- This episode is made possible by Roborace,
the first electric racing series
to combine human and machine intelligence.
Hi everyone, Jade here.
Would you like to hear a story?
In 1968, the city of Seoul in South Korea
built a six-lane highway above the Cheonggyecheon River
in an effort to improve traffic flow.
It worked at first,
but as the years passed, more and more cars began to appear
until finally, if one looked over at the highway
from their balcony, all they would see
were cars jammed back-to-back
and the honking of disgruntled drivers.
In 2005, the mayor of Seoul initiated a project
to tear down the highway and revitalize the river.
This was met with much controversy
as if this major road was already jammed up with cars,
removing it would surely make traffic
worse all around the city.
But to everyone's surprise,
when the road was torn down, travel flow improved
in the city of Seoul with travel times
for its citizens actually decreasing.
How?
This video is about a phenomenon called Braess' Paradox.
Discovered by a German mathematician, Dietrich Braess,
as he was working on modeling traffic,
he noticed that contrary to intuition,
adding an extra road to a traffic network
could actually make travel times longer.
Here's how.
Imagine there are two cities, Origin and Destination.
Two roads connect to the cities upper road and a lower road.
There is a point halfway through each road
called halfway point where the road changes slightly.
From the start of upper road
to the halfway point of upper road,
The road is quite narrow and travel time
depends on the number of cars on the road.
The exact time works out to be
the number of cars divided by 100.
For example, if there are 1,000 cars on the road,
it'll take each car 10 minutes
to get from the city of Origin to the halfway point.
There, the road changes and becomes a six-lane highway.
Now it doesn't matter how many cars are on this highway,
it always takes the same amount of time, 45 minutes.
Lower road has the same setup except reversed.
Now let's say there are 4,000 drivers
who want to get from Origin to Destination.
If they all take upper road,
it'll take each driver 4,000 divided by 100 minutes,
which is 40 minutes,
plus the fixed 45 minutes of the highway,
making the total commute time 85 minutes.
This is obviously a silly strategy.
A rational driver has incentive to switch to lower road
because that would only take them 45 minutes
plus one divided by 100 minutes,
which is roughly 45 minutes, a saving of 40 whole minutes.
Other drivers on upper road would
also want to change to lower road.
This pattern would continue until half the drivers
take upper road and half take lower road,
with both roads taking the exact same time of 65 minutes.
This is a natural equilibrium.
A driver on upper road has no incentive
to switch to lower road, as it will only take them longer.
And a driver on lower road has no incentive
to switch to upper road for the same reason.
This situation, when no one has any incentive
to change their behavior, is called the Nash Equilibrium
in game theory.
The key word here is equilibrium,
which can be thought of as another way of saying
when the system is stable,
opposing forces are equally balanced
and the system will not change unless acted upon.
For example, this balancing stick is in equilibrium.
It won't falter unless there's an outside force like wind
or a monkey.
With half the drivers split evenly between roads,
no one has any incentive to move.
So the system will continue going on this way.
Each driver with a total travel time of 65 minutes.
Now let's spice things up.
Let's add a new highway connecting
the halfway points of the two roads.
We'll call it Braess Road.
It's a very wide highway and it takes virtually
no time at all to get from one end to the other.
So for simplicity, we're going to say it takes zero minutes.
Blanche, a regular upper road commuter,
longs for more adventure in life
and decides to try out this new highway.
To her surprise, it only takes her 2,000
divided by 100 minutes, plus 2,001 divided by 100 minutes,
which is roughly 40 minutes, to arrive at Destination.
This is a saving of 25 minutes from her usual route.
More upper road regulars catch onto Blanche's shenanigans
and start to use this new route too.
Soon, the number of drivers
trying this new route reaches 2,500.
So their travel time is 65 minutes,
which is now the same total time
as the original upper road route they all started on.
Meanwhile, the regular lower road drivers
are slowed to 85 minutes, which is a 20-minute increase
before these pesky upper road drivers
decided to invade their turf.
So now they have incentive to change to the new route too.
With everyone taking this new route,
it takes each driver 4,000 divided by 100 minutes,
plus another 4,000 divided by 100 minutes,
80 minutes to drive from Origin to Destination,
a 15-minute increase from their old route.
So, why don't they change back?
Well, no one has any incentive to.
If people made an agreement
to go back to their original routes,
there would always be that annoying driver
who selfishly uses the new Braess Highway
to cut down their own travel time.
