Scientific modelling
A model is a limited picture of reality. This can be done objectively or theoretically. After Herbert Stachowiak, it is characterized by at least three features:
In addition, other features are occasionally discussed how extension and distortion as well as validity.
- 4.1 Mathematical Models in science
- 4.2 Mathematics and logic
- 4.3 Theory of Science
- 4.4 Social Sciences
- 4.5 Psychology
- 4.6 pedagogy
- 4.7 computer science
- 4.8 Natural Sciences: Chemistry and Physics
- 5.1 Modellplatonismus
Word origin
The word model was developed in Renaissance Italy as Italian modello, from Latin modulus emerged, a scale in architecture, and was used until the 18th century as a technical term in the visual arts. In 1800, the German model displaced the older, directly from the Latin modulus ( measure ( bar ) ) borrowed word model ( pattern, shape, eg cake form), which remodel still in the verb and lives on some special languages and dialects.
Modeling
The modeling abstracted by creating a model of reality, because it is usually too complex to map them accurately. This is also not intended, but only the essential factors to be identified that are important for the considered process.
One distinguishes the structural and pragmatic modeling. In structural modeling, the internal structure of the system is known, but it is deliberately abstracted, modified and reduced. This is called a white-box model. In pragmatic modeling the internal structure of the system is unknown, it can be observed and model only the behavior or interaction of the system. The backgrounds can not be mostly or only partly understand - here we speak of a black-box model. In addition, there is no mixed forms, in which parts of the system are known, others. Not all interactions and interactions between sub- components can be reconstructed - here one speaks of the gray-box model. This hybrid is the most common because it usually is sufficient, due to cost -benefit considerations reflect the system in this manner.
Processes of modeling
In the modeling, the following processes can be differentiated:
- Demarcation: ignoring irrelevant objects
- Reduction: elimination of object details
- Decomposition: Decomposition, resolution into individual segments
- Aggregation: association of segments to form a whole
- Abstraction: the concept of Pupils
Complexity and quality of a model
A goal of a modeler is generally reducing the complexity of the model to reality. A common fallacy is therefore equivalent to a model with reality. In fact, the only model context are determined and optimized. Thus, the earmarking of the model is determined. Further, the model can be varied in terms of complexity. In principle, the model remains in all characteristics except the intelligibility back always behind reality.
Models in various disciplines
Mathematical Models in science
Mathematical models are described in mathematical formulas models. They try to capture the essential parameters of the most natural phenomena. Through the formal description of a model can be calculated and tested scientifically.
Predictability here means both the analytical study and the approximation by numerical methods. In general, the so-called physical models are mathematical models, but they are based on physical laws.
A valid model can be used to predict a future behavior.
Known applications of mathematical models are about predictions of climate change, weather, or the statics of a building.
Mathematics and logic
In the model theory of mathematical logic is not about a picture of reality in mathematics. Here we mean by a model of an axiom system provided with a certain amount of structures that meet the axioms of the system. Proves the existence of a model that does not contradict the axioms; exist in both models with a certain property as well as those who do not have this property, so making it the logical independence of the property from the axioms proved.
In the logic of the model of a formula F is a valuation that assigns the truth value of F
Accordingly, the model is a set of well-formed formulas, the interpretation by assigning semantic values to the formulas contained in the simple terms so that all formulas get the truth value
The model of an axiom system is a subject area and an interpretation of the undefined basic concepts, in which a system of axioms is true or with the words Carnap:
In other words, it is said in the Historical Dictionary of Philosophy: " model is called in logic a system of areas and concepts, in that it satisfies the axioms of a suitably formulated theory. "
In modal logic, a model consists of three components:
The model theory of logic is also used in the model-theoretic semantics.
Philosophy of Science
In the methodology and philosophy of science, a distinction between models that are used for the explanation of known facts or objects, and those based on a hypothetical assumption ( hypothesis) is based and where the context of discovery when testing theories in the foreground. Explanatory models are often scale models that a full-scale with reality have ( toy car ). In contrast, stand analogy models, the structural similarity ( homomorphism ) of the reality depicted produce (to be) such as the planetary model of the atom. Abstract or fictional models are made for theories often. A further distinction is whether models are descriptive (descriptive ) or whether an item is determined by the models ( prescriptive ).
The model is of great importance in the scientific process of understanding. Under certain conditions and determination of goals have models in the study of real objects and processes in different areas of reality and the construction of scientific theories is an important cognitive function. So they serve, inter alia, to simplify complex issues ( idealize ) and our intuition to access.
Fictional models are a means of deeper and broader knowledge of reality. Originating in the process of abstraction with methods of idealization and the construction, they help to reveal real properties, relationships, and relationships to make certain real properties can be detected and practically be manageable. They are mostly formed in order to represent any real objects can apply the means of theoretical, especially the mathematical analysis.
Examples: ideal gas, absolutely black body, mass point, perfect market, among others (see ideal object )
The epistemological and logical possibility and justification of the admissibility of models is only one side. It is essential, ultimately justifying the admissibility of fiction through the active practice, that is the practical proof that the theory constructed with the help of the model can be applied to real objects effectively.
A separate discussion is in the philosophy of science about whether models as representations depict the reality (realism ), or whether it is only theoretical constructions are ( constructivism).
Social sciences
Even in the social sciences the concept of the model is often used. For example, a theoretical framework for the analysis and planning of lessons is referred to as a " didactic model ". This fashionable parlance is probably due to the analogy is that followed in the development of implementation guidelines, the methodological steps formulation, testing, validating each other.
