1.1 Models and their Functions

Models can be classified in several ways. Their characteristics vary according to different dimensions: function, explicitness, relevance, formalization. They are used in scientific theories or in a more pragmatic context. Here are some examples classified by function, but also varying in other aspects. They illustrate the countless multitude of models and their importance in our life.

Models can explain phenomena. Einstein’s special relativity explains the Michelson-Morley experiment of 1887 in a marvelously simple way and overruled the ether model in physics. Economists introduced the IS-LM or rational expectation models to describe a macro-economical equilibrium. Biologists build mathematical growth models to explain and describe the development of populations. Modern cosmologists use the big-bang model to explain the origin of our universe, etc.

There are also models to control our environment. A human operator, e.g., controls the heat process in a kiln by opening and closing several valves. He or she knows how to do this thanks to a learned pattern (model); this pattern could be formulated as a list of instructions as follows: “IF the flame is bluish at the entry port, THEN open valve 34 slightly”. The model is not normally explicitly described, but it was learnt implicitly from another operator and maybe improved, through trial and error, by the operator herself. The resulting experience and know-how is sometimes difficult to put into words; it is a kind of tacit knowledge. Nevertheless one could say that the operator acts on the basis of a model she has in mind.

On the other hand, the procedure for aeroplane maintenance, according to a detailed checklist, is thoroughly explicit. The model is possibly a huge guide that instructs the maintenance staff on how to proceed in each and every situation.

Chemical processes can be controlled and explained using complex mathematical models. They often contain a set of differential equations which are difficult to solve. These models are also explicit and written in a formalized language.

Other models are used to control a social environment and often contain normative components. Brokers often try, with more or less success, to use guidelines and principles such as: “the FED publicizes a high government deficit provision, the dollar will come under pressure, so sell immediately”. Such guidelines often don’t have their roots in a sophisticated economic theory; they just prove true because many follow them. Many models in social processes are of that type. We all follow certain principles, rules, standards, or maxims which control or influence our behavior.

Still other models constitute the basis for making decisions. The famous waterfall model in the software development cycle says that the implementation of a new software has to proceed in stages: analysis, specification, implementation, installation and maintenance. It gives software developers a general idea of how to proceed when writing complex software and offers a rudimentary tool to help them decide in which order the tasks should be done. It does not say anything about how long the software team have to remain at any given stage, nor what they should do if earlier tasks have to be revised: It represents a rule-of-thumb.

An example of a more formal and complex decision-making-model would be a mathematical production model consisting typically of thousands of constraints and variables as used in the petroleum industry to decide how and in what quantities to transform crude oil into petrol and fuel. The constraints – written as mathematical equations (or inequalities) – are the capacity limitations, the availability of raw materials, etc. The variables are the unknown quantities of the various intermediate and end products to be produced. The goal is to assign numerical values to the variables so that the cost are minimized, profit is maximized or some other goals are attained.

Both models are tools in the hand of an intelligent agent and guide her in her activities and support him in his decisions. The two models are very different in form and expression; the waterfall model contains only an informal list of actions to be taken, the production model, on the other hand, is a highly sophisticated mathematical model with thousands of variables which needs to be solved by a computer. But the degree of formality or complexity is not necessarily an indication of the “usefulness” of the model, although a more formal model should normally be more precise, more concise, and more consistent. Verbal and pictorial models, on the other hand, give only a crude view of the real situation.

Models may or may not be pertinent for some aspects of reality; they may or may not correspond to reality, which means that models can be misleading. The medieval model of human reproduction suggesting that babies develop from homunculi – fully developed bodies within the woman’s womb – leads to the absurd conclusion that the human race would become extinct after a finite number of generations (unless there is an infinite number of homunculi nested within each other). The model of a flat, disk-shaped earth may have prevented many navigators from exploring the oceans beyond the nearby coastal regions because they were afraid of “falling off” at the edge of the earth disk. The model of the falling profit rate in Marx’s economic theory predicted the self-destruction of capitalism, since the progress of productivity is reflected in a decreasing number of labor hours relative to the capital. According to this theory, labor is the only factor that adds plus-value to the products. Schumpeter agreed on Marx’s prediction, but based his theory on a very different model: Capitalism will produce less and less innovative entrepreneurs who create profits! The last two examples show that very different sophisticated models can sometimes lead to the same conclusions.

In neurology, artificial neural networks, consisting of a connection weight matrix, could be used as models for the functioning of the brain. Of course, such a model abstracts from all aspects except the connectivity that takes place within the brain. However, some neurologists believe that only 5%(!) of information passes through the synapses. If this turned out to be true, artificial neural nets would indeed be inappropriate models for the functioning of the brain.

One can see from these examples that models are ubiquitous and omnipresent in our lives. “The whole history of man, even in his most non-scientific activities, shows that he is essentially a model-building animal” [5]. We live with “good” and “bad”, with “correct” and “incorrect” models. They govern our behavior, our beliefs, and our understanding of the world around us. Essentially, we see the world by means of the models we have in mind. The value of a model can be measured by the degree to which it enables us to answer questions, to solve problems, and to make correct predictions. Better models allow us to make better decisions, and better decisions lead us to better adaptation and survival – the ultimate “goal” of every being.