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FEM model for stress analysis of a reciprocating piston

A model is a simplified representation of reality. The simplification can be made on sensually, especially optically perceptible objects or in theories. According to Herbert Stachowiak , it is characterized by at least three features:

1st illustration
A model is always a model of something - namely a picture or representation of a natural or an artificial original, whereby this original itself can also be a model.
2. Shortening
In general, a model does not capture all the attributes of the original, but only those that appear relevant to the model creator or model user.
3. Pragmatism
Models are not clearly assigned to their originals. They fulfill their substitute function
a) for certain subjects (for whom?)
b) within certain time intervals (when?)
c) restricted to certain mental or actual operations (why?) .

In addition, other features are occasionally discussed, such as extension and distortion as well as validity . The American philosopher of science Michael Weisberg differentiates between objective and mathematical models at the top level and also sets up computer simulations (computational models) as a separate class of models.

Word origin

The word model originated in Renaissance Italy as the Italian modello , derived from the Latin modulus , a benchmark in architecture, and was used as a technical term in the visual arts until the 18th century. Around 1800 in German , model replaced the older word model (pattern, form, e.g. cake form ), borrowed directly from the Latin modulus (measure (stab) ), which still lives on in the verb ummodeln and in some technical languages and dialects .


The modeling abstracted by creating a model of reality, because it is usually too complex to completely map. This completeness is not intended at all, rather only the essential influencing factors that are significant for the real process and in the model context are to be identified and presented.

A distinction is made between structural and pragmatic modeling.

  • With structural modeling, the internal structure of the system is known, but it is consciously abstracted, modified and reduced. One speaks here of a 'whitebox model'.
  • With pragmatic modeling, the internal structure of the system is unknown; only the behavior or the interaction of the system can be observed and modeled. The background can usually not be understood or only partially understood - this is referred to as a 'black box model' .
  • There are also mixed forms in which parts of the system are known and others are not. Not all interactions and interactions between subcomponents can be traced - here one speaks of the 'gray box model'. This hybrid form is the most common because, due to cost-benefit considerations, it is usually sufficient to map the system in this way.

Processes of modeling:

Process of modeling

The following processes can be differentiated when creating models:

Ignoring irrelevant objects
Omission of object details
Breakdown, breakdown into individual segments
Union, merging of segments into a whole
Concept or class formation

Complexity and quality of a model

One goal of a modeler is generally to reduce the complexity of the model compared to reality. A common fallacy is therefore to equate a model with reality. In fact, only the model context can be determined and optimized. This determines the purpose of the model. The model can also be varied in terms of complexity. In principle, the model always lags behind reality in all of its features, except for the intelligibility.

Models in different categories

Each scientific discipline has its own model systematics. These change with the ongoing development in the respective category and follow new focal points with branches of such a system. The mathematization of individual branches of science, such as business administration ( forecasting methods ), economics ( simulation methods ) or biology ( genetic engineering ) opened up completely new model worlds.

Mathematical models in science

Mathematical models are models described in mathematical formulas. They try to capture the essential parameters of the mostly natural phenomena. A model can be calculated and scientifically tested through the formal description.

Calculability here means both the analytical investigation and the approximation using numerical methods. As a rule, the so-called physical models are also mathematical models, but they are based on physical laws.

A valid model can be used to predict future behavior.

Well-known applications of mathematical models are, for example, forecasts of climate change, the weather or the statics of a building.

Empirical functions are often used in mathematical models .

Math and logic

The model theory of mathematical logic is not about mapping reality in mathematics. Here one understands by a model of an axiom system a set provided with certain structures to which the axioms of the system apply. The existence of a model proves that the axioms are not contradicting one another; If there are models with a certain property as well as models that do not have this property, then the logical independence of the property from the axioms is proven.

In logic , the model of a formula F is an evaluation that assigns F the truth value <true> . It is also said that this rating satisfies the formula. The model of a sentence (formula) is therefore an interpretation that satisfies the sentence (formula).

