The six degrees of separation idea was not inspired by the website. Rather the other way around. Martin Gardner wrote about the idea in Scientific American before Kevin Bacon made any films, and long before the world wide web ever exists. Recent work on the problem suggests that populations (and electrical power grids, and various other things) aren't quite random graphs, nor are they regular graphs, but somewhere in between. Calling it small world theory, a publication in Nature last year suggested that these networks have this short step distance or handshake number because of the relatively few really long jumps. They still cluster, but the clusters have long-range connections. (e.g., you may know lots of people in your home town, but you also probably know someone who knows someone who works in your national legislature or congress; this would take you almost anywhere in your country in about four handshakes.)

Just working out the numbers, this idea seems theoretically possible:

Say the average person knows 100 other people. (some people know many more, some people have no friends ...). These people would know 10000 people. Thus the trend ends up being:

you	 	 	   100 people	102
1st degree	        10,000 people	104
2nd degree 	     1,000,000 people	106
3rd degree         100,000,000 people	108
4th degree      10,000,000,000 people	1010
5th degree   1,000,000,000,000 people   1012
6th degree 100,000,000,000,000 people   1014

So at the end, you have 100 trillion people! If one assumes the world population as of this noding is 5 billion people, then the number of people one knows is greater than the total number of people by a factor of 20,000 (2*104) making it highly likely that six degrees of separation are enough.

This still isn't practically true given the emergence of new undiscovered tribes. However, as time progresses and the world becomes more globalized, this concept will become more and more accurate.

While this theory assumes a fair amount of homogeneity in interpersonal relationships (i.e. a low amount of 'cliquiness'), there are theories that show that this kind of assumption isn't necessarily true. The degree of cliquiness was studied in an article from Nature -Duncan Watts and Steven Strogatz ("Collective dynamics of 'small world' networks", vol 393. p 440, 4 June 1998).

If you live in a "cliquey world", your situation is like that in the circle on the left where you are linked only to your near neighbours. From the dot that represents you, you are linked to two friends to the left of you and two to the right. And each one of those friends has two friends to the left and two to the right. You will find that to travel around this small circle to the opposite side through the friends of friends of friends and so on, takes a surprisingly large number of steps. Imagine how many steps it would take to be connected to everyone in the world. Now try the circle on the right, the "open world", where the connections are random and can leap across and around the circle without any limitation. This is a totally open society where friends can appear at random. Even if you still keep to the rule that on average everyone knows four people, you can travel all over the circle with only a very few links.

Most interesting is the middle situation, the "small world", where people are still clustered mostly in cliques but a few people have connections to a distant place (an analogy might be that if you are living in Britain, you have one friend who has another friend who lives in Australia). Surprisingly, Watts and Strogatz show that just a few of these long-distance connections drastically reduces the number of steps that is needed to travel around the ring.

That's an important general mathematical conclusion that could help to create better designs for cellular phone networks, improve our understanding of the spread of infections and even explain why the brain is wired the way it is. It also helps to answer the original question asked above--the real world does seems rather like the "small world" and this suggests that there is a good chance that seven links will connect you to almost everyone else in the world.

- NewScientist 'The Last Word'

I read somewhere that everybody on this planet is separated by only six other people. Six degrees of separation. Between us and everybody else on this planet. The President of the United States. A gondolier in Venice. Fill in the names. I find that A) tremendously comforting that we're so close and B) like Chinese water torture that we're so close. Because you have to find the right six people to make the connection. It's not just big names, it's anyone. A native in a rainforest. A tierra del fuegan. An Eskimo. I am bound to everyone on this planet by trail of six people. It's a profound thought.... How every person is a new door, opening up into other worlds. Six degrees of separation between me and everyone else on this planet. But to find the right six people.
  --Ouisa Kitteredge, from the play.
Six Degrees of Separation is John Guare's 1990 play of race, class, and manners, based on the true story of a man who scams an upscale New York couple by passing himself off as the son of Sidney Poitier. It won it won the New York Drama Critics Circle Award, the Olivier Award in London, and the Obie Award for best play. In 1993 it was made into a movie with Stockard Channing, Donald Sutherland, Will Smith, and Anthony Michael Hall, directed by Fred Schepisi from Guare's own adaptation. Guare's play is credited with popularizing the phrase, but credits Guglielmo Marconi, not Stanley Milgram, for inspiring his play.

