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