Correspondingly, the model of a set of well-formed formulas is the interpretation by assigning semantic values ​​to the simple expressions contained in the formulas, so that all formulas receive the truth value <true> , i.e. an assignment that verifies the relevant set. More abstractly one can formulate that if “Σ [is] a set of L-sentences; an L-structure that makes every sentence in Σ true, […] a model of Σ [is called]. "

The model of an axiom system is a subject area and an interpretation of the undefined basic concepts in which an axiom system is true, or in Carnap's words :

“Under a model (more precisely, a logical or mathematical model) for the axiomatic basic signs of a given AS (system of axioms) in relation to a given individual domain D, one understands an evaluation for these signs in such a way that both the domain D and the evaluation without use descriptive constants is specified. "

In other words, the Historical Dictionary of Philosophy says: "In logic, a model is a system of domains and concepts insofar as it fulfills the axioms of a suitably formulated theory."

In modal logic , a model consists of three components:

  1. a class of possible worlds;
  2. an assignment function which assigns a truth value to each pair of an atomic statement and a possible world;
  3. an accessibility relation between possible worlds.

The model theory of logic is also used in model theoretical semantics .

Philosophy of science

In methodology and philosophy of science , a distinction is made between models that serve to explain known facts or objects and those that are based on a hypothetical assumption ( hypothesis ) and in which the context of discovery when testing theories is in the foreground. Explanatory models are often scale models that have a true-to-scale relation to reality (toy car). On the other hand, there are analogy models that (should) generate the structural similarity ( homomorphism ) of the reality depicted, such as the planetary model of atoms. Often abstract or fictitious models are formed for theories. Another distinction is whether models are descriptive (descriptive) or whether the model defines a situation (prescriptive).

The model is of great importance in the scientific knowledge process. Under certain conditions and purposes, models have an important cognitive function in the investigation of real objects and processes in different areas of reality and in the development of scientific theories. So they serve u. a. to simplify (idealize) complex issues or make them accessible to our perception.

Fictional models are a means of deeper and more comprehensive knowledge of reality. Created in the process of abstraction with methods of idealization or construction, they help to uncover real properties, relationships and contexts, to make certain real properties comprehensible and practically controllable. They are mostly formed in order to be able to apply the means of theoretical, especially mathematical, analysis to real objects.

Examples: ideal gas , absolutely black body , mass point , perfect market, etc. a. (see ideal object )

The epistemological and logical possibility and justification of the admissibility of models is only one aspect. Ultimately, what is essential is the justification of the admissibility of fiction through actual practice, that is, practical evidence that the theory built up with the help of the model can be effectively applied to real objects.

A separate discussion is held in the philosophy of science about whether models as representations depict reality ( realism ), or whether these are only theoretical constructions ( constructivism ).

Social and cultural studies

In the social sciences , the concept of the model has been used in many ways, not just since Niklas Luhmann . For example, a theory building for analyzing and planning lessons is called a " didactic model". This linguistic usage is based on the model analogy that the methodical steps of formulation, testing and validation follow one another in the development of a manual.

For the anthropologist Edward T. Hall , a culture comprises a number of situation-specific models of the behavior and thinking of its members. These models, in turn, can be described in a highly abstract manner by ethnologists and anthropologists (e.g. in the form of a relationship model ). But such models of thinking can also imply real effects (theoreality) .

Max Weber spoke of the ideal type in social science research and meant nothing more than an abstract, idealized model of reality. An ideal type can describe both social structures ( democracy or medieval city ) and temporal developments ( revolutions or business cycle models ).

In economics , models are used to describe and investigate economic structures and processes. The most important assumptions for models in economics include the perfect market and homo economicus . Models can be classified according to the following criteria:

  • the purpose (description, explanation, forecasting, decision or simulation models)
  • the degree of abstraction (deterministic or stochastic models)
  • static and dynamic models (with discrete or continuous time consideration)
  • Partial and total models (modulation of real systems in parts or in its entirety)
  • Stationary models and growth models: Although this distinction is similar to the former, it relates to the models of business cycle theory. In contrast to the growth models, the stationary models do not have any ups or downs
  • Microeconomic and macroeconomic models: The former are often used to substantiate macroeconomic statements


In psychology , a distinction is made between different “models of man”. These are paradigms that differ in their basic assumptions and methodology.

