Simply Complexity (25 page)

One interesting modification to this model, is to add “super-daters”. In particular, suppose an existing pair can be broken up by the sudden appearance of a more attractive male or female appearing on the scene. In other words, someone appears who is far better in terms of fulfilling the preference list of one of the pair.
We can use these computer models to find out what happens in such a situation by adding people with “magic lists”. In other words, they have pretty much everything a woman or man could desire. It turns out that having relationships break up in this way – for example, by meeting someone better at a dinner party – can give rise to a curious effect in the population’s dynamics. Such supermen and wonder-women tend to break up many weaker relationships, but can only form one relationship themselves at any one time. Although obviously a destructive process, these break-ups indirectly allow the resulting singles to search around for a potentially better match. Although they may then spend time fruitlessly chasing the super-agent, their travels may allow them to accidentally cross paths with someone who is a better match than their original partner.

This entire discussion, while cast in the language of dating, could equally well apply to businesses looking for clients and vice versa, or institutions looking for partnerships, or people looking for trading partners on the Internet, or search engines looking for word matches on web-pages. For example, you may be a customer of a particular gas company but you suspect deep down that there might be another company out there that would be better for you. It is just that, depending on your threshold, you may have a certain reluctance to want to switch unless someone from that other company actually comes knocking on your door and provides you with the impetus you need. However, there is one big difference between this and standard romantic dating etiquette: in the commercial and political arena, the relationships in question will typically be multiple in the sense that one company is in a relationship with many customers. Polygamy is permitted!

Teaming up with Tom Cox, Richard Ecob and David Smith have tried out all manner of interesting generalizations of this model. For example, they have tried introducing the idea of births and deaths to simulate a population which is continually replenished from the outside with a supply of single men and women, while
taking others permanently out of the dating market. It turns out that this situation gives rise to a remarkably stable state within the population – in other words, replenishment of the population in the form of new blood is good for a healthy dating scene. They have also shown that it can be beneficial for a person who isn’t in a relationship to reinvent themselves – in other words, to create a new personal phenotype. Of particular interest is the case where unsuccessful agents try to reinvent themselves by copying successful agents.

David Smith and Ben Burnett have recently taken the mathematical description of the model further by allowing each man and woman to act in such a way as to try to maximize the time that he or she spends in a partnership. The more time spent in a relationship, the more satisfaction drawn. This provides a far more sophisticated set of dating scenarios and situations. They found numerically that there is a highly non-linear relationship between the expected satisfaction level, the threshold for formation of a relationship, and the degree of sophistication of the individual agents. In order to explain this finding, they have developed an analytic theory which depends on the average amount of time which an agent spends in a relationship and the probability of finding a suitable partner on the network. Their analysis can be applied to any network topology, and can be adapted to include biased interactions. For example, it can describe situations where an individual is more likely to meet his or her previous partner. Hmm – I’m sure we all have our own views about such reunions.

There are many situations in life where one would actually like to
prevent
pairs or groups from ever forming, and where these models can therefore provide insight. An obvious old-fashioned example is that of human chaperones in which a third-party is introduced in order to keep a relationship from forming (literally). But there is also an interesting example in the medical setting of superbugs and viruses. Suppose a superbug or virus emerges for
which no cure is known. Given the right kind of third-party chaperone – in other words, a suitable protein, micro-organism or artificial nanoscale machine – it might be possible to keep such a superbug or virus away from particular defenseless healthy cells, tissues or organs.

This raises an interesting question as to which defense strategy such a chaperone should follow – defensive defense, or attacking defense? This problem is possibly easier to understand using a farming analogy involving wolves, dogs and sheep. Imagine you are in charge of a flock of defenseless sheep, and you know that somewhere nearby there are wolves. You have the possibility of deploying a limited supply of dogs to stop the wolves from reaching your sheep. The question is: what strategy should you train your dogs to follow, in order that they prevent the wolf-sheep pair from ever forming (i.e. to prevent the wolf from killing the sheep)? Should the dogs’ focus be to chase after the wolves at the risk of leaving the sheep unprotected? Or should they encircle the sheep hoping that the wolves won’t break through? This problem is currently being studied by Roberto Zarama and Juan Camilo Bohorquez in Universidad de Los Andes, Bogota, and we return to it in
chapter 10
.

There are several ways in which people can form groups. In particular, group formation can be unintentional – for example, certain subsets of people may just happen to be following the same strategy, as in the case of the crowds and anticrowds of
chapter 4
. Or it can be intentional – for example, where individuals are looking for a partner, as in the dating scenario of
chapter 8
. In this chapter we turn to think about what such groups might actually do once they have formed.

Groups of people can be violent. History is riddled with examples of crowds initiating tortures, executions, riots and attacks. But perhaps the most violent act of all is the collective human activity of warfare itself, in which several groups of people simultaneously fight for some kind of gain. This competition to gain something can be seen as a competition for some kind of limited resource – just as drivers effectively fight over space on a potentially crowded road, bar-goers effectively fight over seating in a potentially crowded bar, and traders effectively fight for a good price in a financial market. Even when dating, we are effectively fighting – albeit in our own group of one – for the rare commodity of the perfect partner. Likewise in wars and human conflict, there is a fight going on for a limited resource, where the resource in
this instance corresponds to land in a given country or part of the world – or political, social and economic power.