Soon, other drivers will see what he's doing
and feel ripped off.
So they'll do it too.
Before we know it, we'll be right back to where we started.
Systems tend to move toward their natural equilibrium.
Just try and stop hot and cold water
from mixing into warm water.
With the introduction of the new road,
the system's equilibrium has changed
and become less efficient.
This is Braess' Paradox,
and when we analyze it,
we see that it isn't really a paradox at all,
but follows from one very simple fact.
People are selfish, what's best for the individual
often isn't what's best for everyone.
This same behavior has been seen in other parts of life too.
One study showed that removing the star player
from a basketball team can actually
improve the team's performance.
Adding extra products to the marketplace
can often lead to worse choices made by the consumers.
The effect has even been seen in medicine,
whether removal of sudden enzymes
can lead to an overall improvement in the metabolism.
The message of this video isn't people are selfish
and stop being so selfish,
the message is actually it's not your fault.
See, this counter-intuitive behavior
isn't just caused by people's decisions.
It's to do with something much deeper
about the nature of natural equilibria.
Just so we don't have to feel bad
about our selfish human nature,
I'm going to show you how Braess' Paradox
affects even a physical non-living system
like this setup we have here,
where I'm pretty sure nothing
is a conscious decision maker capable of being selfish.
Here, we have a water bottle filled with water,
which is acting as a weight.
It's hanging from a bar connected
to two springs and two strings.
Now, the way that the springs and strings are connected
is a bit hard to see and it's very important,
so listen carefully.
Tied to the bar is a regular piece of string
which doesn't stretch or anything fancy like that.
It's then tied to the lower spring,
which is connected to the weight.
Another spring is also tied to the bar
and then tied to the lower string,
which is connected to the weight too.
However, and this part is very important,
the two springs are linked together.
You'll see that both the strings
are actually slack at the moment.
There's no tension pulling on them.
This is because they're both longer
than the springs right now.
And as the springs are linked together,
the strings are kind of just hanging there.
At the moment, our spring-string setup
has a total length of about 795 millimeters
from the bar to the pencil.
Now, if I unlink the springs, what do you think will happen?
Will the weight, A, fall, B, rise, or C, stay the same?
Pause the video now and try to figure it out for yourself.
Go back and listen to the explanation again if you have to.
All right, let's take a look.
(drumroll)
(bottle rattling)
Congratulations to those of you
who chose B, the weight rose.
If you didn't get it, don't worry.
You're not alone.
My intuition tells me that the weight will fall.
The strings were slack, so if we unlink the springs,
the string should stretch to full length,
making the setup longer, and so lowering the weight.
But that's not what happened.
See, when the springs were linked,
they alone were bearing the entire weight
of the water bottle.
There was more tension pulling on them,
making them stretch more.
When they're unlinked, the weight divides equally
between each pair of string and spring link.
So now, each one only bears half the weight of the bottle.
So even though there was a lengthening in the system here,
the reduced weight on the springs caused them to compress
and therefore become shorter, making the total effect
and overall shortening of the system and the weight rising.
If you're into circuits,
you can think of the before setup as being in series
and the after set up as being in parallel.
For clarity, let's compare this set setup
to the traffic scenario so we can see
that it is in fact Braess's Paradox at play.
The length of the strings and springs
or the height of the weight can be thought of
as the travel time of the cars.
It's the cost or the thing that we're trying to reduce.
The weight is analogous to the number of cars on the road.
It can be thought of as the load
that we're trying to handle most efficiently.
The strings are analogous to the 45-minute highways
as their length doesn't change depending on the conditions.
Just as the travel time on the highway didn't change
depending on how many cars were on it.
The springs are analogous to the narrow roads.
As the length of them does depend on the load
just as the narrow roads' travel time
depends on the amount of cars on them.
And finally, the linking of the springs
is analogous to the new Braess Highway.
Just as the removal of the Braess Highway
from the road network changed the equilibrium
of the traffic network to a more efficient one,
so too the unlinking of the springs changed the equilibrium
of the setup to a more efficient one.
This same behavior has been seen
in other physical systems too,
like electrical circuits, water pipes, the internet,
anything to do with heat flow.
Basically anything that can be thought of as a network
can fall victim to Braess' Paradox.
So even though in some cases your selfishness
makes conditions worse for everyone, it's not your fault.
It's a fundamental phenomenon of nature
and you can't be blamed for that.
But seriously, I think it's pretty cool
that equilibrium points can have such strange behavior.
