Wednesday, December 08, 2004

All Humans Share a Close Relation I

I read a story like this somewhere: If we trace acquaintanceship starting from a single person to that person's acquaintances, to the acquaintances of those acquaintances, to the acquaintances of those acquaintances' acquaintances, etc., then six times of this tracing covers almost all the people around the world (I'm not sure about the number six, but the calculation explained below shows that this is a reasonable number). Only six times! It means that all humans are in a rather close relationship.

A simple calculation convinces us of the above story. I send New Year and Christmas cards to a total of more than 150 people. I have much more acquaintances than this number, because I also know families of some friends of mine and have acquaintances to whom I don't send the cards. However, this number is possibly much larger than the average number of a person's acquaintances if we take small children and babies into account. Therefore, I divide 150 by 3, and assume the average number of acquaintances to be 50. Tracing acquaintances with this assumed number makes the number of people increase by the multiplication factor of 50 at each step. The final number becomes 506.

Actually, there is overlapping of acquaintances, so that the number does not increase this fast. But I already made a mean estimate in choosing the number 50. Further, this is a rough calculation to find the order of magnitude. So, believe that the final number shown above is a good estimate. That number is calculated to be about 16 billion. The population of the world is about 6.4 billion. Thus the former well covers the latter. Q.E.D.

I thought of this close human relationship from the word "friends of friends of yours" in the e-mail messages of the social networking service "Echoo!" I have joined.

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