20 2 Modelling Basics
principle: in many cases it is possible to acquire about 80% of the
knowledge about a certain domain in about 20% of the time.
• The probability of each prediction coming true is proportional to the
knowledge about the respective domain.
• It is impossible to fully control anything that is not well-known (or learned).
On the other side, only tasks small enough to allow knowing everything
about them, can be automated. Assume the control (of a process) can be
defined as a mapping of a set of input states – problems – to a set of output
states – solutions. Since the automation can be defined as delegating the
control or the decision taking to an artefact (device, software, combination
thereof, or whatever else), the existence of such a mapping and the
possibility of its implementation are crucial. The implementation is only
possible if: a) the number of probable input states is countable and exactly
known, and b) an onto-mapping M of the set of problems {P} to the set of
solutions {S} is known, and c) M is realizable as an artefact.
So, how could models help here? At least the following two reasons for using
models are justified:
a) Models can be used instead of real resources, at least during the early
phases of the development, and thus make even the most intensive
experimenting affordable and (financially) more effective.
b) Models can save time when they are workable or when they allow
automation of experimenting. For software models both conditions are
fulfilled.
In short, the objective of modelling is to increase learning speed and the
amount of acquired knowledge (reason b) and simultaneously decrease the costs of
knowledge acquisition (reason a), supporting thereby indirectly the abilities to
predict and to control. On this basis are built concepts like Digital Factory, Virtual
Factory, or Smart Factory: if anything that has to be build in reality – from a given
product up to the factory producing it – is fully modelled, studied and optimized in
advance, there is a great potential for saving time, money and other resources.
Of course, there are other reasons why we need models, which are more or less
directly related to the discussed abilities to rule and to predict. They will be
discussed in the following section.
2.1.3.1 Why are Models Needed
There are so many reasons for using models that their complete enumeration and
description is almost impossible. Nevertheless, let us try to consider some of the
more important ones (cf. Figure 2.10).
Models contain or reflect only the most important, for a given purpose, traits of
whatever is being modelled. As a result, they reduce the complexity of the
modellee and allow the modeller to ignore unimportant traits in order to
concentrate on the essentials. Therefore, models crucially support and improve the
understanding of the matter. Since the models are a simplified, finite representation
of something, they are easier to handle. In many cases the only way for comparison
of different objects, products, solutions, etc. is to compare their models. For
instance, we (still) cannot compare two screws atom-by-atom, particle-by-particle,
and this would not make sense either. But it does make sense to compare their
diameters, lengths, pitches, number of threads and a couple of other purpose-