Futures, prediction and other foolishness

[Conference draft, subject to revision]

At the beginning of the twentieth century, three big ideas towered over the intellectual landscape. At its end, only one remains. Karl Marx, Sigmund Freud and Charles Darwin each had such a big idea that there must have seemed nothing left to do for fin de siècle intellectuals but to work these ideas through much as tradesmen manifest a brilliant architect's plan. Their ideas were compelling because they directly addressed a big 'why' problem - why are we as we are and not otherwise? They attempted to make sense of the history of the world - Freud at the level of individuals, Marx at the level of societies and Darwin at the level of all living things. Implicitly, they also held out the promise of prediction - if this is how we got here, then that must be the path; and if that is the path, then this is where we must be going.

I will sketch this story in a little more detail because it bears directly on the central concern of this essay - the problem of prediction in complex adaptive systems - because the three big ideas were each an idea about what we would now call complex adaptive systems. It seems that, for the first time, science and its penumbra of science-like rational activity had been able to create some ideas about complex adaptive systems that had at least some of the qualities of scientific theory. Thus, a century ago, ideas whose power depended on their rationality and empiricism were able to replace earlier ideas based on religious or other belief.

We know, of course, how it ended. By mid-century, Freud's psychoanalytic theories had been trashed and replaced by the beginnings of a physiologically based model of behaviour. Marx's ideas were trashed by mid-century too, at least in the West, and finally rejected by most of the communist bloc a generation later. Neither collapse was without cost, whether the cost of several generations of gulled physicians who wasted their lives on a fool's errand (not to mention their poor misled and mistreated patients), or the incalculable cost of the Soviet experiment on its suffering citizens. Darwin's idea, however, went from strength to strength. It is now one of the cornerstones of science, and the key to understanding all living things. Having discovered Darwin, science looked at the world in a new way and was itself changed. It is now not possible to undiscover evolution and go back to the way we were. Evolution has so changed science that it is no longer possible to imagine a scientific theory about living things and the things they make that does not embrace Darwinism either implicitly or explicitly.

It is an interesting thing that the idea that did survive is the biggest idea of all - the idea that made the greatest claims over the greatest intellectual territory. But there is also much to learn from the two big ideas that failed.

For our purposes here, we need to ask two questions about the rise and fall of these ideas. The first is: why were they such attractive ideas - ideas that people would actually die for? And the second is: why did they crash and burn?

I think they were attractive ideas because they offered explanations of history. They each, in their own way, offered a theory of how things got to be as they are. Thus they had the persuasive power of history by telling a rational story about the world. They added to that power by embedding their explanations inside a theoretical framework, and thus offered the possibility of prediction.

But I think the ideas of Marx and Freud crashed and burned for the paradoxical reason that they were scientific, but not scientific enough. Perhaps 'scientific' is too strong a word for such crackpot ideas; perhaps I mean 'science-like'. And by this I mean that they had some of the character of scientific ideas - they were rational, empirical, and even testable. Sadly, by being testable, they could be ultimately exposed and shown to be not part of the fabric of science.

There is something further we can learn from these cases, beyond the fact that science is a powerful way of sorting out loopy ideas from good ones. It is that, while each of these ideas was couched in the form of a story about the world, and those stories offered the possibility of prediction, none, in practice, really offered useful predictions in the way science had hitherto been thought to do.

We need to remember that, at the beginning of the twentieth century, much of the glory of science was invested in its power to predict. The physics of Newton had led the way to a view of science that was strongly predictive, a view predicated on the invention of powerful mathematical tools such as the infinitesimal calculus. These tools brought understanding and prediction first to the heavens and then to more earthly concerns.

But the systems studied by Freud, Marx and Darwin were living systems, and they resisted prediction even as they yielded, through Darwin, to explanation and understanding. Darwin showed that we could have a fully scientific understanding of living systems, an understanding fully consonant with our scientific understanding of physical systems, and yet that understanding would not yield prediction in the way of physics.

