10.9. Conclusion – Model Fidelity and Usefulness
The reasons why different models present different opportunities for confidence building brings us full circle to the philosophical issue of model fidelity and usefulness that began the chapter. What is the value of a deliberately simplified model or representation of business or society? This question lies at the heart of the art and science of modelling and provides an appropriate conclusion for the book as well as an opportunity to review the various models we have covered along the way.
Models range in size from large and detailed to elegantly small and general. The spectrum is illustrated in Figure 10.23. On the left are analogue models, in the middle are illustrative models and on the right are metaphorical models. To appreciate the distinctions along this axis of fidelity compare the dictionary definitions of analogy and metaphor. According to Webster's Dictionary, analogy is derived from the Greek word analogia meaning proportion and equality of ratios. More specifically an analogy is an explaining of something by comparing it point-by-point with something else. For example, one might liken the atom to a miniature solar system (as the physicist Rutherford originally did) in which planet-like electrons circle around a sun-like nucleus. On the other hand, metaphor comes from the Greek word metaphora, a transferring to one word the sense of another. A metaphor is a figure of speech in which one thing is likened to another different thing by being spoken of as if it were that other. Consider for example the description in the following sentence. 'The tram, arriving with a tap-tapping of overhead wires, was like a giant yellow grasshopper rubbing its steel legs together' (Miller, 2001).
Figure 10.23. Modelling and realism – a spectrum of model fidelity
Both analogies and metaphors can help us make sense of the world, but their usefulness for this purpose should be judged differently. An analogy derives its usefulness in large part from the fidelity of the point-by-point comparison and the implications that can be drawn from the comparison. So Rutherford's atom as a miniature solar system was a big step forward from previous analogies that compared atoms to ball bearings or incompressible plum puddings. In that relative sense it was a useful analogy.[] By contrast, metaphors are looser. They do not purport to fit the situation point-by-point. Instead, they evoke vivid images in the minds of readers that help them to better envisage the situation, to examine more closely the imagined similarities, and thereby learn something new about their world. The usefulness of the metaphor is not so much in its fidelity but rather in its ability to stimulate reflection and learning. Hence, the comparison of a tram with a grasshopper mentioned above helps one to visualise the tram scene better. Whether or not the metaphor turns out to be completely accurate is not the main point. It simply needs to be plausible and vivid enough to fire the imagination.
[] However, viewing the atom as a miniature solar system later turned out to be a flawed analogy (though still useful) because it did not predict the stability and longevity of atoms. If one took seriously the point-by-point comparison of planetary electrons orbiting a miniature solar nucleus then the electrons should lose energy through radiation and spiral inwards to the centre, which they don't. This paradox was subsequently fixed with the quantum mechanical atom.
Analogue models portray problem situations with close attention to realistic detail and accurate scaling. Examples shown in Figure 10.23 are the soap industry model, World of Showers in Chapter 4 (as a model to investigate temperature instability among interdependent shower-takers) and, at the extreme of fidelity, an aircraft flight simulator. By contrast, illustrative models portray problem situations in terms of realistic feedback loops, but with less attention to detail and scaling. Examples are the market growth model in Chapter 7, the simple factory model in Chapter 5 and the fisheries simulators in Chapters 1 and 9.
Between analogue and illustrative lie the urban dynamics and medical workforce dynamics models in Chapter 9. They are each of moderate size and complexity (50 to 100 equations). Both models include realistic detail about the institutions they represent (city or hospital) and are scaled with real-world data. The medical workforce model draws its terminology, parameters and structure from the personal mental database of an experienced doctor and from numerous medical journal articles. The urban dynamics model, though quite abstract and dynamically complex, draws its structure and parameters from the collective mental database of city experts. The oil producers' model in Chapter 8 also lies between analogue and illustrative with its structure and parameters drawn from oil industry experts.
Metaphorical models portray feedback structure or inner workings in one domain to aid understanding of a problem situation in an entirely different domain. Examples are World of Showers in Chapter 4 (if used as a model for understanding competition for resources among interdependent business units), or the fisheries simulator in Chapters 1 and 9 (if used as a model for understanding overshoot of global carrying capacity by an industrial society).
Despite the appeal of illustrative and metaphorical models, fidelity of representation is surely important too. Common sense demands that a useful model bears some resemblance to the situation at hand. Simulators of fantasy worlds do exist (such as Tomb Raider featuring Lara Croft), but intense interaction with a fantasy world does not enhance understanding of practical policy and strategy. Nevertheless, it is an interesting question where to draw the line on realism, particularly in models of complex and poorly understood systems.
Consider again the two different uses of the world of showers simulator indicated in Figure 10.23. In Chapter 4, it was presented as an analogue model representing hotel showers whose occupants unwittingly share a fixed supply of hot water. The comfort-seeking shower-takers become locked into an escalating battle for hot water. The result is wild and persistent temperature fluctuations and deep frustration because neither shower-taker achieves a comfortable temperature – just like the real world. However, the same model is also a good metaphorical model to understand the puzzling dynamics of resource allocation among infighting departments of a firm. Internal competition for resources is common among departments that share manufacturing capacity or skilled salesforce. The resulting cyclical behaviour is often dysfunctional, as the shared resource moves back and forth between departments. The shower simulator is a vivid metaphor for this expensive tug-of-war that sparks lively debate among experienced business people about how best to control cyclicality and infighting through improved communication and greater tolerance of temporary performance shortfalls.
The hotel shower model is obviously not a realistic model of a multi-department firm. Yet it stimulates thinking about organisational dynamics because insights from shower simulations are transferable to the firm. A passage by Herbert Simon (1999, p 18), about 'simulation as a source of new knowledge' helps to explain why:
This brings me to the crucial question about simulation: how can a simulation ever tell us anything we do not already know? The usual implication of the question is that it can't ... There are two related ways in which simulation can provide new knowledge – one of them obvious, the other perhaps a bit subtle. The obvious point is that, even when we have correct premises, it may be very difficult to discover what they imply. All correct reasoning is a grand system of tautologies, but only God can make direct use of that fact. The rest of us must painstakingly and fallibly tease out the consequences of our assumptions ... The more interesting and subtle question is whether simulation can be of any help to us when we do not know very much initially about the natural laws that govern the behavior of the inner system ... Artificial systems and adaptive systems ... have properties that make them particularly susceptible to simulation via simplified models ... Resemblance in behavior of systems without identity of the inner systems is particularly feasible if the aspects in which we are interested arise out of the organization of the parts, independently of all but a few properties of the individual components.
In other words, structure gives rise to dynamic behaviour, a theme that is deeply woven into the fabric of system dynamics. Hence, a hotel shower simulator is a useful model for managers interested in dysfunctional dynamics of organisational resource sharing because it captures (in a vivid and amusing way) the feedback structure of interdependent and competing goal-seeking processes.
It is no coincidence that some of the smallest models are also the most insightful. Influential models such as World Dynamics, the market growth model and the Bass diffusion model have achieved their influence because they capture the essential structure and underlying regularities that underpin important dynamic phenomena and are accessible enough that people can test, reflect and learn from them. They are powerful transitional objects for better understanding our complex business and social world.