Kind: captions
Language: en
In 1999, the German newspaper Dzite ran
an experiment. They asked a falafel
salesman and former theater director
Salabani who in the world he would most
like to be connected to. He chose his
favorite actor, Marlon Brando. So, the
reporters then searched for a chain of
friends, family, or acquaintances,
people who knew each other on a
first-name basis who could connect
Bengali to Brando. As it happens,
Bengali had a friend in California. This
friend worked alongside the boyfriend of
a woman who was the sorority sister of
the daughter of the producer of the film
Don Juan Demarco starring Marlon Brando.
So in total it took just six steps, six
degrees of separation. And the idea is
that this is not a unique example that
you could connect any two people on the
planet in six steps or less. But is it
really true? And if it is, how does it
affect our lives? How is this possible
in a world of now 8 billion people that
we could be that close, just six hops or
less? Does that affect how diseases
spread, how information travels? Our
math showed the question is not why is
the world small, it's really how could
it be otherwise. But then I got a call
from the FBI.
We are making the world smaller all the
time. Like it's supposed to be good and
yet it does expose you to toxicity and
malevolence that you might have been
shielded from. You look at the net
effect of it and it's actually been
pretty negative by a lot of measures.
People have suffered.
>> It's not only dangerous in terms of
disease propagation, but anything
malevolent now has conduits that it
didn't used to have.
>> If we were all connected to everyone
else on the planet completely at random,
then it would be almost a mathematical
certainty that any two of us would be
connected through fewer than six steps.
Let's suppose I have my 100 friends out
of 8 billion people. Each of them knows
100 people. So two steps away from me is
going to encompass 100 * 100 people.
That's already 10 4th people. And so if
you do 100 to the 5th power, that's 10
the 10th. And that's more people than
there are on Earth. So that notice that
number is five. I said to the fifth
power. That's the ballpark reason why 6°
of separation is true.
>> But the shocking thing about this is the
calculation you've just outlined is
about having a 100 friends at random out
of 10 billion and they're all over the
world. But we know that in the real
world that's nowhere near what the
distribution of friends are like.
>> Absolutely true. So this this really
crude calculation I did is is absurd for
the reason that you said the world is
very far from random. The truth is
people naturally cluster geographically.
Most of the people you know live close
to you and they also have a higher
probability of knowing each other. If
you calculate the fraction of people you
know who also know each other, that is a
measure of the clustering in the
network. So let's try a model with a
high degree of clustering.
Imagine all 8 billion people on Earth
are arranged into a circle and say each
person knows the 100 people closest to
them. So 50 to the left and 50 to the
right. Well, in this case, the furthest
person you can connect to is just 50
people away. So if you wanted to connect
to someone on the other side of the
planet through a chain of people who
know each other, well, it would take 80
million steps. And to connect any two
people would take on average 40 million
steps. Even just getting 10% of the way
there would take 8 million steps. And
six steps would get you well here.
This is the paradox of six degrees of
separation. We know that we live in
these local clusters of friends and
acquaintances, but we also seem to be
able to connect anyone anywhere in just
six steps. 10 years ago, I did my own
experiment on this and I found that the
average Veritassium viewer was only 2.7°
of separation from me. In social
science, this is known as the small
world problem. named after the
phenomenon where you're say on holiday
somewhere and you bump into a stranger
who somehow knows your best friend and
you say wow it's such a small world
in the mid 1990s two mathematicians
Duncan Watts and Steve Strogatz set out
to solve this small world problem
>> Duncan really sort of had very farseeing
imagination at that point
>> we had computers that allowed us to
simulate environments that were too
complicated for for math to work.
>> Up until then, physicists had studied
networks that were ordered and regular
like crystal latises. And mathematicians
like Paul Erdosh had done lots of work
on totally random networks. But no one
had studied what happens in between.
>> There's must be some enormous middle
ground. And that's what Duncan and I
felt like we're starting to explore.
To study this middle ground, Watson
Strogats imagined a simple regular
network of people or nodes dotted around
a circle, each connected to a few of
their nearest neighbors. And so we had
this idea. We're going to start with the
physicist end of regular. And now we're
going to turn the randomness knob to
make it more and more random through
these random shortcuts.
>> We all have some experience with
shortcuts.