We now know something of the ways of complex adaptive systems: that set that includes all living things, some of the things made by living things, such as ecosystems and economies, and some of the stranger denizens of the worlds of computer modelling and artificial intelligence. So we are not so surprised by the lack of predictive power of science for such systems. And yet, those seductive stories that science tells about the histories of complex and simple systems alike tempt us to ask the question: what happens next?

We need to be able to temper such temptation with a realistic expectation of what science may be able to do with the notion of prediction in complex adaptive systems. We will see below that this will lead us to some new ideas about the nature of prediction and the nature of complex adaptive systems themselves.

The notion of prediction

When we think about prediction, we mostly think about the techniques of prediction, whether through Tarot cards or weather map. Or else we think about the prediction itself: that tomorrow will be fine or that a dark stranger will enter one's life. We tend not to think of prediction as an idea, a notion that we may be able, in some way, to say something sensible about things that have not yet happened, or about places that we have not yet seen.

I want to examine the notion of prediction at a very high and abstract level because, I will argue, the problems of predicting the behaviour of simple and complex systems are disparate. They can only be brought within the one intellectual framework at such a general level. It will also allow me to comment on the nature of this disparity without getting diverted into a discussion about deterministic versus stochastic prediction or becoming bogged down in a discussion about issues of precision and accuracy in prediction. But it will point to a fundamental problem about whether and which systems have a determined future.

Prediction, of course, embodies both the ideas of extrapolation - what happens beyond our purview - and interpolation - what happens where we have not yet looked within our purview. However it is in the sense of looking into the future, the sense of extrapolation, that prediction is mostly couched. It is in that sense that we will explore the notion here.

The notion of prediction is a bundle of different ideas which each need to be examined to see if together they make sense. In this bundle are ideas about objects and their boundaries, domains and environments, classes and instances.

When we predict, we usually are thinking about the future of some distinct thing. We do not as a rule mean the future of everything everywhere, but rather the future of some distinct bit of the universe. Moreover we are usually thinking, in some sense, about the immediate future, rather than all future time. Only some physicists have the hubris to imagine a Theory of Everything, and only some economists have the wit to say 'In the long run, we are all dead'.

Thus we talk about the future of things like the weather, the stockmarket, the solar system or a pendulum. Each of these is some sort of bounded object - we can describe both what it is and what it is not. We can say that this is the weather, and that this, pointing to a rock, or to the stars, or to the stockmarket, is not.

Each of these things exists in some environment or domain, and it is the future of the thing within its environment that we are interested in. Thus we are interested in the weather of Australia or the stockmarket of Tokyo or our solar system or that pendulum there. This also introduces the idea of classes and instances into our notion of prediction. We accept that there is a broad class of weather, but that it is sensible to talk about Australia's weather, just as we accept that there are many stockmarkets, many solar systems, many pendulums, even as we are interested in one particular instance of any of these classes.

Of course the idea of classes of objects brings with it the idea of rational classifications of the world - the idea that we can see various similarities in the objects of the world and that we do not have to assume that the world is composed of singularities. The existence of such similarities is fundamental to the notion of prediction because it is a precursor to a rational empiricism not to mention science itself. But it needs to be emphasised that it is not only science that bootstraps on this idea, all predictive approaches that use what we might call 'a logic' rely on the ideas of classes, objects and domains. Magics that see similarities between man and the cosmos use such ideas, as do neural nets. Science is only distinctive in that it uses scientific theory as well.

Taken together, the ideas of objects with boundaries, of domains or environments, of instances and classes lead to the idea of models. We can create a model object that is like, to some degree of likeness, some object of interest. That is, there is a sense in which the model object and the object of interest are instances of some same class. Likewise, we can create a model environment that is like the modelled object's environment. Both are likewise instances of some same class. If we have chosen our model object carefully it will have the useful property of exhibiting dynamics. That is, it will have a model of time in its environment. And if we are even more careful, our model of time will tick over faster than real time.

In this way, we may be able to observe the state of our modelled object at some future modelled time. All scientific prediction relies on this simple philosophico-logical trick - if the model is like the object, that is, in some class with it, then the object's future is like the model's future. If we play the trick, we call the model's future a prediction about the object's future. It is the same trick whether we talk about big stuff like the future of the solar system or little stuff like the swing of a pendulum.

