Small Worlds and the Groundbreaking Science of Networks
KEYWORDS: complexity - complexity theory - laws of form - organisation -
...the study of networks as part of the general area of science known as complexity theory. In an abstract sense, any collection of interacting parts - from atoms and molecules to bacteria, pedestrians, traders on the stock market floor, and even nations - represents a kind of substance. Regardless of what it is made of, that substance satisfy certain laws of form, the discovery of which is the aim of complexity theory.
Some scientists have disparaged the search for a general science of complexity as a pipedream, and yet the ideas of the core of this book reveal that there can indeed be sound and specific principles of complexity theory. Some of the deepest truths of our world may turn out to be truths about organisation, rather than about what kinds of things make up the world and now those things behave as individuals.
The small worlds idea is one of the newest and most important discoveries in the science of forms, a science that has roots stretching into antiquity. To the Greek philosopher Plato, our world of perfect forms stood behind all real, tangible objects, and the purpose of all "right-thinking" was to come to know those forms, rather than to be led astray by flawed and imperfect representations of physical reality.
The German philosopher Immanuel Kant also saw a deeper reality lurking behind appearances - the reality of the "thing-in-itself", a kind of untouchable essence lying behind all physical objects.
In the emerging theory of networks and in complexity theory more general there is an idea that shares are spiritual affinity with these notions, even if it is grounded not in philosophy about in mathematics and empirical science. For the first time in history, scientists are beginning to learn how to talk meaningfully about the architecture of networks, and to perceive important patterns and regularities where they could see none before. This knowledge alone is leading to some remarkable insights: why does the World Wide Web function so efficiently and crash so infrequently? How does the living cell manage to go on living in the face of all kinds of errors and mistakes at the molecular level? Fundamental insight into these questions tumble straight out of the networks perspective.
The small-world networks first discovered by Duncan Watts and Steve Strogatz, as well as another kind of networks that are close relatives, appear to be pervasive in both nature and human society. The World Wide Web has now well over one million pages, and yet it does not take forever to get from one to another - a few clicks usually suffice, for the very same reason that it takes only six handshakes to go between any two people on our planet. There is a kind of the innate intelligence in these networks structures, almost as if they had been finely crafted and laid out by the hand of some divine architect. Scientists are only beginning to understand where this intelligence comes from, how it can arise quite naturally, and most of all, how we might learn from it.
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