But if wars are just another example of collections of humans competing for some limited resource – as in the traffic, bar, or markets – then they are also examples of Complexity in action. The fascinating thing is, therefore, that we may be able to understand wars in terms of such Complex Systems analysis. This would in turn suggest that the way in which wars evolve has less to do with their original causes and more to do with the way in which humans act in groups. Indeed, it is often reported in wars that many of the people doing the fighting do not actually know why the war started in the first place, nor have they been told the concrete objectives which the war’s originators wished to achieve. A good example of this is the on-going guerilla war in Colombia, South America, where there are several different armed groups. It turns out that many of the present combatants are unaware of their own side’s overall agenda – they simply want to “beat the others”.

In
chapter 6
we mentioned how stock markets in very different parts of the world tend to show the same fractal patterns in their output price-series. We attributed this to the fact that any particular market’s movements simply reflect the activity of its traders – and, irrespective of their origins or nationalities, traders are just human beings making decisions based on the information being fed back to them. Even though they may occasionally respond to particular exogenous events in their own environment, most trader activity is endogenous in that they are reacting to their own collective past decisions – as in the everyday scenarios of
chapter 4
. So why shouldn’t the same reasoning be applied to explain the dynamical evolution of wars? In this chapter we’ll look at some very recent research which offers strong support for this idea of a
universality
in wars, as a result of generic human activity.

Wars used to be simple – or rather, it used to be relatively simple to understand the mechanics of how wars were fought. There were several reasons for this. First, there were typically only two opposing forces – for example, the Saracens and the Crusaders. Just like God and the Devil, or Good and Evil – although, of course, which was which depended on which side you were on.
Second, the weapons which each side had available were similar. In other words, the same technology was available to each side. Third, the sizes of the two armies were usually fairly similar. For these reasons, each side would be willing and ready to fight in a similar way to the other. This led to very conventional warfare. Given such symmetry, the method of confronting the enemy was typically to line up all of your own army on one side and let your opponent do the same on the other side. Then at dawn you would simply try to knock the stuffing out of each other. There was very little element of surprise. When things became less symmetric – for example, when an army found itself fighting on terrain that was much better suited to the other, or with far fewer soldiers – strategies would become more important. However, the basic underlying symmetry typically remained.

As imperial and colonial histories developed warfare became less symmetric. In such asymmetric situations the sizes of the two armies involved are no longer similar, nor is their respective technology and weaponry similar. Indeed, civilians might also be ready to join in the fighting using hand-made weapons – hence the “enemy” for a conventional army might become relatively unorganized, possess more provisional equipment and weaponry, but be far deadlier because of its sheer numbers and potential indistinguishability from the civilian population. Such was the case in Vietnam, Northern Ireland and Afghanistan – and more recently in Iraq and Colombia.

In addition to this increasing asymmetry over time, recent wars have tended to involve more than two sides. Up to the end of the Cold War there was a definite sense of “war games” being played out between just two players. Irrespective of whether they were similar in size and/or technological advantages, side A would react to what they thought side B would do – or, as in chess, side A would make a pro-active move in order to prevent side B from doing something potentially advantageous. As a result the equivalent of a stalemate typically arose. Each side only had to work out what the other side might do, or had just done, in order to know what it should do. So war, while of course still horrific, was relatively simple – like any game involving just two players.

Wars involving three or more players – be they insurgents, guerillas, paramilitaries or national armies – are far more complicated. Just as we mentioned in
chapters 2
and
8
, frustration can arise. If A hates B, and B hates C, does that mean that A must therefore like C? Not necessarily. Hate is many-sided, just as love can be. Again we only need to think about the ongoing insurgencies in places such as Colombia, where there are many armed groups, to see the potential complications. A sides with B, B sides with C, but A hates C. Therefore A starts to fight B so as not to favour C – and the whole process carries on. Indeed, such frustration may be why many modern conflicts seem to go on and on without reaching any definite conclusion.
Two is company, three is Complexity
– and as we have seen throughout this book the dynamics and time-evolution of such “many-body” situations is very complicated. And like other Complex Systems, any given war will have the unfortunate ability of being able to generate extreme events all by itself – just as a market can spontaneously produce crashes and the traffic can spontaneously produce jams.

The evolution of such many-player wars can be thought of as an ecology in which there are many co-existing species. In Colombia, for example, the war involves several guerilla groups, terrorists, paramilitaries and the army. But what makes such wars so complex is that nobody knows exactly how these different species will interact at any one moment. For example, if a guerilla group from army A meets a guerilla group from army B, will they fight? Or will they choose to collaborate by ganging up on a nearby army C? Or will they simply ignore each other – or maybe even consciously avoid each other? And how does all this change in time?

Adding to this complexity is the fact that a modern war such as that in Colombia, and to a lesser extent Afghanistan, will take place against a backdrop of illicit trade such as drug trafficking. This activity provides “food” for some of the groups in the form of money for buying supplies and weapons, and thereby helps feed the war as a whole. Just as in the case of a growing fungus or cancer tumor, Colombia in particular has multiple nutrient supply-chains corresponding to (1) the flow of cocaine along supply-routes from the jungle to the cities, and then to the U.S. and Europe; (2) the flow of cash which this cocaine supply then
generates; (3) the flow of kidnapped victims from the cities back to the jungle. So just like the fungus which thrives in the forest, or the cancer tumor which thrives in the host, these armed groups are fed by a rich source of nutrients which allows them to self-organize into a reasonably robust structure – and just like the fungus or cancer tumor, this makes the problem very hard to get rid of.