One of the first people to "prove" this theory--and it must be admitted that he only proved 160 of the billions of cases--was the psychologist Stanley Milgram. In the late 1960's, he asked 160 people in Omaha, Nebraska to mail a packet to a friend of his who lived in Boston. The catch was that they didn't have his address--they had to mail it to someone who they thought would get it closer to Boston. For each step, the idea was to get the letter one step closer, until someone could say "Oh, I know this guy!" and mail it to the rightful recipient. He found that somewhere around 90 percent of the letters that arrived did so in 5 or 6 steps.

One of the stranger facets of this experiment was that a majority of the letters he received came through just three acquaintances. Astonishingly, the idea of "six degrees" has become something of a paradigm (cough, cough): before the results were widely known, and before various publicity enhancing stories, plays, and urban legends, the people Milgram consulted for early estimates thought that it would take more than one hundred steps. Granted, that was before the Internet, but Milgram proved that on average, five connections will suffice, and six degrees is a near-certainty.

Other notable occurrences of the meme include

The six degrees of separation theory, while most interesting as a theory, has several major flaws - not least in practicality. For the sake of this experiment of thought, let's say that a "friend" is someone you are on mutual first-name-basis with (i.e. Bill Gates is only your "friend" if he knows your name, too), and whom you have had communications with in the past year.

Immediately, we see that what is emerging is effectively a network of nodes and links between these nodes. The people are the nodes of the network, and the links are the mutual first-name-basis friendships.

To communicate through this network, we have to send packages. If we imagine, for a moment, that this entire network is an electronic network, it is easy to imagine how you could test the theory. If I were to send the message "Hello, Charles, meet me at the London Eye on New Years' Eve of 2008" to an arbitrary person in Botswana, the first step would be to broadcast that message to all the people in my network. They would then have to re-broadcast the same message to all the people in their network, et cetera, until Charles actually receives the message.

if you know 100 people, and they know 100 people, in six steps you have 1014 people in your network (there are only about 6.5 x 107 people in the world). Considering this, chances are that the message will arrive at the right place, due to the sheer numbers involved.

Or will it?

The funny thing with these types of nodal networks is that people tend to know the same people. Look at your network, for example - If you are "A", and you are friend (as above) with B, C and D, then chances that B, C and D will know each other are a lot bigger than if B, C and D were arbitrarily chosen people. Hence, the network is inclined to converge on itself a lot more strongly than it would expand.

Which is where the concept of hubs comes in. If I just - quite boldly - use myself as an example: I have friends in a lot of different communities. I am a martial artist, so I have 10-20 martial arts friends. I am a photographer, so I know 10-20 photographers. I have my housemates (1), my ex-housemates (7 or so), my ex-girlfriends (a handful), my E2 friends (perhaps 40), my LiveJournal friends (10 or so), the friends I have in Norway (40-50), the friends I have in the US (5-6), my family in the Netherlands (40-50) - etc. With people like me existing, the network is suddenly a lot wider, because - through me - the network comes together.

But people like me are only a minor hub, compared to some. Imagine somebody like Elton John, or a PR professional, or an investigative journalist - all of whom have jobs that involve being in contact with hundreds - perhaps thousands - of people around the world.

A degrees-link between me and Bill Gates may go a little something like this: Me - Journalist at the Guardian - Brian Eno - Bill Gates. That's only four steps. Anybody who is my friends is - at most - five steps removed from Bill Gates - but they may not know it.

But what about arbitrary links? How about someone in Russia? (we used to have a tenant who was a professional olympic cyclist from Russia, who knows lots of media people in Russia, and hence I could probably connect to most people in russia in only a few steps). How about Africa? (I have a pen-pal in France whose dad works for the Corps Diplomatique in Botswana) How about Australia? (My sister studies International Relations in Australia). How about America? (E2 - what can I say - and I used to live there). How about Asia? (One of my journalism tutors is a prominent peace researcher from Hong Kong, my parents used to live in India and have friends there, and I know a load of exchange students from various parts of IndoChina). As you can see - even just going out 2 degrees, I got every continent covered. I bet that within 3 degrees, I have got to every single country in the world.

