Thanks to Brilliant for supporting this episode
of SciShow. Go to Brilliant.org/SciShow to learn more. [♪ INTRO] Thanks to the internet, it’s possible to
instantly connect with people all over the globe. And thanks to social media, you can curate
a list of friends that can be hundreds, or even thousands, of
names long. All these connections make our world seem
pretty small. And the math has shown that it kind of is. You may have heard that any two people on
the planet are connected through only a small handful of intermediates,
usually six, hence the name for the phenomenon, the Six
Degrees of Separation. And it turns out that’s probably true. Sociologists and mathematicians have worked
together over the past few decades to determine exactly how connected the world is, and they
keep arriving at numbers around 6 or less. But that’s not even the coolest part. The mathematical models that explain how people
are connected, appropriately called Small World Networks,
don’t just apply to social interactions. They have uses and implications for everything
from the spread of epidemics, to the structure of the internet, and even
the neural networks that make up your brain. This idea of Six Degrees seems to first appear
in short story from 1929 where a character is challenged to find anyone
on Earth through a chain of at most five people. By the 1960s, scientists had started to get
in on the idea. The most famous experiment was conducted by
sociologist Stanley Milgram, yes, that Stanley Milgram. In 1963, the same year he tested people’s
obedience by seeing whether they’d shock others on
command, he sent the first chain letters. He picked people from several US cities and
asked them to forward the letters on with the intention of getting them to reach
a specific person. The experiment wasn’t hugely successful. Turns out people in the 60s didn’t like
responding to spam, either, but of the letters that did make it, the average
number of jumps needed was about 6. And that ‘six’ number has become totemic,
mostly thanks to a 1990 play called Six Degrees of Separation which was loosely
inspired by this idea. Of course, the play says everyone has at most
six connections in between them, and that might be a bit of a stretch. For example, in 2016, Facebook did a study
of the users on their network and found that the average number of friends
separating two active users was 3.5. But even though it’s the largest social
network, Facebook doesn’t come close to including
all of humanity, and 3.5 is an average. There could very well be people who you’d
need a dozen or more jumps to get to. The study didn’t try to pinpoint a maximum
number of degrees of separation. Still, even if six isn’t the upper limit,
the number is probably pretty small. We can also apply the Six Degrees concept
to collaboration networks, where the ties are stronger, people who have
actually worked with one another. The most famous example of this is the Six
Degrees of Kevin Bacon game: for any given actor, you name an actor they’ve
been in a film with, who’s been in a film with another actor,
who’s been in a film with another actor, until you get to Kevin Bacon. The number of steps needed is the person’s
Bacon number. For instance, Kevin Bacon and Viola Davis
were in the film Beyond All Boundaries, so she has a Bacon Number of 1. But Viola Davis was in Ender’s Game with
Stevie Ray Dallimore, who was in Paper Towns with John Green, who
faced off against Hank in a SciShow Quiz Show that I hosted, giving
me a Bacon number of 4! Bacon once famously claimed to have worked
with everyone in Hollywood, or someone who’s worked with them, hence
his central role in all this. And it turns out he wasn’t far off. Research has found he’s one of the most
connected actors in Hollywood. The vast majority of actors have a Bacon number
of less than 6, with an average of about 3. Scientists have a similar concept called the
Erdős number, where you work out how many scientific paper
collaborations you are from prolific Hungarian mathematician Paul
Erdős. Oh and if you’re the kind of overachiever
who likes to act and do science, then your Erdős-Bacon number is the sum of
the two numbers: Natalie Portman is 7, and Carl Sagan’s is 6. All of these fun examples illustrate how well-connected
our world is, but what they don’t tell you is what’s
going on under the hood, how such inter-connectedness happens. Even in this internet age, you tend to be
friends with people near you. And if that were always the case, it would take thousands of friendship steps
to reach around the world. But of course it’s not true. People do sometimes meet and form social bonds
with people from distant places. You may not be best friends with that one
French exchange student you met in school, but you definitely know them. And that one loose connection ties you to
a whole other country of people. In a 1973 paper, a sociologist called special
attention to these quote “weak ties”. He pointed out that the weakest connections
can sometimes be the most important. Like, in your friendship network, they might
be the ones that open you up to new ideas by giving you the perspective of a different
culture, or by introducing you to new people. But it would take another 25 years or so for the real importance of these so-called
weak ties to be revealed. You see, it wasn’t until the late 90s that
a pair of mathematicians created a model for this kind of network,
which they called a small world network. The researchers, Steven Strogatz and his PhD
student Duncan Watts, were inspired by the six degrees phenomenon, and wanted to understand where it comes from
mathematically. The tools they used are from the field of
math called graph theory, which looks at the different ways points can be connected
to each other in something called a network. For instance, let’s say you wanted to draw
a network representing the structure of a crystal, with points representing the atoms or molecules, and the lines between them representing chemical
