Hack 72. Feel Connected

The concept of "six degrees of separation" is more than just a New Age metaphor for community or a party game involving the actor Kevin Bacon. If you want to actually test the idea that we all know someone who knows everybody else, find out how closely linked you really are to everyone.

I know a guy who knew a guy who used to work for the President of the United States. Small world, eh? I'm not saying I have great connections, but I am just two handshakes away from the leader of the free world. Before you get too impressed, you should know that you probably are just a few links away from almost anybody in the world.

It is probably true that any two people are within six degrees of separation, and that magic and oft-quoted number of 6 is actually taken from a real scientific study! Here are some clever research methods to let you reveal the invisible connections that unite us all, or at least link you to that person on the other side of the cocktail party.

Six Degrees of Separation

There is a play called Six Degrees of Separation by John Guare and a movie based on that play starring Will Smith. There is also a popular party trivia game, sometimes called Six Degrees of Kevin Bacon, that attempts to link any actor or actress through a series of movies and other performers until they share a connection with actor Kevin Bacon.

The phrase and concept come from a study that considered the small-world problem. Have you ever been at a party or been chatting with a stranger at a coffee shop and discovered that you both know the same person? Social psychologist Stanley Milgram was curious about this phenomenon in the late 1960s (when there were a lot more cocktail parties than there are now). How much overlap was there in social networks? If we could all get together and list everyone we know, would there always be some connection? Probably, eventually, as we explored further and further out of the center of our web of acquaintances, we would find some connection with almost everyone. But how many links would it take?

Just one degree of separation means we all know everyone. Well, I don't know you (no offense), so we know that one is too few links to connect everyone. Are there just two degrees of separation? If we don't know each other, maybe we have a friend in common?

The question, therefore, is how many degrees of separation are there between you and anyone else? To get the answer, do a big study or a small study using the methods in this hack.

Doing a Big Study

How could one study the problem of whether we actually live in a small world? The best way is to duplicate the methods used by Stanley Milgram.

Choose a target

Milgram started by picking someone he knew who worked in Boston, Massachusetts, where Milgram lived. It wasn't Kevin Bacon, but a stockbroker who agreed to act as the target, the final end of a chain that Milgram hoped to build. You could pick your best friend or your school principal or your University's president. You gotta ask their permission first, though (something about ethics).

Recruit participates

Milgram then randomly sampled from two communities: Boston and Omaha, Nebraska. This sampling scheme was meant to represent the two extremes of likelihood that anyone would know the target. Start with people close by and people far away, and the average of their data should be fairly representative of the population. Milgram used 300 randomly chosen recruits. You should use as many as you can afford or have time for.

Train participates

Milgram sent a packet in the mail to each recruit. The packet contained instructions describing the study and a letter for the Boston broker. They were asked to deliver the letter to our guy, but only if they knew him personally. If they did not know him personally, they were asked to record some information, such as their name, and send the packet on to someone who they did know who they thought might have a better chance of knowing him. Those next people in the chain received the same packet with the instructions and the letter. They might have sent it to the broker if they knew him, or sent it on to a third link in the chain, and so on.

In your own study, make sure to write the instructions clearly and simply, and, these days, you might explain that this is legitimate research, not a commercial solicitation and not a chain letter (though it literally is, I guess), and all the disclaimers you think will help. You should also include contact information for you if anyone has any questions about the legitimacy of the project.

Collect and analyze the results

After a reasonable amount of time, check with your target and gather all the letters received. On each letter, count the number of names that form the chain. Average all the different lengths of chains to determine the typical number of connections. Find the smallest number necessary to include even the longest chain, and you have the maximum distance.

The Boston target in Milgram's study eventually received about 100 letters. Of those, the average number of links was sixthus, the origin of the number six in "six degrees of separation."

Notice, however, that not all letters arrived, so we don't know from this one study that six is really the right number. The study also took place in the U.S. only, not worldwide, so grander views of there being only a few degrees of separation between any two people on the whole planet are philosophically based, not empirically derived.

The response rate that Milgram enjoyed was very high, considering the complicated requests made of participants. This is not surprising, because Milgram knew something about obedience. Stanley Milgram is probably better known for another clever study with more disturbing results he conducted some years before his small world study. With his obedience studies of the early 1960s, Milgram demonstrated that when people of authority (such as research assistants in lab coats) ask study participants to do something that makes them uncomfortable, such as administering (or believing that they are administering) an electric shock to another research subject, a surprising number of people will do it. His research led to much insight as to why people might "obey orders" even if they disagree with them.