It is a matter of enormous moment that, for many systems, this trick works and works brilliantly. But it is also a matter of enormous moment that for some systems it does not work at all. How we distinguish those systems is the matter I will now turn to.

Simple models, good models

This sort of prediction depends on a whole lot of things being right, and getting them right is a creative act as much as a scientific one. This is why good predictive modelling is as much art as it is science, and why words like elegance and beauty can be used in modelling as in mathematics. To build a good model we need to get the object and its environment right, as well as its class membership, and then we need to do the same for the model. We need to take particular care to ensure that the model and the object are each instances of some same class that will help our understanding.

Good models capture the essentials of the modelled object and its dynamics, but are usually simpler in ways that aid understanding. Some physical systems make this process relatively easy. They are composed of relatively few different sorts of entities with strong clear interactions, and are often dominated by inverse square relationships, so that only the strongest and nearest entities really matter. Modelling such systems is relatively straightforward. We can create models that are so elegant that we call them physical laws, whether Newton's deterministic laws of motion or the more statistically based gas laws.

Such models are able to create powerful, detailed and precise predictions of the dynamics of the modelled objects. Indeed, such systems are highly determined and inherently predictable, and the modelling problem really is to find the model that best displays the predictions.

Models of complex adaptive systems are more problematic. They challenge the idea, developed since Newton's time, that good models equals simple models equals predictive models. Or put another way, they challenge our philosophico-logical trick. In the first place, complex adaptive systems are characterised by many different entities, most of which are more or less weakly interacting, and with interactions that are diffuse and non-linear. As systems they show openness, fuzziness, messiness, individuality, novelty, learning and adaptation. They blur the distinction between object and environment. Their dynamics show surprise and emergence. It is not clear in what sense they are determined, or if they are inherently predictable at all.

When we use the same ideas to analyse the modelling of these systems as we use to model simple physical systems, we come up with different results. We find that 'getting things right' and 'capturing the essentials' are themselves more complex processes than for simple systems. We find that the character of the modelled complex adaptive system is embedded in the fine detail of the many entities and their interactions, not in the gross pattern of a few strong linkages. We find, in fact, that we need to build a model complex adaptive system in order to model a complex adaptive system.

In fact, we have to 'set a thief to catch a thief'. These model systems are simpler, to be sure, than the systems they are modelling, but running them in 'model time' does not create dynamics that have the same character of prediction as does running a model of a simple physical system. The model systems show the characteristic adaptive and emergent behaviours of complex adaptive systems that make them unsuitable for predictive purposes.

Hogeweg and Hesper's bumble bees

Let me descend from these abstract, theoretical heights by discussing a concrete example - bumble bees. Paulien Hogeweg and Ben Hesper are theoretical biologists at the University of Utrecht. They have been working for many years on complex adaptive systems, in fact since well before they were called complex adaptive systems. They published an elegant paper in 1983 on the dynamics of bumble bee societies (Hogeweg & Hesper, 1983) using a modelling technique that they then called 'individual oriented modelling', but which we now call 'agent based modelling'. The paper is of particular interest here, in that, being a pioneering work, it clearly describes how it departs from the more traditional modelling.

The natural history of bumble bees is fascinating from the point of view of emergent behaviour. In the spring, new colonies of a few dozen individuals are created from eggs hatched by a queen. These eggs hatch into larvae that then pupate into adult worker bees that forage for the colony, and do other chores about the nest. The bees have a social dominance hierarchy led by the queen which leads to the emergence of two castes of workers - elite workers which interact frequently with the queen and who will lay eggs later in the season, and common workers who never lay eggs. The queen and the elite workers use their dominance to control the production of eggs. In the late summer or early fall, the queen may lose control of the nest and new queens rather than workers may be produced. This switch from worker to generative offspring can be a chaotic time in the nest with workers shifting their dominance levels dramatically, elite workers reverting to common workers, new elite workers emerging, and the queen sometimes being driven off the nest. The process is brought to a halt by the onset of winter in which the bees hibernate or die, sending out new queens in the next spring.

Ethologists are not able to predict, from a knowledge of the natural history, which of the initially identical workers will become elite workers, when or if a switch will occur, or what its consequences might be.