>> I belong to this club called the
Internet Chess Club. I got to be very
friendly with a guy in Holland. That
connection makes the world small because
now even though my friends don't realize
it, they're only one step away from a
guy in Holland. And so that kind of
connection where you sort of connect to
someone outside your normal circle is
what we came to call a shortcut. So they
went round the circle disconnecting some
of the links and reconnecting them at
random to a different node in the
network. And as they did that, they
watched what happened to the average
number of steps it took to get from any
one node in the network to another,
hopping between connected nodes. In
other words, the degree of separation.
This is now the moment for the big
reveal. As Duncan turned the knob in his
computer simulations, as soon as he
introduced a few shortcuts,
the world immediately gets as small as a
random graph. When they had rewired just
1% of the links to shortcuts, the
average degree of separation dropped
from 50 in the original fully ordered
network to 10. But Watson and Strogats
also tracked how clustered the network
was. That's the fraction of a node's
connections that are also connected to
each other. Or in other words, the
fraction of my friends who are also
friends with each other. What they found
is that clustering remained high for
much longer.
The world immediately gets as small as a
random graph, but it stays as clustered
as if it were still regular. So you
could simultaneously have the clustering
that we know is real and the small world
that we know is real.
Now in Watts and Strogats's model, they
looked at a thousand nodes. But if you
apply their model to the 8 billion
people on Earth, well then you would
only need three out of every 10,000
friendships to be a shortcut. and the
average degrees of separation drops to
six.
>> Our math showed the question is not why
is the world small, it's really how
could it be otherwise. Duncan started
saying to me, this is about discovering
a whole new universe and and its
properties and laws.
I I recognized that he was right. I just
wanted to to sort of reflect on what you
said about these sort of shortcuts. the
I think I've had this phenomenon happen
to me sometimes in my life where I'm
sort of invited to an event and it seems
like a very random event. Often I kind
of feel like I don't really want to go,
you know, none of my friends are going,
but then maybe at the last minute I just
say like, well, let's just roll the
dice. And I find that almost invariably
those are productive
meetings. I'm kind of wondering if
there's a takeaway for people here,
which is that they should put themselves
in situations where the probability of
forming these shortcut links, would it
sort of increase the luck in your life?
>> You um have just put your finger on a
very famous phenomenon in sociology that
is called the strength of weak ties. Cuz
you ask people how they got their job
and people would say, "Oh yeah, I heard
about it from, you know, Randy." And
then he'd say, "Oh, is Randy a friend of
yours?" And people invariably would say,
"No, he's an acquaintance. I wouldn't
call him a friend. He's an
acquaintance." That's a weak tie. The
strong tie is your best friend or your
circle of friends.
>> Excited about their breakthrough, Watts
and Stroats wanted to test their small
world model on some real world data. But
this was 1996. We had to think, well,
where are we going to get data on big
networks where we could test this? And
it was not so easy. The internet was not
mapped out. But Google didn't exist.
>> So they turned to an unusual source.
>> There was only one nervous system that
had been mapped at that time, which was
the worm C elegance. Tiny worm like a
millimeter that you can find in the
dirt. A favorite of neurobiologists.
They knew every cell in the body of sea
elegance from the time it's a single
cell till it becomes a whole organism.
So they had the total wiring diagram of
that organism.
Watson Strogats tested their model on
the worm's neural network. The worm has
precisely 282 neurons and on average
they're connected to 14 others. If you
lay that all out in a line along the
worm's body, the neurons at the ends
would be separated by around 40 steps
and the average degree of separation
would be around 14. But when Watson and
Stroats ran the calculations, they found
the average degrees of separation
between any two neurons was just 2.65.
To put that in context, if they were
connected totally at random, it would be
2.25.
And yes, okay, so bingo, that was a
small world. Then we were popping the
champagne. I mean, that was really
exciting that nature had done that. So
then we thought, well, okay, but this
should be true of a lots of networks
because nature can't resist this
mechanism. So they looked at Hollywood
actors and power grids across the US.
Sure enough, they were both small world
networks. For example, in the database
of over 200,000 Hollywood actors, the
average degree of separation was less
than four.
>> Dangerfield was in Catty Shack with Bill
Murray and Bill Murray was in She's
Having a Baby with Kevin Bacon.