Two more recent studies have confirmed that the average number of connections between people in social networks is about six or even a little less.

Doing a Small Study

There are a couple of ways to use these methods that don't take quite as much work. The goal of the activity could be scientific or just party fun.

Milgram via email

Duplicate the Milgram study, but use the convenience of email. Here, the question would be how many links between people using their email addresses. Email is easier to work with than snail mail and is virtually cost-free.

Of course, choosing recruits through email is probably more difficult. It is hard to choose email addresses randomly, because there isn't a big phonebook-type list to sample from. Also, your email requests might quickly be mistaken(?) for spam and ignored. By the way, because your research interest is legitimate, you shouldn't have to worry about violating any Internet protocols.

Throw a party

When hosting a large party (Milgram would have loved it if you used a cocktail party, the inspiration for his original study), hand out supplies to your guests. Give them each a large index card and a pen. At the bottom of each card, list the name of a guest at the party. If guests don't know the person listed below, they should sign their name at the top of the card and hand it to someone else who they think might know the person.

The process should continue, just as in the Milgram study, until the cards reach the person who is named on the bottom. That person then turns the card in. At the end of the party, you can analyze the data and prove to your guests that they all really know each other.

Just Doing the Math

Even without scientific studies, however, a quick mathematical analysis might convince you that the number of people between you and anyone else is a fairly low number. How many people do you know by their first names? 100? 200? Let's say it is about 100. They each know about 100 people by their first names, too, presumably, so you are already connected to 10,000 people through just two degrees of separation. (Actually, 10,100, in total, counting the 100 people who are within one degree of you.) It wouldn't take too many degrees before you are connected to a whole lot of people, as shown in Table 6-21.

Table Degrees of separation and corresponding connections
Degrees of separation Connections
1 100
2 10,000
3 1,000,000
4 100,000,000
5 10,000,000,000

In fact, with just five degrees of separation, you should be connected to 10 billion people, more than there are on earth!

So, why, in reality, are a greater number of connections needed to really link all people? The problem is that the groups of 100 people that each person knows are not independent of each other. There is not a different group of 100 friends for each of your 100 friends. A good proportion of the 100 people that you know well are on many different lists for that group.

There is much overlap in social networks. This overlap actually helps increase the chance that there will be a fairly direct link between you and anyone else who lives relatively close to you (in the same country, say).

The Grandparent Paradox

A similar problem related to network overlap is the Grandparent Paradox. You had two parents. Your parents had two parents each, so that's four grandparents. Each grandparent had two parents and four grandparents. You don't have to count back more than a few generations to get to a huge number of people.

Count the grandparents going back 40 generations ago, and you require a trillion people. That's more than have ever lived on earth for all time combined. And that's for just the last 1,000 years or so. Where did we get all these other grandparents? Jupiter, perhaps?

The answer, of course, is that somewhere along the way there must have been some overlap on the genetic tree. Some already related family members must marry occasionally and have children. For the sake of decorum, I'll suggest they were second cousins or something like that.

The technique that Milgram usedthe small-world methodhas been found to be very useful in all sorts of social network research. The concept of a few degrees of separation has an intuitive appeal because it makes us all feel part of a small community.

It is also reinforced every time we do find a connection with a stranger through some common friend. I don't know about you, but in my own world, I have such importance that I can easily connect myself to all sorts of famous people. For example, as a college student at the University of Kansas in Lawrence, Kansas in the early 1980s, I was an extra in the ABC TV-movie The Day After, an acclaimed film about the potential after effects of nuclear war in the U.S. The Day After featured actor John Lithgow as a science professor. Lithgow later appeared in the film Footloose, starring Mr. Kevin Bacon! It's a small world, after all.

See Also

  • The two more recent studies confirming six or less degrees of separation are described in the Psychology Today article "Six Degrees of Separation" by Darby Saxbe, which appeared in the November/December 2003 issue.

  • Watts, D.J. (2003). Six degrees. New York: Norton. A book on the new science of networks provides a comprehensive and fascinating discussion of the connected age in which we live, including the six degrees of separation concept:

Statistics Hacks
Statistics Hacks: Tips & Tools for Measuring the World and Beating the Odds
ISBN: 0596101643
EAN: 2147483647
Year: 2004
Pages: 114
Authors: Bruce Frey

Similar book on Amazon

flylib.com © 2008-2017.
If you may any questions please contact us: flylib@qtcs.net