Hogeweg and Hesper built an agent based model - itself a complex adaptive system - of a bumble bee colony, emphasising the natural history of the bees, with the basic element of the model being an agent - a bee - that 'lived a life' and interacted with other bees. The model used a simple dominance rule for these interactions as well simple rules for the feeding, foraging and housekeeping behaviours seen in the bees. They show 'how individual behaviour, based on simple rules and using little information, generates a social structure, which being the environment of the individuals, causes a more structured behaviour of the individuals and individual variation in their behaviour'. Their model shows emergent behaviour strikingly similar to the real thing: elite and common workers emerge and progressively differentiate themselves during the life of the nest, the switch to production of new queens frequently occurs, and sometimes the queen is driven from the nest.

But this study is important for what it does not show, for it does not show prediction. It shows instead a model which allow us to explore what we might call 'bumble bee space'. This space is quite unknown to us, and the model is like a simplified map, a sketch, of the space. The model colony is like a real bumble bee colony, but yet more simple than any real one. It is recognisably a bumble bee model, not a honey bee model, say, and yet it is not particularly more like one species of bumble bee than another. We may think of it as a new species of Bombus. Just as we learn something of all species in a genus by studying one species, we learn something of bumble bees in general by studying the model.

There is a sense in which we may say that the model explores the potential or possibilities of the space just as each species within the genus explores the potential or possibilities of the space.

However the model, like each of the real species, does not exhaust the potential of the space. Each is created from, or emerges from, the local interactions, and so is strongly contingent on its own local history. This sort of emergence is distinctly different from the emergence of ensemble properties of a gas, say, where we may generate a statistical dynamics which is a general solution to the 'gas space'. Our model is a purely local solution or exploration of the space.

There can be many models, of course, each exploring different parts of the space, but together they do not exhaust the space either. Because of the intense individuality of each model, it does not make sense, except at a very high and abstract level, to think of the ensemble properties of the collection of models. Thus it does not make sense to collect such models and produce statistical averages and so forth.

We can now see that, when used as models, complex adaptive systems create a third class of models that are explanatory but not predictive. They are distinct from deterministically predictive models of the dynamics of individual entities, such as pendulums, on the one hand and stochastically predictive models of ensemble or populations, such as gases, on the other.

Lessons for ecology and economics

I conclude with some thoughts on what this means for ecology and economics, disciplines whose project is the understanding of particular complex adaptive systems.

The first has to do with the fitness of models. The best models of complex adaptive systems, in the sense of increasing our understanding of them, will be other complex adaptive systems. I argued earlier that model and object need to be both instances of some class. The 'tightness' of the class bears on the fitness of the model. The essential qualities of any complex adaptive system, such as its individuality, emergence, novelty, learning and so on, can really only be effectively captured by another complex adaptive system. It follows that the most powerful models of ecosystems and economies will be complex adaptive systems.

The second is that economies and ecosystems, as complex adaptive systems, are inherently unpredictable as a whole. Their futures are not determined. Their global behaviours emerge from their local interactions in complex, historically contingent and unpredictable ways. It may not even make sense to talk about prediction of these systems.

The third is a corollary of this: the extent to which models successfully predict bits of these systems is a measure of the extent that the bits may not be important to the understanding of the system. Thus the successful prediction of global variables like M3 in economies or carbon flow in ecosystems may be an indication that these variables are not really coercive in the behaviour of the system. Hogeweg and Hesper would say they are not 'interesting' variables.

The last says that using models for exploration is not a proxy for prediction, it is instead of prediction. Its purpose is to enhance understanding, not to describe the future. We may even say that prediction is all we are able to do in simple systems, whereas the interesting problems, the scientific problems, await exploration.

Exploring is not only what we do with complex adaptive systems, it is what complex adaptive systems themselves do. Science itself, I have argued elsewhere(Bradbury, 1999), is a complex adaptive system, and it is this system that does the exploring of the worlds of models and reality. Having complex adaptive systems explore the behaviour of other complex adaptive systems that model yet other complex adaptive systems is a piece of recursion that I will explore another day.

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