The concept of model continues to play a central role in learning theory ; the educational psychology focuses on this form of learning (see learning , observational learning, model learning, imitation learning, learning on the model). The theory of model learning or learning from the model explains how behavior comes about, namely by imitating the behavior that a person (the model) has realized. It plays z. B. a role, which relationship the imitator has to the model (parents, teachers, educators etc.) or how successfully a model can shape its behavior (in social situations) or what social standing a model shows. It can be assumed that especially complex chains of behavior in the social environment come about through learning to imitate.

Basically, learning research has found:

  • If the learner and model have a good relationship, behaviors are more easily adopted. The context plays an important role in educational processes.
  • If the model itself is successful in various social situations, its behavior is more easily adopted by learners.
  • Models with higher social prestige are usually more effective in terms of behavior adoption.
  • Adopted behavior that is successful in its social environment is more likely to be retained by the learner (see also learning : operant conditioning; reinforcement learning ).
  • Observed and imitated behavior of great importance (for the imitator) is more likely to be retained than behavior of lesser importance.
  • Insecure and fearful people are more willing to adopt behavior from models.

Field theory : The psychologist Kurt Lewin (1890–1947) was a great master in designing models for complex issues in psychology ( field theory in the social sciences , Bern 1963), for example in motivational psychological work.


In pedagogy, the question of the model is above all the question of how the educator sees himself. (In everyday language, the word role model is more used.) The acting educator has to put up with the question of whether he realizes in his behavior exactly what he is prepared to demand theoretically and practically in educational situations as appropriate to optimal in order to act as a model (Role model) to function. If he is unwilling or unable to do so, it is generally understood that he lacks credibility. An educator who is responsible for the child / adolescent z. B. demands trust, but is petty to adhere to regulations that he may have formulated himself, produces a contradiction between his demands and the concrete behavior. As a model he would be deeply implausible.

Parents who exhibit many contradictions of this kind cannot be successful in their work, as they inevitably lead to conflicts with the children and adolescents which they are moreover difficult to explain or justify. Being a credible model requires a lot of self-criticism and reflection on what you do.

The credible model is formed by the educator who not only represents his values, educational ideas and teachings verbally, but lives them in a visible way for everyone - initially regardless of which educational ideology he represents. Since one cannot assume that an educator can work completely without blame or blame, one would have to demand an educator in this sense who reduces his internal contradictions to an acceptable level in order to be able to become a credible model. A professional educator can only be one who is ready and able to reflect on his contradictions.

A model ( role model ) of historical proportions, for example, was Janusz Korczak , who went to the gas chamber with the children from his children's home in the Warsaw ghetto, even though the Nazis had offered him not to accompany the orphans. But he decided not to leave the children alone on their last walk.

Computer science

In computer science , models are used on the one hand to depict a section of reality in order to solve a task with the help of information processing. Such models are called domain models . This includes e.g. B. Models for software to be created, both for their architecture (architecture model) and their code (in the form of, for example, program flowchart diagrams ) and data models for describing the structures of data to be processed from an operational / technical perspective or from a technical data storage perspective. On the other hand, models can serve as a template for the conception of an information system, one then speaks of model systems . This includes, in particular, reference models that can generally be used as design samples. Reference models are used, for example, for the design of specific computer architectures , network protocols , application systems , data storage systems and portals .

