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We've been thinking about the global social network
as a whole object, and in particular, thinking about the paths
that link all of us together.
And when Stanley Milgram went to test this,
he found-- at least through the experiment
that he devised-- the median number of steps
it took people to actually forward letters
to distant targets in the social network was six--
this number, six degrees of separation.
What I want to talk about now was how we might reason about
the global social networking-- again, very conceptually.
We're not going to try to map it out, but where we actually arrive at a sense
that six feels like sort of about the number you in fact
maybe should have expected.
So here's how we can think about this.
Why are the paths in the social network extremely short?
One way to think about how the social network expands outward from you
is the following picture that is intentionally simplified-- and in fact,
massively oversimplifies one important dimension.
Here's how we think about it.
Here's you.
And let's say that when you think about how you could construct paths
to other people, there may be roughly 100 friends
that you could imagine that you might send a letter to
with these instructions, to forward it on to this distant target.
Maybe some people, it could be 200 or 500.
Maybe some people can only think of 50.
But let's think of 100 as kind of a round number of,
not everyone you know, but sort of a set of people that you could call on
for help in this kind of situation.
OK.
So that means one step out, there are 100 people you could reach.
Now each of them has 100 friends on average.
And so if I go two steps out, then the number of people
I could potentially reach, potentially, could be like 100 times 100, or 10,000.
I go out three steps, it's now 100 times 100 times 100.
That's a million.
So three steps out, there could be like a million people
that I could effectively reach.
Four steps out, 100 million.
So now we're talking about, we're starting
to approach the population of very large countries.
We're starting to sort of see a fraction of the world's population.
And if I multiply by 100 one more time, ten billion potential people-- which
is actually more than the population of the earth after five steps.
So there's an argument that it's entirely plausible
that five steps away from you is basically anyone at all,
because the number of reachable people might
be expanding by this factor of 100 at every step.
Now, there's a number of things that are oversimplified here,
but there's a massive thing that sort of should come to your mind
first that I've left out.
And that is triadic closure-- the fact that there
are lots of triangles in a social network.
So the social network doesn't really look
like this massive branching structure, where each of your friends
knows a whole new set of completely different friends.
Your friends all know each other, right?
And so that actually cuts down the amount of branching you get.
I have my 100 friends, but many of their 100 friends are each other.
And many of the links out all kind of hit the same people.
So the network is not expanding nearly as rapidly
as my previous picture made it seem.
A lot of the links in effect are being wasted on links among your friends
that are not helping you reach new people.
And of course they're serving many other important social purposes,
but they're not letting you get out into the world as efficiently as possible.
And so there's this tension.
And the tension is between the links that
reach out to the world and triadic closure, which
keeps them bottled up in your own communities.
And in a sense, it's sort of back to this trade off between weak ties
which carry you long distances, and the strong ties
which are more likely to be involved in triangles.
And effectively what the results of the small-world experiment show,
is that the weak ties in the end win out.
There just so many of them that, despite triadic closure
and despite the way in which the links close up on themselves,
you're still able to reach many, many new people each additional step
you take.
And so in five or six short steps, you can indeed be almost anywhere at all.
So it's not like the world looks like this completely wide-open branching
structure.
It does have all these triangles.
But it contains that branching structure inside it,
thanks to all of the weak ties.
Remember that the other thing the Milgram experiment showed,
which was really maybe even more surprising,
was that despite the fact that no one had a map of the social network
or anything close to it, they could still somehow get to the target.
They could make guesses about which friend to send it to and get there.
And people began to think about, what does
the network need to look like for that to actually happen?
For example, we could start with a picture.
And in fact, Milgram himself had a hand-drawn A
of this in his original article about this in Psychology Today in 1967.
We have a little picture of a map of the US and one of these chains--
or sometimes it's actually a kind of composite chain superimposed on it.
And the first step from Nebraska gets you maybe
halfway there-- gets you to Chicago or Cleveland.
The next one gets you to Pittsburgh or Buffalo.
You get to the Northeast.
You get into Boston.
You get into the suburbs of Boston.
You find the target.
And effectively this is what the network actually
needs to do if it's going to let people find the paths.
It has to be that wherever you are relative to the target,
you have to have a reliable way to shrink
your distance to the destination.
So when I'm in Nebraska, I need links that
carry me long distances across the country.
But when I'm in the Northeast, if I'm in York City,
I need links to carry me short distances-- that carry me,
say into Boston.
And once I'm in the suburbs of Boston, I need
links that carry me very short distances.
I need to be able to maneuver within say Sharon, Massachusetts, to actually find
this guy who lives there.
And so that's really one of the other insights from the experiment--
that our social network has links that live at many scales at the same time--
the long world-spanning ones, the very short ones are our neighbors,
and all those scales in between that let me cut down my distance as I approach
and close in on the target-- two things about the network-- the very
short paths, and the way in which it spans distances.
It spans geographic distances.
And in fact, it spans other kinds of distances.
For example occupational distances.
If I'm trying to get to a stockbroker, I need
to first enter the financial community.
I need to enter the community of stockbrokers.
I need to enter that firm, and so forth.
So we're closing in on many different dimensions all at once.
A final point that actually has emerged from analyses of this and from attempt
at replication-- is that, it's also the case
that some targets in this experiment are simply much easier to find than others.
And in particular, it seems to have been important for the Milgram experiment
that the stockbroker was someone of relatively high socioeconomic status.
He had a high-paying job.
He worked in this large urban area.
And so there were many ways to get to him-- many paths led to him.
And when people have attempted replications of the experiment
but they've made the target someone of much lower socioeconomic status--
someone who is poor, who hasn't traveled very widely, who
lives where they grew up, and doesn't know people
in a lot of different parts of the world--
it turns out to be much, much harder to find them.
Because effectively, the number of available paths that lead to them
is corresponding much more impoverished.
And so what we find actually, is that by thinking about this one experiment--
the experiment about constructing paths--
we actually learned many things about the social network.
We've probed it in a number of different ways.
And we found that not only are the paths very short,
but that the links span many different scales of distances.
And they also span different levels of socioeconomic status,
with links tending to funnel in easily toward high-status people,
and to be actually much weaker and much less effective
in the vicinity of low-status people.
And all of this is fed into it lively area of research
that's thought about networks and their global properties
and these kinds of social phenomena and societal consequences that
come from the way in which the structures are arranged.