A model is a simplifying image of reality. The image can be either a sensorily, above all optically observable artefact or given purely theoretically. According to Herbert Stachowiak, a model is characterized by at least three properties:[1]
1. Mapping
A model always is a model of something—it is an image or representation of some natural or artificial, existing or imagined original, where this original itself could be a model.
2. Reduction
In general, a model will not include all attributes that describe the original but only those that appear as relevant to the model's creator or user.
3. Pragmatism
A model does not relate unambiguously to its original. It is intended to work as a replacement for the original
a) for certain subjects (for whom?)
b) within a certain time range (when?)
c) restricted to certain conceptual or physical actions (what for?).
For example, a street map is a model of the actual streets in a city (mapping), showing the course of the streets while leaving out, say, traffic signs and road markings (reduction), made for pedestrians and vehicle drivers for the purpose of finding one's way in the city (pragmatism).
Additional properties have been proposed, like extension and distortion[2] as well as validity.[3] The American philosopher Michael Weisberg differentiates between concrete and mathematical models and proposes computer simulations (computational models) as their own class of models.[4]
References
Herbert Stachowiak: Allgemeine Modelltheorie, 1973, S. 131–133.
Thalheim: Towards a Theory of Conceptual Modelling. In: Journal of Universal Computer Science, vol. 16, 2010, no. 20, S. 3120
Dietrich Dörner: Thought and Design – Research Strategies, Single-case Approach and Methods of Validation. In: E. Frankenberger et al. (eds.): Designers. The Key to Successful Product Development. Springer-Verlag, Berlin et al. 1998, S. 3–11.
M. Weisberg: Simulation and Similarity - using models to understand the world. Oxford University Press, New York NY 2013
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
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