Six Degrees of Separation

It’s a small world after all. Three years ago we went on a leadership course, and met a Vancouver couple (A&B)* whose work is missionary care within a denominational mission agency. We kept in touch, and recently when they came to Toronto to conduct a training workshop we had breakfast together to catch up. It turned out we had more things in common than we realized.

The first connection was when Ellen started learning Spanish two years ago and looked for a tutor. My brother’s wife said her brother has a niece from Guatemala who is visiting him in Toronto. She speaks Spanish fluently and could give Ellen some pointers. We met, and it “happened” that this niece is a Christian who attends the church where A&B used to pastor in Guatemala City! That’s four steps from us to them, had we not known each other directly.

The second link was through one of our engineering classmates C in university. C and his wife D have two children. Their younger son E initially also studied engineering, but did not enjoy it. Interestingly, he went on a short-term mission to, of all places, Guatemala City, where he met A&B. C&D were concerned about E’s safety, and wrote A&B to look after him. E liked missions so much that he returned to Canada to attend bible college, and after graduation moved his family to Guatemala to start a bed and breakfast place for ministry. C&D visited them to show support and became friends with A&B too. That’s three steps from us to our missionary friends.

The last connection was through Ellen’s sister’s (F) husband (G). F&G went on a reunion with his extended family to Hawaii. However, in the middle of the celebrations G’s brother’s (H) wife (J) was struck with meningitis, and had to fly back to Calgary for treatment. H&J are dedicated members within their denomination, and active in promoting missions in Chinese churches. That’s where they got to work with A&B. When J recovered sufficiently, H threw a thanksgiving dinner and invited all their friends and church brothers and sisters, including A&B. That is again three steps from us to A&B.

My first thought was it’s a small world after all! True, our sample may be skewed by the fact that we are Chinese Christians involved in missions, but still you can’t help but wonder our circles are so limited and intersect with each other. Don’t do anything foolish, or else it will spread to who knows where, even without email, FB or WhatsApp!

The second thing that comes to mind is “six degrees of separation“, the theory that everyone everywhere can be connected to any other person by way of friend introducing friend, in six steps or less. Our example took only 3 or 4 steps, but even if it were a complete stranger in a foreign land, the theory is that you can be connected to him/her in a maximum of six steps.

Mathematically this seems possible. In a random network of n nodes, with each node having k acquaintances, the average distance between two nodes is ln n/ln k (ln = natural logarithm). Assuming the world’s population to be 7 billion people (n), and that each person knows an average of 50 people (k), then the average number of steps to link one person to any other person is:
ln 7,000,000,000/ln 50 = 22.67/3.91 = 5.79, rounded to 6.
Obviously, the larger k is, the lesser the number of steps.
If you solve for k in ln 7,000,000,000/ln k = 6, the largest integral value for k is 44. In other words, if each person connect with at least 44 acquaintances, then anyone can be introduced to anyone else in a maximum of 6 steps.

This has interesting implications for evangelism and missions. We tend to think of reaching the world for Christ as “too big” a task and would require a very long time. But let’s assume the message to be delivered is the gospel. If I find the right contacts with the right connections, then I can share the good news with anyone in the world, including the top Muslim cleric, or the Dalai Lama, within six links. This assumes that those who received the message are ready and willing to pass it on, and that some will have to cross geographic, linguistic, cultural and/or class barriers. But what this tells us is that it is not an impossible task, and that we can share Christ with anyone anywhere in the world, so that they can make an intelligent choice whether to follow Him.

*Names changed for privacy purposes.