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We've been talking about how social networks regulate
the flow of information through the world.
And we've also seen how networks can be used to model friend and enemy
relations and phenomena like polarization.
Now what I want to do is actually step back
and take in the global structure of the entire network,
and to think about the paths that connect all of us,
connecting you to your friends and even on to linking you by several steps
to far flung strangers around the world.
So the idea is that not only are we all on this giant component together,
but we're very short distance apart, if I
define distance between the number of hops in the path.
Now, this idea that we're all close together,
that was already conjectured a long time ago before people ever really
started collecting data on social networks at large scales.
And you actually find it articulated very cleanly and very nicely
in a short story by the well-known Hungarian, Frigyes Karinthy.
And he speculated in this story about these kind
of pictures, these short chains that connect us to other people.
But here's a question.
How can we make these thought experiments more concrete?
We can all imagine this, but can we put actual numbers
on these social distances.
This was actually first done by Stanley Milgram in the 1960s
through a very creative experiment that launched a lot of subsequent work
in both the social sciences and in graph theory.
Here's how his experiment worked.
He wanted to test the idea that we really
are all very closely connected in society.
And so what he did was he tried to create a situation
where people were asked to build these chains
step by step using the help of their friends.
So he picked a target person that all the chains should end up at.
And this was a friend of his who was a stockbroker who
worked in Boston, Massachusetts.
Stanley Milgram was at Harvard at the time.
And this person lived in Sharon, Massachusetts,
which is a suburb of Boston.
And then what Milgram did was he picked 300 starting people
who were all going to try constructing paths to the stockbroker.
100 of them were in Boston so that there was no geographic barrier.
And 200 of them were in Nebraska, so they could be 1,000 or more miles away
and have to span not only social distance, but geographic distance.
And he sent each of them a letter.
He explained the experiment.
He said, we would like to construct these short chains that
link us in society.
And so what I want you to do is think about this target person.
Each starter he gave the target's name, their address, their occupation,
some other facts about them.
But he said, even though you have their name and address,
you can't just mail the letter to them.
That would just be a test of the US Postal System.
Instead, we're trying to test out the social network.
So you should mail this letter to someone
you know on a first name basis with the goal of getting
the letter to the stockbroker as fast as possible.
Because if it could get quickly to the stockbroker,
it would mean that it followed a chain of friends that was very short.
So for example, maybe one starter in Nebraska
thought, OK, I know someone in York City who lives on the East Coast.
I'll send it to them because they're geographically closer.
And the person in New York City might have thought, OK, I
know someone who's a banker who works in Boston.
So now I'm in Boston.
I'm in the financial industry.
That would be good.
Someone else said, oh, I actually know a financial analyst who's in Chicago.
So that's still the Midwest, but now I'm in the financial industry.
Maybe that'll be good and maybe they had a colleague in Boston.
And again, in two steps, I'm in the financial sector.
I'm in Boston.
I'm closing in on the target.
And this is how these chains worked.
People made their best guess as to how to get there.
And in this way, step by step, the letters
all closed in on the target using the social network.
Now, of the 300 initial requests, a bit more than 200 took the first step.
Because people got the letter, many of them just threw it out.
They didn't want to participate.
They forgot about it.
But slightly more than 200 took the first step.
And at each step along the way, some people dropped out.
And others tried their best.
They thought of a friend they could send it to.
And 64 of these chains actually completed.
They arrived at the stockbroker and they had
made their way through the social network.
And if you look at these 64 chains, each of them
took a number certain number of steps.
And the median number of steps they took over these 64 chains
was 6, which is this number that subsequently entered pop culture when
John Guare entitled his play, Six Degrees of Separation.
He was referring to this experiment and its numerical punchline, this number 6.
So this was a very creative, interesting experiment.
And it did a couple things.
First, it was really a way with-- in a very lightweight.
I mean, Stanley Milgram was doing this without massive data sets,
without computers, with an operating budget of $680.
And yet, he had somehow managed to probe the social network of the world,
or at least the social network of the United States
where the letters were all circulating around.
And one thing he found was the paths are very short.
He actually managed to put a number on the median path length, at least
among the paths that completed.
He also, in a way, did something that was ultimately more surprising,
although it took a couple decades to realize
this was sort of punchline of the experiment as well.
It wasn't just that the paths were there,
but people had been able to find them.
This wasn't the case where he was able to map out the whole social network
and then find what was the actual shortest path.
He was telling people to do a very complicated activity--
to guess which of their friends were most
likely to move the letter forward and get it there quickly.
And so the social network is somehow set up not just to have the shortest paths,
but to make them findable.
And that was sort of a second amazing thing to come out of this experiment.
The experiment was, of course, extremely challenging.
It was done in an era when people were somehow willing to participate
and willing to forward the letter on.
And so quite a large number of the chains
actually got there, despite all the dropouts at every step.
But it's challenging in the sense that subsequent attempts at replication
have suffered from massive attrition problems
and have been very difficult to get everyone
to participate so the chains actually get there.
And so sort of a difficulty in replication.
And that sort of points to some of the challenges in trying
to conduct experiments at this massive, full network scale.
So what I want to do next was actually think
about how we might model some of what's going on in this experiment--
why it should be in fact plausible that the paths were very short,
and how we might reason about the way in which people embedded in the network
might still be able to find these paths that are there,
but not visible to any one person.