In addition to these models, which are concretized in hardware and software as well as in databases, there are also planning, control and organizational models. Typical objects to be modeled are the workflow structure of a business process , mapped in a business process model , and the structure of an operational organization, mapped in an organizational chart . ( Lit .: Broy)

In business informatics, models mainly serve to describe real and socio-technical systems, see model (business informatics) . When modeling human-machine systems - a domain of business informatics - both technical and human components must be modeled. Different models are available for humans, which simulate different aspects of human behavior and human abilities and which are selected according to the objective of the investigation. Driver models or pilot models model people in a very specific work situation, controller-human models in their general ability to regulate a variable. The adaptability of humans to cognitively different demanding tasks is simulated in the three-level model according to Rasmussen. One of the subjects of research is to use cognitive architectures such as ACT-R / PM or SOAR in application-oriented modeling and simulation (MoSi) of human-machine interfaces .

Special uses of words

  • A computer model is a mathematical model that, due to its complexity and / or the sheer number of degrees of freedom, can only be evaluated with a computer.
  • In computer graphics and related fields, 3D models of bodies are created with the help of geometric modeling .
  • A digital terrain model (DGM) or digital elevation model (DHM) is a digital, numerical model of the terrain heights and shapes. In contrast to the digital surface model (DOM), a DTM or DEM does not represent any objects on the earth's surface (e.g. trees or houses).

Natural sciences: chemistry and physics

In chemistry , models are used in particular to illustrate the smallest particles, such as atoms and molecules , and to explain and interpret chemical reactions , which are often also simulated . Model experiments often represent the function of technical processes.

In physics , as in chemistry, models play a major role in illustrating and understanding atoms and elementary particles . Physical theories and models are closely linked and determine thinking in models for gaining knowledge and understanding relationships and structures. Examples of theories are atomic theory , kinetic gas theory , wave theory of light, and relativity theory . Modeling also includes the mathematization of physical laws. In the didactic area, models are often used in the sense of analogies between the object area to be examined and areas already explored. In addition, demonstration models are used as simplified images (e.g. the planet model ). In addition to illustrating physical relationships, simulations serve to check hypotheses . Experiments often have a model character, not only in physics lessons , in that they simplify complex reality and restrict themselves to the essentials in the inductive derivation of laws. Function models have a meaning, for example, to illustrate the function of simple machines .

Special approaches

Model platonism

The term was coined by Hans Albert . It critically marks the deviation of the neoclassical style of thinking in economics from the methodology of empirical social science. The law of demand , quantity theory and growth theory serve as examples .

Although the neoclassical theory with its model considerations is obviously directed at the economic behavior of people, the social causation of human behavior, as it takes into account in different ways in empirical social science, is largely eliminated. Some theorists even deny the intention to provide causal explanations and are satisfied with statements that have nothing more than a reference to reality (i.e. mention real things) instead of statements that have informational content because they can fail on empirical data. This approach is associated with the tendency to design the statements in such a way that they are true due to their logical structure. This is achieved through tautological formulations or the application of conventionalistic strategies ( immunization strategy ), including, for example, the use of an explicit or implicit ceteris paribus clause . This methodical style of thinking in models, which are consciously or unconsciously isolated from any empirical verifiability, amounts to a new form of Platonism , which is not always overlooked by its followers in its practical consequences for the applicability of the analytical results . Plato was convinced that reality was known through purely logical thinking; instead of observing the stars, we should fathom their laws of motion through thinking.

At that time, the school dispute between conceptual realism ( essentialism ) and model platonism dominated German economics . Albert considers this front position to be wrong for methodological reasons; Instead, he advocates economics, understood as an empirical social science. In this sense he also speaks of market sociology or a “sociology of commercial relationships”.


  • Wolfgang Balzer: Empirical Theories: Models - Structures - Examples. The basics of modern philosophy of science . Vieweg, Braunschweig 1982.
  • Manfred Broy , Ralf Steinbrüggen: Modeling in Computer Science . Springer, Berlin / Heidelberg 2004, ISBN 3-540-44292-8 .
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  • Herbert Stachowiak: General model theory . Vienna 1973, ISBN 3-211-81106-0 .
  • Herbert Stachowiak (Ed.): Models - Construction of Reality . Wilhelm Fink Verlag, Munich 1983, pp. 17-86.
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  • Natascha Adamowsky (Ed.): Digital Modernism. Matthias Zimmermann's model worlds . Hirmer Verlag, Munich 2018, ISBN 978-3-7774-2388-3

