(This is Part 6 in a series. Go back to Part 5.)
To me, this special quality of self-organization that all of nature's networks share is part of the mystery of the un-namable. After all, the universe could easily be one in which self-organization is not one of its qualities. It's easy to imagine zillions of potential universes that don't have the quality of self-organization—and yet this one does, to an incredible extent.
How extraordinary that this so! In this universe, we see everything self-organizing, from cycles in eco-systems to pre-biotic proteins to a rainstorm to a school of fish.
A friend recalls scuba diving in 15-16 feet of water and seeing a network of bait-fish spontaneously self-maintaining itself as a dynamic sphere. She watched as a baracuda launched itself into the sphere, selecting its meal. The sphere simply fluttered for a moment and then dynamically reformed itself into a sphere. She watched this, transfixed, for 15 minutes as the baracuda launched itself again and again into the sphere and the sphere simply kept dynamically reforming itself.
Researchers have discovered that if the lead bird in a flock of birds is taken out, the flock simply and instantly reforms with another bird at the lead. There is no "leader." The flock itself is the leader, self-organizing itself continually. An anthill has no leader either, or rather, the anthill self-organizes to lead itself.
Self-organizing systems have another interesting quality, that which researchers call the small-world quality. What happens is that as a network fluctuates in its process of self-organizing, certain nodes of the network become a little more "popular." That is, they become a little more connected to other nodes in the network.
It's been demonstrated mathematically that these more "popular" nodes are then much more likely to attract even more connections and become even more "popular." Scientists refer to this phenomenon in all seriousness as "the rich get richer." It can also be called "preferential attraction." Jesus recognized this principle implicitly when he said, "Those who have...will get more."
Preferential attraction means that the most popular nodes in a network tend to become more and more popular over time. It's even described by a mathematical law, called power law scaling, that states that, on average, as the "popularity" (connections) of a node doubles, its "competition" (the number of other nodes of its type) decreases by a constant percentage.
A colloquial way of saying all this, in the realm of economics, is that "wealth tends to concentrate in fewer and fewer hands." We see this phenomenon happening today in virtually all countries. Nothing surprising about this; it's the natural way that networks grow, economic and otherwise.
This preferential attraction, whereby the most popular nodes in a network tend to grow and become even more popular, has a strong positive benefit so long as it doesn't go too far. The benefit is, it creates this "small-world quality," referred to above, that is essential to a self-organizing network.
But what exactly is this "small-world quality"?
(This is the end of Part 6. Go to Part 7.)
—jim sloman, 12.8.02 for 1.24.03
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