>> Then the real payoff for us as people
interested in dynamical systems more
than graph theory was okay. So what you
know, so what if the world is small?
Does that affect how things get in sync?
Does it affect how diseases spread? Does
it affect how information travels?
Whatever. And so we did a number of
experiments again in the computer like
that.
>> Take disease. I wanted to know how a few
shortcuts would affect how disease
spreads through a network. So I asked
Casper and the team to make a
simulation.
>> And then a question to you is do you
want to start with a completely regular
world where it's completely clustered or
do you want to start with completely
random?
>> I would start with a regular world.
Okay,
there it goes.
this the spread of infections.
>> Yeah. So, it takes over the world
completely. Well, if every step was a
day, it would take 73 days to for the,
you know, infection to take over this
entire world.
>> Let's introduce a few shortcuts and see.
>> Okay, let's make it small world. Like
10%. Let's go.
>> Boom. Wow. That's really dramatic,
>> right?
>> That's really dramatic and very fast.
>> Yeah. So fast. Yeah. After 26 days, the
whole world
>> and that ramp up does look exponential
at the beginning and then it
>> it kind of looks linear there as well,
but it's almost like you can't go any
faster.
>> Yeah. Okay. So, now let's make it a
completely random network.
>> Boom.
>> Crazy.
>> How many days now for a fully random
network?
>> 25.
>> Basically identical,
>> which is crazy because in the random
case, all your links are random. You
know, in the small world case, it's just
10%. It's like if one out of your 10
friends are a shortcut, which, you know,
for some people might be a bit much, but
I reckon for you, it's probably about
right.
>> Yeah, I got lots of shortcuts.
>> But the crazy thing is that in this
simulation, we only used 100 nodes. And
if you use the same model to the 8
billion people on Earth, then you would
actually need less than 1% of all your
links to be shortcuts.
In 1998, Watson Strogats published their
findings in a three-page article in
Nature, and the paper took off. Within a
few years, the paper already had
hundreds of citations. By 2014, it was
ranked the 63rd most cited paper of all
time. And today, it's got around 58,000
citations. That's higher than Peter
Higgs paper on the Higs Bzon and almost
three times as many as Watson and
Crick's Nobel Prizewinning paper on DNA.
So it's it's probably worth making that
distinction that citations are one
measure of impact. We're cited a lot
more than Einstein and I think you know
who's more important.
It's not it's not us. But it does mean
people thought it was worth citing. We
had many tens of thousands of citations
from people in far-flung fields from
neuroscience to sociology to graph
theory to computer science even you know
English literature. People would do
things like draw networks between words.
Is there any irony in the fact that this
paper on small word networks goes viral
itself?
>> Um I yes I I think so maybe so
>> but then things got a little weird.
That's when I started getting some
strange phone calls. I got a call from
somebody at the FBI. I was a little
scared. What's the FBI calling me about?
And so I call back and the person who
picks up says hair and fiber.
I was calling the hair and fiber network
at the FBI, the people who do, you know,
criminology based on what telltale hairs
or fibers are left on the victim's
clothes after they've been murdered.
There was a guy who said, "What happens
when um the police have a suspect and
they say you have fibers on your sweater
that match the hair of the victim?" And
then the defense lawyer says, "Well, you
know, maybe the victim was on a bus and
left her fibers on the bus and then my
client sat on the a secondary transfer,
they would call it, of these fibers.
That doesn't prove anything." So the FBI
wanted to know what's the probability of
secondary transfers compared to primary
transfers from actually killing the
person. And like I I don't what do I
know?
>> Now that's a Steve Strogat problem. For
most of us, a random caller telling you
they're an FBI agent is probably a scam.
Chances are they got your number from a
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So, I want to thank Incogn for
sponsoring this video. And now back to
networks.
In 1998, Albert Llo Barabashi was
studying the internet. At that time,
there were around 800 million web pages.
But despite the web's enormous size,
Barbashi found that on average, you
could connect any two sites with just 19
clicks. Apparently, the web was a small
world, too. But the strange thing was it
didn't look anything like the small
world network in Watson Strogat's model.
We ended up mapping out a region of the
worldwide web and we had a very clear
expectation of how that network should
look like.
>> Barabashi thought the distribution of
pages and links would resemble a bell
curve similar to what you'd get for
people's height across a population.