Web links

Wiktionary: model  - explanations of meanings, word origins, synonyms, translations
Commons : model  - collection of images, videos and audio files

Individual evidence

  1. Herbert Stachowiak: General Model Theory , 1973, pp. 131-133.
  2. ^ Thalheim: Towards a Theory of Conceptual Modeling . In: Journal of Universal Computer Science , vol. 16, 2010, no.20, p. 3120
  3. ^ Dietrich Dörner: Thought and Design - Research Strategies, Single-case Approach and Methods of Validation . In: E. Frankenberger u. a. (Ed.): Designers. The Key to Successful Product Development . Springer-Verlag, Berlin a. a. 1998, pp. 3-11.
  4. ^ M. Weisberg: Simulation and Similarity - Using Models to Understand the World. Oxford University Press, New York NY 2013.
  5. Quality orientation ( Memento of the original from January 30, 2012 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. (PDF; 140 kB) @1@ 2Template: Webachiv / IABot /
  6. Complexity and Quality (PDF; 69 kB)
  7. Hoyningen-Huene: Logic . 1998, p. 255.
  8. Hügli, Lübcke: Philosophielexikon . 1991, ISBN 3-634-22405-3 .
  9. ^ Godehard Link, Karl-Georg Niebergall: Logic: From Epimenides to Gödel. In: E. Fischer, W. Vossenkuhl: The questions of philosophy. Beck, Munich 2003, p. 107 (118)
  10. ^ Wilhelm K. Essler: Introduction to Logic (= Kröner's pocket edition . Volume 381). 2nd, expanded edition. Kröner, Stuttgart 1969, DNB 456577998 , p. 244.
  11. ^ Rudolf Carnap: Introduction to Symbolic Logic. 3. Edition. Springer, Vienna / New York 1968, p. 174
  12. After Helmut Glück (Ed.): Metzler Lexikon Sprach. 4th edition. Metzler, Stuttgart / Weimar 2010: model.
    Similarly, in another formulation Rainer Stuhlmann-Laeisz: Rainer Stuhlmann-Laeisz: Philosophical Logic. mentis, Paderborn, 2002, p. 21
    "A model U for a language MAL is a structure (K, i, R, V) made up of four components:
    (i) K is a non-empty class or set of objects,
    (ii) i is one of the objects in K: i is an element of K,
    (iii) R is a two-digit relation on K: R is a subset in K × K,
    (iv) V is a mapping that assigns a truth value to each atomic proposition of MAL with respect to the object of K; V: At × K → (W, F) (in this notation the term 'At' stands for the class of atomic statements (expressive letters) of MAL). "
  13. ^ ET Hall: Beyond Culture. Random House 1976, p. 13.
  14. N. Kühne, p. 53 ff.
  15. Reinhard Tausch , Anne-Marie Tausch, Göttingen 1971, pp. 49–73.
  16. See Tausch / Tausch, Göttingen 1971, pp. 49–73.
  17. ^ Hans Albert: Model Platonism. The neoclassical style of economic thinking in critical lighting. In: Ernst Topitsch, (Ed.): Logic of the social sciences. Kiepenheuer & Witsch, Cologne / Berlin 1965, pp. 406–434; quoted from: Friedrich Karrenberg, Hans Albert (Ed.): Social Science and Society Design. Festschrift for Gerhard Weisser. Duncker & Humblot, Berlin 1963, pp. 45-76.
  18. ^ Hans Albert: The logical character of theoretical economics. In: Yearbooks for Economics and Statistics , 171, 1959, pp. 1 ff.
  19. Hans Reichenbach: The rise of scientific philosophy. Friedrich Vieweg & Sohn, Braunschweig 1968, p. 42.
  20. See also Hans Albert: Market Sociology and Decision Logic. (Mohr Siebeck) Tübingen 1998, especially Chapter IV. And his lecture The Idea of ​​Rational Practice and the Economic Tradition (PDF)