I was reading about the Small World Experiment and the Erdős Number, and thought: maybe they'd work well together. If you don't know about the small world experiment, go have a brief look (the first para) at it to understand what I'm going to talk about.
Interestingly, the results of the small world experiment may be rather inaccurate since it relies on people trying to guess the next person that would bring the package closer to the target. What would be needed would be some kind of automated system that could do it all. Facebook would be nice, but unfortunately, alot of users are not on facebook, and hence no computerised system could do this.
I propose a manual system then. It is similar to the Erdős Number. For example, if I take myself to be number 0. Let's call this number the Levy number for ego sake. All my friends, relatives and all those who know and have spoken to me would be considered to have a number of 1 (as opposed to collaborated in a paper as in the Erdős Number). Their friends, relatives and those who know and have spoken to them, but do not yet have a Levy number would then have a Levy number of 2, and their relations, 3, and so on.
This can be done simply by trying to promote this study. Like for me, I'm telling all of you who know and spoken to me that you have a Levy number of 1. So if you go tell whoever you know, that they have a Levy number of 2, and they do so, we'll eventually get this numbering system to spread pretty wide.
After a reasonable time period, say, 5 years? (this is due to some people spreading the number faster than others and hence we must wait for corrections to take place, e.g. a person discovers he's actually a lower number than he previously was due to late information) I then could randomly pick a person from the world (okay, this thing may not spread so far) or maybe the country, or just the school and take note of the number. After a number of randomly chosen people, we should have enough data to do an estimate to the normal distribution that governs the numbers sampled, and thus find out the mean number of relations from a person to a person, which should be more accurate than the Small World Experiment carried out before.
Anyone up for this?