Most sites would have some average
number of links and there would be very
few outliers either side. But that is
not what he saw.
>> And so we measured the distribution and
it didn't look anything like what we
expected. The curve started out steep.
Loads of websites had not many links.
Then there was this really long tail.
>> And here we saw web pages that had not
only a little more but sometimes 100
times more links than the average degree
or the average node on the website.
>> These were websites like Yahoo, super
connectors that linked to thousands of
other sites. Barabbashi called them hubs
because when he mapped out the network,
they resembled the hub of a wheel with
spokes going out to hundreds of other
pages. And it was these hubs that made
the web a small world, not shortcuts. So
Barabashi wondered, how could this apply
to other networks, too?
Most real networks or virtually all
large networks
follow two very fundamental principles.
First, any large network out there never
pops out as a large network, but it
grows, right? You have a tiny worldwide
web in 1991 and now we have trillions of
notes on the worldwide web. How did we
get one to a trillion, one node at a
time, one website at a time, all the
networks out there, no matter how old,
how fast they emerged, they always
emerge to some kind of growth process.
So if you think about networks you must
build in that growth process. Number two
when a new note comes in you join
Facebook who you going to connect to
right and it is somewhat unpredictable
but it's biased. Your connections are
always biased towards the more connected
nodes simply because you are more likely
to know a more connected node than a
less connected n. He named this process
preferential attachment. Verbashi
reasoned that these two principles could
explain how hubs naturally emerge when a
network grows. So together with his
colleague Reika Albert, he ran a
simulation. We've also got a simulation
for this. They started with a simple
network of just a few connected nodes.
Then they began adding new nodes to the
network one at a time. With just one
condition, they'd be more likely to
connect to nodes that already had more
links.
That's so cool. Looks very biological,
very organic. Also, I like how the nodes
come out and they don't just sort of
stop in one spot. They kind of like
wiggle around and like find their
location. I I I really enjoy this. Like
a space station.
>> That's what I was thinking.
>> Or or like a space colony, right? Like
the
>> Yeah. Yeah. Right. Like each little
center one could be a planet. Then
you've got all the sort of stations
going around it.
>> Yes.
>> So when Barabashi and Albert let these
networks evolve, hubs emerged
>> and we showed that growth and
preferential attachment together
naturally lead to the merges of the
hubs.
>> With this simulation, Barabashi and
Albert showed how hubs could emerge in
virtually any complex network. Take
airports for example. In 1955, Chicago
O'Hare opened to commercial flights.
Unlike neighboring Airport Midway, it
had long runways and plenty of space for
new jet aircraft. Airlines began
shifting service there. As more airlines
connected flights to O'Hare, passengers
had more options to connect, making it
increasingly attractive. After
deregulation in the 1970s, more airlines
were free to add routes, and the
feedback loop accelerated. Each new
route made the airport more useful to
passengers and more appealing to other
airlines. Today, O'Hare is the most
connected airport in the United States
with direct flights to well over 200
destinations.
But we don't just see hubs in man-made
networks. In food webs, you have a few
keystone species like Atlantic cot that
connect hundreds of predators and prey.
And in the metabolic networks in our
cells, you have a few molecules like ATP
that govern hundreds of chemical
reactions. In the neural networks in our
brain, you have a few regions like the
prefrontal cortex that link hundreds of
different functions. Now, as each of
these networks evolved and grew over
time, you had new species, new
reactions, and new circuits that latched
on to what was already well connected.
And so, you get this sort of natural
growth. Now, preferential attachment
isn't the only mechanism that can create
hubs. There are plenty of other factors
at play, particularly in these more
complex biological systems. But what
Barbashi's and Albert simulation showed
is that all it takes is a tiny bias when
growing a network and hubs end up being
inevitable.
>> Once hubs are there, they fundamentally
change the way the system behaves and
the way we understand that system. Hubs
like O'Hare mean you can get pretty much
anywhere in the world in just a few
flights. But that connectivity also has
consequences.
In August 2025, thunderstorms shut down
Chicago O'Hare and 280 flights were
cancelled and 80 were diverted. Overflow
hit at least six other US airports while
some planes stuck in Chicago never left
for Europe or Asia. Bad weather in
Chicago totally changes not only the the
the travel pattern in Chicago but within
24 hours the whole country is being
affected by that.
