Simply Complexity (12 page)

Memory is a form of feedback. It represents a feedback of information from an earlier point in time. Other forms of feedback include information being fed back from somewhere else in space – like a cell phone call from a knowledgeable friend. In our office-filing scenario in
chapters 2
and
3
, we saw that feedback could be introduced into the filing system via a single object – an intern. However, a Complex System contains a collection of objects with each object potentially giving and/or receiving feedback in one form or another at any given moment. Moreover, the feedback in a real-world system comes both from within the system itself as well as from the outside – and the net effect will therefore tend to be much more complicated than in the case of the single intern and the files. Hence the resulting behavior or dynamics of the system – as observed from the output time-series – will tend to be far richer.

We know that a collection of inanimate objects such as a pile of files – or the pile of socks in your laundry basket – cannot re-order itself without adding some feedback. In other words, it requires the helping hand of the intern – or some blood, sweat and tears on behalf of the owner of the socks. By contrast, collections of people, animals and even cells are able to do this, forming well-defined groups or crowds for example. This is because the individual objects in question are alive, and hence each is able to put in effort and energy to make decisions and take actions. In addition they each have some kind of memory of the past which can guide their actions. It is this intrinsic feedback generated by these objects, both individually and as a whole, which is ultimately the source of the Complexity which arises in collections of all living objects – from collections of cells which produce organs, to collections of organs which produce humans and animals, to collections of humans and animals which produce crowds.

But is there anything more that we can say about the behavior of collections of living objects such as humans? After all, people are complicated – yet somehow their combined decisions and actions give rise to well-defined effects such as financial market crashes and traffic jams. It sounds like a hopeless task. That is why sociologists, economists, anthropologists, historians, and political scientists are all so gainfully employed – often analyzing the same human phenomena over and over again, yet managing to provide a multitude of different explanations. The idea of complementing this process, or possibly even replacing it in some cases, by a scientific theory of collective human behavior sounds ridiculous. However, there are signs on the horizon that the task is not actually as crazy as it first sounds – for the following reason. Even though we humans are complicated in terms of our tastes, thoughts, beliefs and actions, the
ways
in which we are each complicated as individuals may not be so important when we are put together as a group. So even though there are many differences between all our different personality types, these differences may cancel out to some extent when we are in a large enough group – and hence the group as a whole behaves in such a way that these individual differences don’t matter so much. This in turn opens up the possibility of building realistic simulations of
collections of humans using a computer program containing populations of “software people”. Such simulations may then mimic the overall behavior of a human Complex System such as a financial market or traffic – at least in terms of its general behavior. Indeed this is exactly what is now being explored in research laboratories such as ours across the world, exploiting the recent advances in virtual-world building as developed by computer game programmers, and by the so-called many-body mathematical machinery of physicists.

So although it might take volumes of books and TV documentaries to try to explain the complex life of someone like Winston Churchill, a randomly chosen collection of such famous people would likely behave in a similar way to a randomly chosen collection of the rest of us. A good example is given by
Big Brother
and
Celebrity Big Brother
: it makes little difference whether the individuals in the group are well-known celebrities or not, nor whether they are cooks, construction workers or clinicians – as a collection of humans, they seem to produce fairly similar dynamics when faced with the same everyday problems, as viewers are beginning to realize after putting up with series after series of these reality shows. In other words, a randomly chosen group of people tends to exhibit somewhat similar traits to any other randomly chosen group of people.

I am not saying that groups of people behave in a
simple
way. Nor am I saying that the ways in which groups behave is simply some scaled-up version of how individuals behave. Far from it – after all, the behavior of emergent phenomena such as traffic jams and financial market crashes does not typically reflect the behavior of any particular individual. What I am trying to suggest is that the overall behavior of such groups can be quite similar. In particular, even though the traits of any two individuals can differ wildly, the groups to which they belong can behave in quite a similar way. For this reason, traffic jams tend to look the same in Japan, U.K., U.S.A. and Australia, and so do financial market crashes – and yet the individuals involved can be very different. In other words, the ways in which collections of humans tend to “do” financial markets and traffic – and even, as we shall see in
Chapter 9
, wars and conflict – can be remarkably similar, despite
their individual differences in terms of geographic location, background, language and culture. This is one of the reasons why the patterns which emerge from such Complex Systems can be so similar – or in techno-speak,
the emergent phenomena have some universal properties.
You can see how this might arise as follows: we are all sufficiently different that any particular collection of us is likely to include people with a somewhat opposite character to us. For real-world examples, just think of your own extended family, school or college class, or office colleagues. Hence in terms of the behavior of the collection as a whole, our individual quirks tend to get cancelled out to some extent. So the variation between groups of us is less noticeable than the variation between any two of us as individuals.

There is a very important consequence of this for researchers attempting to build virtual worlds containing populations of software people, in that these software people don’t have to be individually as quirky as real humans. In short, they can be individually far simpler than real humans and yet still create a realistic overall collective behavior. And given that nobody knows how to create a real software person, this “safety in numbers” represents a fantastic simplification. Indeed, not only should this approach apply to collections of humans, but it should also apply to any other collection of objects which are individually complicated and hence exhibit a diversity of possible behaviors – for example, we should be able to apply it to cells in the modelling of a cancer tumor. This is the key idea that we pursue in the rest of the book, based on the extensive body of research which is now emerging in this area.

