both versions of this paradox but never put together as an analogy to each other. This was a fantastic presentation!
this reminds me of a situation- finding a good empty hang-out spot and going there frequently, and later finding out that other people also started going there and now the spot isnt empty anymore
A brilliant demonstration!
Thinking about the forces in this problem reminded me of the Hyatt Regency walkway collapse, and how a small change in the design can completely change how the forces are applied.
In the physical spring example, it also depends on the length of the red and green rope in relation to the spring constants and weight applied. For example if the red and green rope were extended to double their initial length while all other items in the setup remained the same, the weight would lower once the blue rope is cut.
The same applies for the cars, if the roads are too long the time wouldn't reduce, even if we close the blue one. It will actually increase.
I mean I havent watched the video. But ai dont think the length would change. The weight hasent changed so why woukd anything else.
@@EvelynnTheBorderCollie let’s put it this way. If the blue string is already cut and then you extend the red and green strings, will the weight go down? Of course it will.
As an architect, I will remember that, thank you!
This perfectly explains why self-checkout provides a superior customer experience, and why opening another belted lane actually increases wait times.