It is hardly news anymore, but there is a definite shift going on in science. Where the focus used to be almost exlusively on reductionism ie. an effort to understand the world by looking at ever smaller pieces and trying to understand them separately, now more and more attention is spent on the relations between objects.

Mark Buchanans book small world, uncovering nature’s hidden networks covers one part of this “new” science namely the discoveries in networks that have come very recently in many different areas. So what exactly is the common theme between the internet, fireflies in Thailand, neurons in our brains and the social networks that we’re all part of?

Structure! It seems that many of the different networks found in nature and constructed by us humans share the same structure, namely that of small worlds. This is why it’s possible to travel half way around the globe, only to run into the sister of an old neighbours. This is also why it is possible to link any of the 250.000 actors listed in the imdb to Kevin Bacon in an avarage of 2.9 steps. And it is the basis of the conecpt of “six degrees of separation”, that any person can be linked to any other in typically six steps.

The idea is this: If you have a network (ie. a number of nodes connected by lines – a graph in mathematical terms), there are many ways to “connect the dots”. You could do it randomly by connecting each node to 10 other random nodes. This would give you a network that is extremely connected and the average number of steps required to go from one node to any other would be very low (this is known as the dimension of the system).

Alternatively, you could wire each node to the 10 nodes closest to it. This would give you a very clustered network, but the dimension would be extremely high, ie. going between two nodes that are far from each other could require a huge number of steps.

It turns out, that many networks share both traits, they are both clustered and have a low dimension. This is possible because most connections go to nodes close by, but som connections (dubbed weak connections) can go to totally different places.

Mark Buchanan examines many such networks and describes two basic kinds, and also looks at the different conditions that will create such a small world network. He also examines the implications of the small world theory, and while these kinds of networks are not inherently good or bad, they have the ability to balance on the edge between chaos and order all the while maintaining a certain stability.

The book references the tipping point several times, and indeed it seems that the theory of small worlds is at least part of the theoretical underpinning for the phenomena of sudden large scale change described in that book.

I recommend this book highly. It explains a quite complicated and abstract area of science in an entertaining and informative way. And while the implications before us after only a few years of study in this field are already huge, there is no doubt in my mind that there are many more exciting discoveries ahead.