Simplifying the complexity of life by writing about it...
Raima:Forgive me for jumping in here to offer a general comment and ask a question. I'm a retired Marine Biologist who has been studying and writing about complex systems for years. I totally resonate with your blog site. My compliments to you!! Currently, I'm focusing on writing about patterns in nature (PIN) with the premise that PINs are not just pretty mathematical objects but are indeed manifestations of the organizing principles that define our universe. I'm writing an eBook on the subject and am currently tying scaling, self-similarity, and self organization together. One stumbling block is that there are a number of claims that self-organized systems are self-similar (fractal). But, no real explanation or proof is offered. To me it is an interesting topic because Geoffrey West has been talking a lot about power law distributions being a hint that there may be an underlying unity of organizational principles. I'd enjoy hearing your view. Contact info is at my blog site noted. Bill
Again:Like yourself, I see a very strong connection between Nature's aesthetic, spiritual, and logical voices. I anxiously await your new book.Bill
Hi, Bill,Thanks for your comments. I'll see if I can find a good place to leave a comment on your blog, but it's not arranged in the usual fashion. Perhaps we could connect on Google+? You can find me there at: https://plus.google.com/108153055530371640578/about?hl=enOne thing about your comment, though...just wanted to say that I don't agree with whoever it is that is claiming self-organized systems are always self-similar. Not true! Self-similarity is an interesting concept, related to chaotic behavior and fractals, obviously, but it is not directly connected to self-organization. Do you have a reference that shows where people make this assertion?
Hi Again Raima:I might add that self-similarity is present in complex systems where there might not be chaotic behavior. Patterns in Nature are complex systems driven by underlying networks. These networks are usually scale-free (self-similar). See Barabasi, et.al, Strogatz, Watts.Regarding the main question: One cite is by Laurienti, et. al "Universal fractal scaling of self-organized networks". What I'm beginning to see is that systems associated with networks can be scale-free. And, a large number of networks associated with Patterns in Nature are scale-free. The self-organization of a fish school (bird flock) is more like a regular network which I don't think is scale-free. But, the behaviors of fish (or birds) are claimed to be self-similar. I'm still trying to get it all sorted out in my own head and still trying to gather more information. But, I have seen numerous (and usually unsupported) statements on the Internet that self-organized systems are self-similar. Bill
Once more:You say:"Self-similarity is an interesting concept, related to chaotic behavior and fractals, obviously, but it is not directly connected to self-organization" One example where this statement is false is the Internet. Here we have a self-organizing system that uses preferential attachment. This is very much a scale-free system.It is being shown that many biological systems (ecosystems in particular) organize in much the same manner as the Internet example. So, one could say that self-organizing systems are scale free. I think the key concept is preferential attachment.Bill
Ah - I see what you're getting at, Bill. Self-similar NETWORKS are not what I would refer to as self-similar systems. They're interesting, but they're a subset of the ones I was talking about. The flocking birds example you mention is probably not easily thought of in terms of a network, but it displays self-organization, as do other examples from biology you're probably familiar with (slime mold aggregation, for example).It is possible that somebody has proved self-organizing networks to be self-similar, but I don't know enough network theory to really comment. The phrase "scale-free" refers to networks, but doesn't make a lot of sense if networks aren't involved.Anyhow, I think we probably need to be careful about distinguishing between networks and other systems that can display self-organization. The sentence you pulled out of my previous comment wasn't really about networks...it was about systems such as those the Lorenz attractor might be described by, for example.Out of time! Hope to continue this conversation later...somewhere. :)
Thanks for your comments and your help Raima. Because of you I'm now on G+ but need to find time to learn the nuances. What I'm reading is that G+ may be overtaking Facebook and Twitter. My entire focus of interest is on patterns in Nature. So, when I comment, I come from that bias/operspective. Since all patterns in Nature are complex systems and are highly connected, I look at network theory pretty closely. What is most interesting to me at the moment is the ubiquity of power law distributions AND apparently defined by an exponent that is a multiple of 1/4 for all sorts of pattern relationships within Nature (see Geoffrey West). Like yourself, I'm very spiritual (I see and feel God as I engage Nature) and I'm amazed that the ancient Chinese concept of the "Li" (that Nature can be described through organizing principles) is now starting to happen in Western science as the reductionist stuff fails to explain complex systems.Ciao !!