Friday, September 10, 2010

A Few Thoughts on Networks, Self-Organization, and Complexity

Networks with maximum efficient connectivity are neither orderly nor chaotic, but exist on the border of these two. At the border between order and chaos, you get a far-from-equilibrium state and self-organization. To have self-organization, you have to have a power law distribution of elements. Self-organizing, far-from-equilibrium systems are complex and maximally creative. The more complex a system, the more creative (or, more rapidly creative) it is. Greater complexity is achieved thorugh the creation of a nested hierarchy -- the social network is made up of people with minds, which is made up of an embodied neural network, which is made up of cellular networks, which are made up of chemical networks, which are made of atomic networks, which are made of subatomic networks. The most connected and, thus, complex networks are those made of both strong and weak bonds (friends and acquaintances). Which are likely to be more complex, though: networks of homogeneous or of heteroegeneous members? All homogeneous polycellular organisms are simple; all heterogeneous multicellular organisms are complex. Note, though, that multicellular organisms have difference cells programmed by identical DNA. When humans are homogeneous, they live in simple tribes. As the tribes grow, they become increasingly heterogeneous, allowing them to become even more heterogeneous, until humans reach a high level of complexity. Heterogeneous networks are thus more likely to be complex networks.
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