The Six Degrees of Separation ~ Part 1
I’m currently listening to Malcom Gladwell’s Tipping Point and it has heavily inspired this post. I highly recommend you give it a listen or a read. Something that this book covers is how a seemingly small influencer or event can lead to immense outcomes.
The first question he asks is how tall do you think a single piece of paper would be if you folded it simply 50 times. This is physically impossible but if you could how tall would that little piece of notebook paper stretch. Take a guess without looking, ask your friends, then go find out for yourself. I’ll answer in the next post assuming I remember.
I wanted to extend this to another phenomena he talked about which was the Six Degrees of Separation between any one person and any other person. When this was originally discovered it was ground breaking and nobody expected it, surprising given how its just kind of a joke now.
But as I was driving home I started thinking about it. How surprising is this really? One of the notes from the book is that on average a person knows about 40 people by the time they are twenty and double that by the time they are forty. We are going to lowball this thing and stick with 40 number, adding additional age just makes the case for this even harder and I don’t think that is necessary.
When we think about the SDS (Six Degrees of Separation) we marvel at how we are six points from someone as powerful as the President or someone as insidious as Kim Jong Un. This view requires an incredibly centric lifestyle, bordering on hubris. We see it as special because we only see ourselves and the target. We see this tendril reaching to them and it marvels us.
But what we don’t see is the network that lead to there. It isn’t just you that truly knows 40 people, the forty friends you have also know 40 people, and we’ve already reached 1,600 people in a single jump. By the sixth degree you are looking at a network of potentially 163,840,000,000 unique people. That’s roughly 23 times the current population of the Earth, which is way more people than I’d like to see around on this rock.
You are probably grumbling at this math because obvious that first node of people also know 40 people but who is to say that those 40 people would be unique to them? If two people know the same person that person does not count twice, they only count once. This is fair and with each new degree of separation that saturation becomes even more ridiculous, but keep in mind that this saturation is a product of the exponential growth of this system. We are also assuming that everyone in the world is only twenty, the varying ages of our population make the average considerably higher.
Imagine if every person knew only 26 unique people compared to everyone they know. Just 26, not 40, we won’t go that high.
The first person knows 26 people, those 26 know 676 between them, those 676 know 17,576 between them, those 17,576 know 456,976 between them, those 456,976 know 11,881,376 between them, those 11,881,376 know 308,915,775 between them, and finally that 6th degree knows 8,031,810,176 between them. Which is around 300 million more people than are on the Earth (or basically another United States worth of people).
Obviously this raises the question, why the hell do all these numbers end in 76? That’s neat right? Well yeah, that is really neat and it is something I’m going to need to look into because that kind of stuff delights me. While the exact math is probably very simple I’m a bit too tired to give you the exact number of people you’d need to uniquely know in your web to hit the world population but its roughly 25.565 which again is a pretty neat number.
For me I don’t think that the six degrees of separation are unlikely, it seems rather obvious by the nature of fractals and exponential growth.
Back to that original question then, with this thought in your mind. How tall has that little sliver of paper gotten after you’ve folded it fifty times?
Does this look very bad to anyone else? That’s an awfully big population bulge that is about to be leaving the work force in the states. (They’ll also start voting far more often at the same time, should be fun!)