Complex systems are more interesting than linear ones.

I have a big problem with making lists. Lists are not actually very informative. They are an ineffectual way of presenting information, because they are not very intuitive or visual. Lists are linear, unlike most of reality, which assembles itself into complex networks and systems.

They do not effectively portray the relationships between their elements. I wish I could draw/write lists in systemic networks effectively, and I spend a lot of time thinking about how I could do that. The best solution appears to be in the form of images, which is why I’m beginning to invest time and energy learning how to draw.
Here is a far more effective way of ordering information. The manner in which the information is ordered becomes a valuable source of information in itself. We are able to see and appreciate complex systems with more clarity, and this helps us both understand them better and make better and more effective decisions in manipulating them.

Diagram of different network topologies.

Image via Wikipedia

I think our love for linearity stems from the human desire for a narrative. Things just seem to make sense to us a lot easier when we move from point A to B. And indeed, I think it’s safe to say that we begin our learning in terms of simple A to B relationships. It often confuses a young child to hear Mama calling Papa by a different name, or to hear that a circle can be blue and round at the same time. I imagine that a young child’s mental network is simplistic and largely one-to-one. As it builds more and more relationships, it becomes tedious and ever-long, and somewhere along the way a leap is made from having many one-to-one relationships to several one-to-many and many-to-one relationships instead. Well, that’s my theory, anyway. I’m no early child developmental specialist.

Here we have a network representing language. Imagine that the colored dots represent various language elements – orange for vocabulary and yellow for grammar concepts. The larger ones have been around longer. They’ve seen more. And heard more. As a result they’re stronger, and better developed, than the smaller ones. The lines that connect the elements suggests relationships – one element following another, depending on it, always appearing with it, being related somehow in meaning or function.

Now, imagine when you first learn a new language- say, Mandarin, or French. You initially build your network in terms of simple one-to-one relationships- “Good Morning” is Bonjour, you memorize. But you cannot claim to truly speak or understand the language until you have developed some sort of systemic proficiency, until you have built a massive network. Concepts like grammar and syntax are not independent of these relationships- they are borne out of them.

I believe the same thing applies to consciousness. See also: Anonymous authority, social pressure, patriotism- all of these things are precipitated out of the relationships of many elements in complex networks, that cannot possibly be studied and/or understood independent of the nodes.

This image depicts the network of emails in an organization.

Characteristics of complex systems:

  • Feedback loops
  • Self-regulation of behaviour
  • Non-determinist, non-linear
  • Spontaneous emergence of order and collective behaviour from “democratic” and local interaction of the system’s elements
  • Bottom up
  • Patterns emerge
  • Complexity borne out of simple local rules

The Modern View of the Universe

This is a section of the Universe.
.

If you pay enough attention, you will find systems and networks everywhere you go. Anything of depth and complexity assembles itself into networks, just like language, economies, human knowledge and academia, cities, consciousness…

Visualisation of Wikipedia page linkage network in a small subgraph of pages, by Ian Pearce. [ source ]

Weighted, directed graph of online citation network, by Rosvall & Bergstrom. [ source ]

Rosvall & Bergstrom rendered this directed, weighted graph visualising an online citation network between several thousand academic papers. The volume of citations is expressed in link widths and colours, the size of the nodes communicates the amount of time spent surfing papers in that topic by readers. In this analysis they found hierarchies of topics, with many flows from the applied sciences directed at a smaller set of natural sciences. These natural sciences in turn form a ring-like topology of citations between themselves.

So in these knowledge networks we see different topologies at different scales, we see scales of connectivity.

Something I find terribly interesting is how aesthetically pleasing these networks are. Our brains are somehow capable of making sense of them (the brain itself being one such complex network!), and it looks beautiful and coherent, rather than random chaos. I have a theory that aesthetically pleasing abstract art often contains such patterns and networks- which is why some abstract art captivates the eye, while my random splotches of paint on canvass are worthless eyesores.  I think there is a science to aesthetics- pi, the circle of fifths, the golden ratio and all that- perhaps nature appears to be so beautiful because we are somehow intuitively able to make sense of it- that is why trees are relaxing to look at, I think, because they are made up of self repeating patterns and are hence easier to absorb.

Below is the map of the bus routes in London- you can see how they resemble the circulatory system of a living, breathing organism- and that is what London is, as is language, and consciousness, and any other complex-enough system.

I have, in my haste to put this blog post together, failed to properly list out my sources. Credit is due to men and women far more learned than I- I’m simply echoing and sharing their observations and adding a few of my incoherent and unrefined thoughts. My purpose is not to prove a point so much as it is to provoke you to think and hopefully look at things in a new way.

There is a lot about all this stuff that I don’t know anything about at all, but I find it absolutely fascinating, riveting. Just thinking about it gets me excited. The future of human knowledge, language, consciousness, of social structures, politics, economics- all of these things will surely benefit from a deeper study and understanding of systems and networks.

About Visakan Veerasamy

I work at ReferralCandy, write at PoachedMag and blog at... here. This is my blog. You can find me on Twitter at @visakanv. I deactivated my Facebook account a while ago because the noise was too much for me to handle. How does this authorship nonsense work?
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3 Responses to Complex systems are more interesting than linear ones.

  1. visaisahero says:

    I will continue to edit and refine this post to make it easier to understand and to correct the mistakes, inconsistencies and opacity that are sure to arise. Your help is greatly appreciated!

  2. nicole says:

    your post reminded me of this, perhaps they may be of some interest to you- nothing conclusive of course, but just a cool concept

    http://www.wired.com/wiredscience/2010/01/slime-mold-grows-network-just-like-tokyo-rail-system/

    http://news.sciencemag.org/sciencenow/2010/01/21-01.html

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