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.


Ashwin said...

Troy - I'm sure you already know this but Stuart Kauffman has done a lot of work on the thesis of complex adaptive systems existing at the "edge of chaos". I'd also recommend Simon Levin's book "Fragile Dominion" which has a great philosophical discussion of the topic especially in the last chapter.

Enjoy your posts on complex adaptive systems - you should definitely try and write some of these concepts up in more detail. There's a lot to be explored in the connections between biology, ecology and macroeconomic systems. It's a longstanding amateur research project of mine - you may find this post interesting

Troy Camplin said...

I am quite familiar with Kauffman. I have his 4 books. Levin's book I just put on my Amazon wishlist. I am thinking through these ideas precisely because I am writing a paper on Hayek's spontaneous order theory of the mind. I have also applied these ideas in a paper titled "The Spontaneous Orders of the Arts", a link to which you can find on the left side of the main page of the blog. I have also written on the relations between the spontaneous orders of the mind and moral evolution. The link to that paper is in the same section.

Ashwin said...

Looking forward to the paper on Hayek!

Troy Camplin said...

Let me know when you've finished it. We can discuss it here if you'd like :-)

Jim said...

Hayek, as an Austrian, did a great deal of research on complex systems to explain the economy.

Much of the research on complex systems, I humbly believe, bogs down because it attempts to find utility in complex systems using traditional mathematics.

But the inherent value and structure in complex systems is that they are inter-causal and therefore adaptive.

I have done a great deal of research on complex systems in the last two years. I am writing a book proposing that complex systems predict how to organize the hierarchy or structure of organizations to improve their dependability and creativity at the same time.

Some of those thoughts are on my website: Leis Network. You are welcome to read it if you are interested, although I have not fully fleshed those ideas out there.

Troy Camplin said...

Sounds like we're on the same page, more or less. The great thing about blogs is that you can use them to flesh out ideas.