Six Degrees of Separation

Introduction

Supposedly, you know someone, who knows someone, who knows someone, who knows someone, who knows someone and that last “someone” could be any person on the planet. The six degrees of separation is a common game played with actors in films, though the concepts of it are often applied to the entire planet. But there are about 8 billion people currently alive on planet earth, many of them living in small communities, and many of them living in countries that don’t even speak the same language as you. It seems impossible that the six degrees of separation could be real. But when you’re dealing with large numbers, and the power of exponents, those large numbers get a lot larger quickly. This experiment will show, numerically, how likely it is that you are connected to every person on the planet within six degrees of separation.

Research Questions

• Why do people believe in the six degrees of separation?
• Do the six degrees of separation work for people in films?
• How many people does an average person know?

Terms to Know

• Exponential growth

Materials

• Paper
• Pencils
• A few friends to help
• A few of your friends’ friends or a few relatives from another town

Experimental Procedure

1. Make a list of every person that you know. Take at least a couple of days to do this as you won’t be able to remember everyone at once. It may help to carry the list around with you, adding names as they come to you. Only list people who you know at least the first name of.
2. Have a few friends or relatives make similar lists.
3. Have your subjects from step 2 ask a few of the people on their lists to do the same thing. Try to find at least a couple people that live in other areas.
4. optional) If it’s possible, get a few people from the lists generated in step three to do the same.
5. Gather all the lists together.
6. Count how many people there are on your list.
7. Place this information on a chart such as the one below.
8. Count how many people are on the lists from the subjects in step 2.
9. Place this information on a chart such as the one below.
10. Count how many people are on the lists from the subjects in step 3.
11. Place this information on a chart such as the one below.
12. Count how many people are on the lists from the subjects in step 4.
13. Place this information on a chart such as the one below.
14. Average the results for each step.
15. Use exponents to extrapolate how many people you are connected to through just those in the “Your Friends” column. (optional) You can remove people on the list that are mutual acquaintances and use those numbers for the exponent step. For instance, if you know 1000 people, and each of those people knows 1000 people, but 700 are the same as the people you know, use 300 as the exponential factor.
16. Take the number of people you know.
17. Take the average number of people your friends know.
18. Use a calculator to multiply your number by the exponent in step 17. This number is the number of people you are two degrees separated from.
19. Continue in this process until you reach six degrees of separation.
20. Compare this number to the number of the people on the earth.