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10. 6 degrees of separation

July 9, 2013

You are, according to mathematicians, 1 degree of separation away from anyone you know. Then two degrees from people they know and son on.

Professor of mathematics Jason Brown explained in the Chronicle Herald, California, how the 6 degrees of separation theory works:

pic 19 holding_hands_six

 For example, suppose that you are or have been acquainted with, say, 400 people. Each of those may know 400 others, giving rise to about 400 times 400, or 160,000 people, you may know in two steps.

Again if each of those individuals knows 400 people, you would only be three steps away from about 400 times 160,000, or 64 million people, and so on.
six-degrees

This is exponential growth.

Assuming we each know 400 people.

x = total number of people involved.

n = degrees of separation

 

x = 400n

If n = 6

x = 4006

x = 4 x 1015

As the population of the earth is only 7 Billion or 7 x 109, it seems likely that we can be linked to anyone else on earth in less than 6 degrees of separation, 4 maybe.

 pic 18sixdegsep

6 degrees of separation Myth busted.

 

Exercise:

Here is an awesome Middle School Maths PDF from PBS MATHONLINE based on Rumours.

It is an excellent introduction to exponential functions.

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