bonds. The network would have lots of points that
are only connected to other nearby points. In other words, it would look very ordered. And on average, it would take a lot of jumps
to get from one side of the network to the other. By contrast, let’s say you wanted to draw
the network for something like Facebook, with points representing users, and lines
representing friendships. It would look more chaotic, random, and messy,
with lines going all over the place. But there would still be some structure to
it, for a couple reasons. Firstly, your friends are very likely to know
each other, because they have something in common: you. And secondly, people tend to be friends with
people who live near them, so you’d see a lot of locational clustering. So really, it would look a bit like the crystal
lattice, but with a few random jumps across the network
to faraway points. This small world model was designed to recreate
the structure and the messiness of a social network, all
before the rise of online social networks. And the technique they used to make the model
was simple: they started with an ordered, crystal lattice-like
network, and then gradually re-wired it. Specifically, their recipe was to take one
link on the ordered network, and randomly change one end of it to simulate
a person having a faraway connection, then repeat this multiple times. They didn’t care how strong the connection
was between the two points, just that there was one: your best friend and
that foreign exchange student count the same. And they found that it only took a small number
of re-wirings, just a handful of ‘weak ties’, to make the average path length between two
points drop drastically. Specifically, they proved that the average
number of jumps scaled logarithmically with the number of
points in the network. ‘Logarithmically’ is the mathematical
opposite of ‘exponentially’. If something grows logarithmically that means
it grows really slowly. So even a network of, say, seven billion humans
will have a tiny average path length, maybe under 10, thanks to a surprisingly small
number of weak ties. And recent studies have suggested that, with
modern technology, these so-called ‘weak’ ties aren’t even
all that weak. Maybe you keep in touch with that exchange
student over WhatsApp, so you know them better than you know your
neighbor! In addition to giving us a fun Hollywood trivia
game, the small world phenomenon has found uses
in a number of scientific fields. For instance, Watts and Strogatz showed how
diseases can spread more easily in a small world network because it’s easier
for the infection to reach faraway places quickly. It’s important for scientists to know this
sort of thing so they can model diseases more accurately, and that helps
them to work out where to deploy resources, and how to stop
a pathogen from spreading. And now that scientists are looking for them, it seems like these small world networks are
cropping up all over the place. In fact, Watts and Strogatz found that as
long as it’s possible to make any long-range connections in a network, the
resulting network was almost guaranteed to have small world properties. And that means understanding how small world
networks work is essential to understanding the behavior of these networks
and how signals travel through them. Computer scientists have found that the hyperlinks
between web pages look like this too, for example: almost any web page is only a
handful of clicks away from any other one. So understanding small world networks can
help scientists understand how information moves on the internet. And understanding these network properties can
help scientists understand biological systems, too. Take brains, for instance. Some researchers have claimed that the network
of neurons in vertebrate brainstems resembles a small world network, with lots
of clustering, and the odd link to faraway places. And that affects how signals travel through
the brain. One study showed that the small world networks
of neurons are better at rapidly synchronising activity across the
whole tissue because those ‘weak ties’ between distant regions help
signals spread far and fast. And it’s also been shown that neural activity
lasts longer in these networks, because it’s easier for a neuron that’s
been activated by a signal to be re-activated. In the end, models of the human mind may look
a lot like Kevin Bacon’s colleague network. As for the Six Degrees idea, well, it may
take a few more connections than that to reach some people on the planet, but you’re
probably about 6 degrees away from most people. The small world phenomenon reminds us that
everyone around us is closer to us than we think. Each person you walk past is a potential new
friend, and a potentially meaningful connection, helping to tie over seven billion humans into
one messy little network. We might not be able to draw out the whole
network for humans on this planet just yet, but computer scientists can do a lot of cool
things with neural networks. And if you want to understand how and why,
you might want to try out Brilliant.org. You see, Brilliant offers interactive courses
in math, science, engineering, and computer science. So whether you’re looking to brush up on
subjects you took years ago or learn something new, they’ve got you
covered. For example, their Artificial Neural Networks
course has everything you need to know about how these computer-generated
networks work. You can brush up on perceptrons or dig deep
into advanced network architectures, even when you’re on the go, because Brilliant’s courses can now be taken
offline on their new iOS app. And to sweeten the deal, the first 200 people
to sign up at Brilliant.org/SciShow will get 20% off an annual Premium subscription. So you can save money, sharpen your math and
science skills, and support SciShow all in one fell swoop. [♪ OUTRO]