Our challenge in the rest of this chapter is to develop a generic, yet realistic, description of a collection of decision-taking objects such as people. Everyday human examples include whether or not to take a particular route home, whether or not to attempt going to a potentially crowded bar, whether or not to go to a particular supermarket, and whether or not to buy a particular stock. In fact such “whether or not” questions are part of a general set of decisions that we, and everyone else, are taking all the time – either consciously or unconsciously. Indeed, although many decisions we have to take are very complicated in their details, they
can pretty much always be broken down into “whether or not” type questions. Put more formally, they can be broken down into “choose 0 or choose 1” questions. So, the two possible routes home can be represented by 0 or 1; selling or buying in a market can be represented by 0 or 1; not going or going to a potentially crowded bar can be represented by 0 or 1. And since 0 and 1 are binary numbers, we can refer to this type of “whether or not” question as a binary decision problem. Such binary decision problems are like games which we are all playing all the time. In these games, there is an underlying competition for some kind of limited resource, or food. It might be space on a road or in a potentially crowded bar – or in a financial market setting, it might be competition for a good price. It doesn’t matter about the context: we each need to make a decision and hence take an action, and the net result of all our actions will generally determine which decisions were individually the best. But because of the limited resources, we cannot typically all be winners all the time.

Why is the competition for limited resources so important in producing Complexity in real-world systems? The answer is simple. In real-world situations where there is no competition, it matters little what decisions people actually make. In other words, if there is an over-supply of desirable resources – space on roads or in crowded bars or in supermarkets, money, fame, jobs, land, political or social power, food etc. – then it doesn’t matter very much what we decide to do since we will still have enough of everything we need, and more. In such situations, we could each go round acting in whatever way we wanted, either cleverly or stupidly, and yet still end up with an embarrassment of riches. Hence there is no need to learn from the past, or adapt. The need for feedback then becomes pretty meaningless since we are all getting what we want all the time. The end result is that the collection of objects in question will behave in a fairly simple way. In particular, the lack of dependence on any feedback or interactions between the objects will make the overall system
non
-complex.

Most real-world systems of interest do feature some kind of limited resource – and the individual objects in the system will typically fight tooth and nail to get hold of it. This competition might even lead to local cooperation within groups in order to gain some
kind of competitive edge – but the overall atmosphere is still one of competition. Examples include a financial market where traders are trying to compete for the best price; traffic where commuters are all trying to use a particular road; the Internet where surfers are all trying to access particular downloads more quickly; wars and terrorism where the different armed actors are all fighting for control of land or political power in a particular country. And remarkable things can then happen – for example, the emergence of crowds and opposing crowds which we call “anticrowds”. We’ll look at these more closely in a moment – but suffice to say, the spontaneous formation of such self-organized, collective phenomena is a true signature of Complexity. So not only do such binary decision problems represent a common everyday situation for all of us, it also turns out that they provide the perfect example of real-world Complexity. Furthermore, they provide the research community with an extremely challenging scientific problem which has, so far, no exact mathematical theory to accompany it. And yet all this richness arises from a situation as familiar as the daily commute to and from work, and a situation as fun as a trip to your favourite bar. So let’s take a closer look at such binary decision problems, casting the discussion in terms of that all-important issue of a Friday night out at your favourite bar.

It is Friday night and there is a great band playing at your favourite bar or club. Actually they play there every Friday, and you like to go there as many Fridays as possible
provided
that you can get a seat. But how do you know in advance whether you will get a seat? The answer is, you don’t. It is a small bar, and there is only limited seating – and there are also likely to be many others wishing to go as well. So what should you do? Make the effort to go all the way to the bar, only to find you can’t get a seat? Or stay at home and risk losing a great night out?

Let’s take a closer, more detailed look at this problem since it embodies what Complexity is all about. Indeed this is why Brian Arthur of the Santa Fe Institute first introduced it. Suppose that the
bar gets very uncomfortable to be in if there are more than sixty people present – in other words, the comfort limit of the bar is sixty. Let us write that in mathematical form by saying that the comfort limit of the bar is represented by the symbol
L
, and therefore
L
= 60. How many other people are also making a decision as to whether to attend on a given Friday night? Again, we will represent this as a symbol – this time called
N
. Unfortunately for all the potential attendees, there is no way of knowing what that number
N
actually is. Probably it is OK to guess that more or less the same group of people want to attend each week, in other words
N
is the same number each week. But that still doesn’t tell you what the number
N
actually is. For the purposes of our example, let’s pretend that there are 100 people who want to attend on any given Friday night. In other words, or rather in our mathematical words, this means that
N
= 100. So there we have it: the comfort limit
L
= 60 and the number of people wishing to attend on a given Friday night is
N
= 100. And therein we have a typical everyday example of a collection of humans competing for some limited resource, which in this case is seating in a potentially overcrowded bar. We also have the archetypal Complexity problem in the making.

Now the fun and games begin, literally, because every one of these one hundred potential attendees is – whether they like it or not – playing a game: a gambling game, to be precise, since they each have to decide whether or not to go through all the effort of getting dressed up, arranging for a babysitter if necessary, going out to the car, driving to the bar, finding parking, walking up to the door of the bar . . . just to run the risk of being stuck in a bar which is over-crowded. At the same time, they could simply decide not to bother, and instead sit at home . . . just to run the risk of being told later that they missed a heck of a night out in a bar which had seats to spare. It is a gamble. Not only is it a gamble, but the correct decision as to what to do will depend on what everyone else decides to do. There is no absolute right and wrong decision – it depends on what everyone else thinks is right or wrong. If they all go to the bar, clearly the right decision is to stay at home. On the other hand, if everyone decides to stay at home, the right decision would have been to go to the bar. It is a competition for a limited resource, and not everyone can win.