>> And we see the same phenomenon in
natural networks. Knocking out one
keystone species like Atlantic cod can
destabilize an entire ecosystem.
>> So this is what we call the Achilles
heel of networks. And this could be good
news or it could be bad news, right?
Good news. If you want to create drugs
to to uh to kill bacteria, then you're
going to go for the H.
>> This idea has created a whole new field
of network medicine where researchers
develop drugs to target crucial parts of
a disease's metabolic network. But
understanding the role of hubs doesn't
just help develop cures for a disease.
It can help us control its spread. In
1990, Thailand was facing one of the
fastest growing HIV epidemics in the
world. The government tried broad
campaigns like posters, TV ads, and
school talks telling everyone to use
condoms. But the infection kept
spreading. So in 1991, the government
tried something different. They started
targeting hubs. They told brothel around
the country that every client must use a
condom or else they'd be shut down. And
the impact was huge. For example, HIV
infections among young men joining the
military dropped by more than 50%. And
by 2013, Thailand's Ministry of Public
Health estimated the policy had
prevented over 5 million infections. All
because they realized the importance of
hubs.
Hubs and shortcuts make any complex
network more connected than it seems.
That means things spread quickly,
whether that's airport delays,
information, or disease. But could that
impact run even deeper? I mean, could
the structure of our social network
influence our very behavior and beliefs
without us even being aware of it?
Back in 1997, Watson Strogats
investigated just that using a game
called The Prisoners Dilemma. It's
probably the most famous problem in game
theory, and it's used to represent a ton
of different conflicts we see in the
real world. We've actually done a full
video on it before, but here's a quick
recap. The premise is simple. A banker
with a chest full of gold invites you
and another player to play. You each get
two choices. You can cooperate or
defect. If you both cooperate, you each
get three coins. But if you defect while
your opponent cooperates, you get five
coins and they get nothing. And if you
both defect, then you each get one coin.
So what would you do? Suppose your
opponent cooperates, then you could also
cooperate and get three coins. Or you
could defect and get five coins instead.
So, you're better off defecting. But
what if your opponent defects? Well, you
could cooperate and get no coins, or you
could defect and at least get one. So,
no matter what your opponent does, your
best option is always to defect. Now, if
your opponent is also rational, they'll
reach the same conclusion and therefore
they'll also defect. And as a result,
when you both act rationally, you both
end up in the suboptimal situation of
getting one coin each when you could
have gotten three.
But in 1980, Professor Robert Axelrod
found that if you play your opponent
hundreds of times, well, then
cooperation wins out. He ran a
tournament among the world's leading
game theorists, and all the most
successful strategies were nice. The
winning strategy was called tit fortat
because its default position was to
cooperate and it would only defect in
retaliation. He also showed that a small
cluster of cooperators can work together
to overcome a world of defectors. So
that's kind of the scene we're set in,
right? you get to this realistic place
where you get tit for tat like
strategies to sort of dominate the world
because in Exor's tournament every
strategy played against every other
strategy or they only interacted sort of
with their near neighborhood which is
you know the small cluster and now you
could wonder well what if we start
changing the way this works what if we
put them on a network well Watts and
Stroats simulated their own version of
the prisoners dilemma that did just that
they set up a regular network where each
player was connected to a few players on
either side. Then they would
simultaneously play against all of their
connections. The rules were simple. If
most of a player's connections
cooperated, then that player would also
cooperate. But if most of their
connections defected, then they would
defect in retaliation. They started with
a small cluster of cooperators
surrounded by defectors, and they
watched the network evolve. Over time,
what they saw was cooperation spread,
just like what Axel Rod had found. But
then they reran the simulation, this
time with a few links rewired to
shortcuts. And all of a sudden, the
cooperators were crushed and they ended
up with a world of defectors.
And when they started from a totally
regular network and gradually increased
the fraction of shortcuts, they found
there was this critical fraction beyond
which the percentage of cooperators at
the end of the game drops to zero.
