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*10
4) 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'