We usually think of them as pretty boring lukewarm areas
where nothing that interesting happens.
Scientists tend to be more fascinated
with behavior that happens at extremes
far away from equilibrium points,
like hurricanes and earthquakes
and galaxy formation and the creation of life.
So, I think it's pretty fascinating
that even areas we think of as mundane
and normal can exhibit such counterintuitive behavior.
It really goes to show that there's no part
of science that isn't interesting.
Fascinating as it may be, in most cases, Braess' Paradox
is an annoying problem that we want to get rid of.
It could be costing billions of dollars
per year in inefficient road networks
and slow internet and low-pressure water pipes.
So ,can we do anything about it?
Well, like most things in life,
if you want to fix something, you first need to identify it.
The first question we should be asking is
is there a way to identify when Braess' Paradox
is slowing down a network?
Well, the thing about networks is that
it's hard to change a part of a network
without affecting the whole thing.
What's more is that it's hard to see
how changing part of the network
will affect the whole thing.
If we remove this piece of road,
it could improve traffic in its local region.
But how do we know it's not making traffic worse over here?
There's a common engineering folklore
that a local improvement may only
transfer the problem somewhere else.
The way the system is connected
and how different parts affect each other isn't obvious.
And the only way we've figured out how to analyze it so far
is by running computer simulations.
Removing a road here, plugging it into a computer
and seeing how it affects the overall traffic.
Then maybe removing a road here
and running the simulation again
to see if it's more efficient, rinse and repeat.
The number of possible variations
is given by two to the power of the number of roads.
So in a small traffic network of about 10 roads,
this would be fine.
There'd be just over 1,000 variations,
so we could just plug them all into a computer simulation
and see which one is the most efficient.
A pretty ordinary computer could
manage this calculation pretty quickly.
However, if we take a city with 100 roads,
things get complicated fast.
Two to the 100th power is this gigantic number.
It would take the fastest computer in existence today
three billion years to run all the possible simulations
and see which one works best.
In reality, there are a lot more
than 100 roads in any major city.
So the only method we've figured out so far
to detect Braess' Paradox isn't practical
with today's computing power.
This sounds like pretty bad news, but not all hope is lost.
Most approaches to solving the paradox so far
have focused on figuring out the best network structure.
But what if instead we focused
on changing the way that the cars interact?
One interesting avenue researchers are exploring
to reduce Braess' Paradox
is the idea of Collective Intelligence.
Basically meaning that instead of each person
acting as an individual, everyone acts together
as a whole to try and reach the optimal state.
This solution may be close to becoming a reality
with the recent progress in self-driving cars.
Self-driving cars would act more like a hive mind,
with each car being electronically connected
to all the others.
They could be controlled by some kind
of central intelligence whose aim
is to optimize traffic flow for the system as a whole,
getting rid of the whole game theoretic
aspect of the problem.
What causes the paradox in the first place
is people acting selfishly
or at least acting as individuals.
With the cars acting as a single mind,
there are no longer individual interests to consider.
So in theory, this should sidestep the paradox altogether.
We're actually beginning to se the first application
of swarm intelligence in autonomous car racing.
At the beginning of May, Roborace,
the world's first AI driverless
electric racing series competition,
saw two of its autonomous cars
complete the world's first self-driving car race
in Monte Blanco.
Their self-driving cars, which they call Robocars,
are able to communicate with each other
through the use of various sensors installed
to maintain awareness of their surroundings.
Car-to-car communication could be used
to find the most efficient route for all cars on a road,
making Braess' Paradox in traffic networks
a problem of the past.
Racing has a history of using competition
to encourage technological development
before rolling these developments out for mass production.
Roborace aims to accelerate the development
of autonomous vehicle technology
through the use of competitions and challenges,
which are part of the Roborace entertainment platform.
The game is simple, the team with the best AI wins.
If you'd like to learn more about what Roborace is doing,
you can see the videos
in their show me how it works playlist,
join their mailing list for updates on upcoming races,
or follow them on Instagram
to check out their latest models.
Links to all of these are in the description.
I think Braess' Paradox can teach us
a lot of important life lessons.
Sometimes less really is more.
Acting selfishly usually makes things worse for everyone,
including yourself.
Your natural state often isn't your most efficient state.
And sometimes the solution you think is best
can have catastrophically terrible consequences.
But I wanna know what you think.
What important life lessons can we learn
from Braess' Paradox?
Let me know your thoughts in the comments below.
(upbeat chiptune music)