Monday, 8 July 2013

Reality is Made of Loops But All We See Is Straight Lines


We tend to think in terms of straight lines. It is difficult to abandon linear "Euclidean thinking", or visions of cause-reality in a world goverened by a multitude of positive/negative often intersecting feedback loops. 

So it's all about networks. And networks of networks. When it comes to networks one immediately thinks in terms of transmitter and receiver nodes, hubs, or the shortest path from one node to another. However, networks also contain loops.

The cyclomatic number of a network (such as the one depicted below) is defined as C = L - N + 1, where L is the number of links (edges) and N is the number of nodes. The number represents the number of independent loops, or cycles, which may be identified within a given network.

In the example below there are 126 links and 20 nodes, which means that C = 107! This gives an idea of how intricate the information flow can be even in such a small network of 20 nodes.

Below we illustrate two example of such cycles which may be identified within the above map.

These are just two out of 107 possible loops! In case of the entire European Union (comprising 27 countries, each described via 24 macro-economic parameters) and which we analyze every quarter, there are a total of 648 nodes and 45180 edges (results from Q1 2011 analysis). The map is shown below.

This leads to 44533 independent cycles in which information flows in a non-stationary and turbulent manner, sprinkled with a little bit of chaos and irrational human decisions! You then wonder, for example, what is cause and effect in such a situation. How do you manage such a system. Can it be managed? If so, how? How can there be experts on such systems?

By the way, note how the system has evolved over the years to become almost critically complex and highly fragile - only a one-star rating!