As I have shown, if we utilise the broadcast model of testing the six degrees theory, it is not implausible that I can get any message to any person anywhere in the world via less than six steps.

The problem, of course, is that using a broadcast model is incredibly impractical, due to the incredible amount of data that needs sending. If I were to telephone all my friends, and each telephone call took 3 minutes, I would be on the phone for 5 hours straight. If they called all of their friends, that would be another 5 hours. If they immediately called all their friends, and they call all of theirs, we are talking a hundred million simultaneous phone-calls, and the phone switchboards would melt. While it would prove the theory, it doesn't mean that the theory is of any use whatsoever in practice.

Of course, using the internet, it would be possible to simultaneously broadcast (email with 100 blue carbon copy addresses), but we still have the problem og having a hundred million e-mail-messages circulating within three steps. If 5 people were to start this project simultaneously, the Internet would grind to a halt.

Practicalities of non-broadcast based six degrees experiments

Imagine, for a moment, that the thing we want to send to an arbitrary person is not information, but something that cannot be duplicated and passed around to everybody I know. Say, I want to send a bicycle to somebody who lives in Gambia.

As mentioned in an earlier node, the researchers asked people to send the package to someone who they thought was closer to the person in question - which is where the fault lays: The 6 degrees theory depends on an incredible amount of knowledge about people - a type of knowledge you wouldn't normally have about people you are merely on first-name basis with.

Let's illustrate with an example: If I were to try and send that bicycle to someone in Gambia, I may start off shipping it to my uncle in the Netherlands, because I know he works in Africa a lot. He sends it to a friend of his in Egypt - so it is on the right continent, at least. His friend, bemused by what the hell he is supposed to do with a bike, ships it off to another friend, who lives in Egypt as well, but who has a cousin who lives in Niger. This cousin remembers that his old business partner (who lives in Egypt) is married to someone who is from Senegal, and ships the bike back to Egypt. The wife of his business partner sends the bike to her family in Senegal, who know someone in Gambia, and get the bike to the right country. From here, it goes to the local priest, who has a friend who works in the same village as our target, who gives the bike to the right person.

Not only did we spectacularly fail to hit the target of six degrees (there are 10 steps in the description above), but also illustrates the amount of information that is needed to ship the bike to the correct location: I need to know that my uncle works in Africa. His friends needs to know that his friend has a cousin who lives in Niger. He just ships it off to a friend, but his friends needs to know the nationality of his business partners' wife. The local priest needs to know the place of where this person that needs the bike lives - et cetera.

As you can see - even in this simple example, the people in my network need to have some pretty specific, high-level information about their friends' friends. Put differently, they need information about nodes twice removed in the network from themselves - which isn't usually the case...

What I didn't know, is that John, the milkman who every day delivers my milk at the door, had a nanny who was from the neighboring village in Gambia, and that there could have been 2 steps of separation, if I had only had enough information.

The problem lays in that even though you may know someone on a first-name basis, you have no way of knowing the intricacies of their network - and far less of someone else's network. For example: John could plausibly have mentioned to me at some point that his nanny was from Gambia, and in that case I would have given him the bike directly - but this is not the sort of information I am likely to tell my friends from martial arts, so even though they are only 3 steps separated from this person in gambia, unless they utilise a broadcast-model degrees of separation theory, they are highly unlikely to get the bike to Gambia in any fewer steps than myself, because they lack the information needed.

In summary; While the six degrees of separation theory is an interesting one, and may make for some interesting thought experiments, it is incredibly unlikely to have any practical impact on our lives for a long time to come, because of the sheer amount of network topology information that is required to get a message from A to B in as few steps as possible.

None, really, the whole thing is basically just a rant-cum-thought experiment on the six degrees of separation theory.

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