>> I think the thing that's really crazy is
that you've taken the exact same
strategies with all the same properties,
same character traits and personalities,
if you will, and you're not changing any
of that. All you're changing is the way
they're connected. And you go from a
world where everyone's completely nice
and working together to one where it's
filled with nastiness and people
betraying each other only by changing
how they're connected. It's like if the
bulk of your interactions are sort of
negative, then you start being negative
too and you just contribute to the
overall negativity. Whereas if like a
few people are nice, then you can
imagine, oh, that makes me feel good and
so I'm going to be nicer to that person.
The intuition for that is that
cooperation is fostered by having little
clumps. If I have a little clump of of
people that are kind of my buds, we get
to have a lot of encounters. And
cooperation tends to emerge from
familiarity. The same way that iteration
helps that if I know that I'm going to
see you again, I'm going to encounter
you again. It ends up being to my
advantage to cooperate. Whereas like the
world of the internet where anyone can
get on Twitter and badmouth anyone else
that tends to discourage. We don't have
um pockets. You don't have communities.
>> It kind of explains this keyboard
warrior phenomenon and that Yeah. People
say things on the internet they wouldn't
say.
>> They wouldn't. Most people are nice in
real life.
>> Yeah.
>> It's funny that the small world I know
you think the small world Well, because
that's a Disney song, right? It's a
small world after all. like it's
supposed to be good and yet it does
expose you to toxicity and malevolence
that you might have been shielded from
in the in the small town.
>> Social media has kind of been toxic. The
initial idea being, hey, we connect up a
bunch of people and people have been
separated geographically. We connect you
with your old friends. You look at the
net effect of it and it's actually been
pretty negative by a lot of measures.
Intrigued by the findings, Watts started
wondering if the results applied to the
real world, too.
>> For years after I did this work, I had
wanted to test the hypothesis with
actual human subjects.
>> So, he got some volunteers to play a
similar game called the public goods
game across different network
structures. He was expecting that, like
they found previously, more shortcuts in
a network would make cooperation less
likely to emerge. But what he found was
the structure of the network had no
effect. Cooperation was just as likely
to emerge in a totally clustered network
as it was in a totally random one.
>> We were very puzzled by this result and
then we kind of did some more work. When
Watts dug deeper, he realized that the
network structure did matter. In the
more clustered networks, people were
more likely to copy each other. So if by
chance someone started out cooperating,
then everyone would cooperate. But it
was equally likely that someone would
start out by defecting, in which case
everyone else would defect. And over all
the games they played, these two effects
canceled each other out, which is why it
seemed like the network structure didn't
matter. It's sort of on a knife edge,
right? Where like one person does
something selfish and everything goes
south. uh in in another world, everybody
kind of holds it together and everything
goes well.
>> It's crazy that the world could be like
on a knife edge like that, you know,
could tip one way or the other. Kind of
just depends on how someone gets out of
bed that day.
>> But then what's realized something? See,
in real life, you can choose who you
hang out with. So he reran the
experiment, allowing players to change
who they were playing with. And this
time he used the prisoners dilemma so
that players could easily identify the
defectors.
>> And the finding was clear. The more you
allowed players to choose who they were
playing with, the more likely they were
to cooperate.
>> You can make this a lot better for
yourself by just acting and being
decisive and being proactive about
things.
>> Yeah. Yeah. It's the thing I try to
teach my kids, too. Like if someone's
annoying you, just ignore them. Like
there's nothing to be gained by
continuing to interact with people who
are bringing negativity into your life.
>> In fact, making a choice can be powerful
in more than one way.
>> There's something about the world that
makes it prone to those upheavalss.
Meaning, it's always kind of poised on
an edge of instability and that gives
each of us more power than you'd think
we would have. It is actually possible
for individual people to start movements
that grow and take off and ultimately if
you look at history that is what
happens. It's always one person who is
stubborn and does something that leads
to 10 people a thousand people and
things change because of it. It always
starts with one person somehow.
>> It's the Steve Jobs quote, right? But
the people who are crazy enough to think
they can change the world are the ones
who do. And the wonderful thing is it
all starts with you believing you have
that power.
>> Yeah.
>> Learning all about network science has
taught me many things, but perhaps the
most important is that our networks
shape us, but our actions shape the
networks. So, choose both wisely.
[Music]
Hey, if you made it this far, all the
simulations we ran through with Derek,
we will actually make them available on
a website that you can go to so you can
play around with them yourself. So,
thank you so much for watching. We
really appreciate it. And yeah, see you
for the next