A complex system is a system that is made up of numerous parts or elements interconnected with each other, so that unpredictable emergent behavior is generated from the individual behavior of each part. There is an aphorism that comes from ancient China and classical Greece that states that the whole is more than the sum of the parts, and that is precisely what a complex system is.
With an example you will understand it easier. Take the brain which is made up of neurons and other interconnected cells. The functioning of the brain gives rise to thoughts, emotions, behaviors, etc. No matter how much we studied each neuron in particular and knew its science perfectly, we could never predict how a person is going to behave or what their emotions are going to be.
This is the idea of emergence that forms the essence of what complex systems are. There is a very interesting aspect about them, and that is that, although they belong to different fields, they have common characteristics. For example, I am dedicated to the study of complex networks. Complex networks are representations of complex systems made up of discrete units, that is, in which the parts are individual units such as neurons, countries, computers, etc. What we have learned by studying these complex networks is that although they belong to very different fields, such as economics, biology, technology, infrastructure, etc., they all share a series of properties and behaviors.
A key property found very frequently in these systems is that there are elements that are connected to many other elements in the system, while most elements are connected to very few. This is a property that we find regardless of the type of complex network we study. Another fundamental property is what we know as the small world property. It consists of being able to navigate from one element of the system to another in a very small number of steps by following the network connections. For example, if we take a plane to go from a small town near here to the most remote city in central Japan, perhaps it is enough to take three planes, that is, the journey requires only three steps since it takes advantage of the property small world airport network. In social systems, this phenomenon is also known as the six degrees of separation. It’s the same idea, one person is connected to every other person through a chain of acquaintances with very few intermediaries. Another typical property is transitivity in interactions or, following the example of social systems, we can say that my friends’ friends are my friends. And there are many more, such as the existence of communities, etc.
Studying complex systems helps to make correct decisions. I give you a specific case. In the 1990s, Canada faced a crisis due to the depletion of cod fishing stocks, on the brink of extinction on the Canadian Atlantic coast. The authorities ruled that the seals were to blame for the collapse, since they had proliferated greatly and were threateningly preying on the cod populations, so they decided to exterminate them. They killed nearly half a million seals, yet the result was surprising: the cod population declined even further. The error was in assuming an inverse linear relationship between seals and cod, fewer seals meant more cod, but this is not the case. An ecosystem like the one where seals and cod cohabit in Canada is a complex system where many species interact with each other, with millions of food chains connecting the two species. What had happened by not taking this complexity of the ecosystem into account was that, by eliminating the seals, other species proliferated, such as certain types of sharks, which preyed on the cod with greater voracity. If you do not know all the chains that are interconnecting the elements of a system, it is very difficult to make correct decisions.
María de los Ángeles Serrano Moral ICREA professor at the University of Barcelona, researches complex networks.
Question sent via email by Julia Mayor.
Coordination and writing: Victoria Toro.
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