Previously I mentioned Preferential Attachment (the “rich get richer” phenomenon of some networks) which explains why popular nodes in a network become highly connected, and are highly connected because they are popular, and are popular because they are highly connected, etc. We see this on the Internet as things either go viral or things basically don’t move at all, plummeting to obscurity and beyond! It happens with people, some of us are highly connected, some are effectively islands, and most have just the average amount of connections. However, we may be connected to highly connected people on social networks, such as the Fry, the GaGa, the Kutcher types. Those superstars tweet it all and get retweeted by so many followers to their followers in turn, and the cycle is thus reinforced.
However, we could be being fooled here, as the size of the connected population is huge. Our intuition is that one follower may be fairly easy to gain, two followers must be twice that much work, ten followers, ten times that time and effort. A hundred thousand followers must take more than a lifetime to achieve!
How old are you? More than likely somewhere in the range of 20s to 70s, with a few outliers outside of this range. It’s rare to encounter someone older than 100, it is predicted that the first 150 year old person has already been born. Maybe. Maybe in the distant past a person did reach 150 but nobody wrote it down. Maybe H5N1 will mutate into human to human transmissible form soon and wipe out two thirds of the worlds overpopulation. Who knows? The point is, we’re used to a certain range of ages, and to find someone over a century is unusual. We never encounter a person over a thousand years old. Or a hundred thousand years old. We never encounter a person taller than the tallest building. We never encounter a person several thousand times more intelligent than average. What about strength? What about shouting loudest? What about jumping highest?
These parameters are kind of within “human scale”. We’re used to thinking about a kind of tangible scale, expecting measurements to fall within certain familiar boundaries, and applying a linearity to these dimensions. A ten year old took ten years to get there, a thirty year old, three times that much! I dug a hole 1 metre deep in a day, in ten days it was 10 metres deep. And so on.
However, in some networks, we experience an alternative dimensionality of Scale-Free networks. These are networks in which certain dimensions might have a mean of a certain value but it’s easy to find a few instances of crazy escalation up into the sky. That’d be like walking around and seeing most people about the age of a human, but now and then meeting someone that was around in the Cretaceous era. This is a scale-invariant situation — there’s no human scale to it any more. The results might be said to follow a power law distribution or Pareto distribution. Superstars getting insane amounts of connections in social networking while the rest of us will never get beyond a few thousand (or a few, in many cases). The spread of the World Wide Web and the quantity of websites on it. The relative growth of wealth of Bill Gates, Mark Zuckerberg, Larry Page, Sergey Brin, compared to the growth in earning power of all those in the same class as those people at school.
Most people work in a job and get paid. The job requires a certain amount of work as the input, and in a fair situation, it pays somewhat under what you’re worth as a reward. Therefore we’re used to thinking about income in a way that has a linear relationship. I do a certain amount of work in a week, I get paid a certain amount of money in a week. Sounds fair? That’s how it is. So how is it we have examples of super-rich billionaires? Do they do vastly more work than you and I? I’ve only got 24 hours in a day, and so have they, so how do they get a hundred thousand times more work done than I can? It’s not fair. Why can’t we go to our boss and ask for a pay rise, of a hundred thousand times what we’re getting now? Sounds fair? Sounds fair to me.
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