Max Weber spoke of the ideal type in the social sciences, referring to nothing more than an abstract, idealized model of reality. An ideal type can be both social structures (democracy or medieval city ) and time courses ( revolutions or economic models ) describe.
In economics, models are used to describe and study of economic structures and processes. Among the most important assumptions in models of economics are the perfect market and the homo economicus. Models can be classified according to, among others, the following aspects:
- The application ( description, explanation, prediction, decision-making or simulation models )
- The degree of abstraction ( deterministic or stochastic models )
- Static and dynamic models ( with discrete or continuous time into account )
- Partial and total models ( modulation of real systems, in part or in its entirety)
- Stationary models and growth models: This distinction is indeed the former similar, but refers to the models of economic theory. In contrast to the growth models desktop models have no ups and downs
- Microeconomic and macroeconomic models: the former are often used for the foundation of macroeconomic statements
Psychology
In psychology, to distinguish different " models of man". It is to paradigms that differ in the assumptions and methodology.
The concept of model continues to play in the learning theory a central role; also educational psychology focuses on this form of learning (see Learning, observational learning, model learning, imitation learning, learning at the model ). The theory of the model on learning or learning at the model explains how behavior comes about, namely by imitating the behavior that a person ( the model ) has realized. It does, for example, a role which relationship of Imitative to the model (parents, teachers, educators, etc.) has or how successful a model can make its behavior ( in social situations ) and social prestige which shows a model. One can assume that particular complex ( social) behavior chains come through imitative learning about.
Basically, the learning research has found:
- Have learners and model a good relationship are adopted behaviors easier. The context plays a prominent role in educational processes. (see: Education )
- Is the model itself successfully in various social situations, his behavior of learners will be easier accepted.
- Models with higher social status are more effective in general, with regard to the acquisition of behavior.
- Acquired behavior that is successful in his social environment, the learner rather retained ( see also learning: operant conditioning, reinforcement learning).
- Observed and Imitated behavior is of great importance (for the imitator ) is rather retained as a behavior with less importance.
- Uncertain and anxious people are more willing to take on behavior models.
(see ref: Reinhard exchange, Anne -Marie exchange, Göttingen 1971, pp. 49-73 )
Field Theory: Kurt Lewin Psychologist (1890 - 1947) was a great master in the design of models for complex issues in psychology ( " Field theory in the social sciences ", Bern 1963), about the psychological motivation works.
Education
The question of the model is in education, especially the question of the self-understanding of the parents. ( In everyday language, we rather use the word model. ) The active educator must leave the question like if he exactly realized in his behavior, what he is willing theoretically and practically to demand in educational situations as adequate to optimally to serve as a model to act ( a model ). Is he not willing or not able, he lacks credibility, as generally understood. A parent families, for example, the trust asked by the child / young person, but even is petty on the compliance of which he has perhaps formulated itself, produces a contradiction between his demands and the actual behavior. As a model it would be so deeply implausible. (See exchange / barter; Göttingen 1971, pp. 49-73 )
Parents who have many contradictions of this kind can not be successful in their business, as they inevitably conflicts with the children and adolescents cause, they can also hard to explain or justify. To be the credible model, requires a lot of self-criticism and reflection of its activities.
Thus, the model is credible educators, represents its values , educational ideas and teachings not only verbally, but visible for all lives - initially independent of what educational ideology he represents. Since one can not assume that a wholly -parent can work flawlessly, you would have in this sense, an educator demand, which reduces its internal contradictions to an acceptable level in order to be a credible model can. A professional acting teacher can only be the one who is willing and able to reflect his contradictions.
A model ( model ) of historic proportions was about Janusz Korczak, who went with the children from his orphanage in the Warsaw ghetto to the gas chamber, although he had offered the Nazis, he would not accompany the orphans. He decided, however, for not to leave the children in their last walk alone.
Computer science
In computer science models are used for imaging a reality for a section to solve a task with the help of information processing. Such models are called domain models. This includes, for example, models for software to be solely responsible for the architecture ( architectural model ) as well as their code ( in the form of, for example, program flowchart diagrams) and data models for describing the structure of data to be processed from operating / multiple logical point of view or from a technical data management point of view. Secondly, models can serve as a template in the design to an information system, one speaks then of system models. This includes primarily the reference models that can be widely used as a design pattern. Reference models are used for example for the design of specific computer systems, network protocols, data warehouse systems and portals.
In addition to these models, which start to appear in both hardware and software as well as data sets, there are also planning, management and organizational models. Typical objects are to be modeled in this case the sequence structure of a business process, displayed in a business process model, and the structure is an operational organization, depicted in an organizational chart. (Lit.: Broy )
In economics, computer science (WI) models are mainly used for the description of real and socio- technical systems, see model ( economic computer science ). In the modeling of human-machine systems - the domain of computer science economy - must be modeled, the technical and the human component. For humans, there are different models available that simulate various aspects of human behavior and skills and be selected according to the study objective. Driver models or pilot models model the people in a particular work situation, controller -human models in its general ability to control size. The human adaptation to different cognitively demanding tasks is simulated in a three -level model according to Rasmussen. An object of the research is, among other things, cognitive architectures, such as SOAR ACT-R/PM or in application-oriented modeling and simulation ( MoSi ) use of human- machine interfaces.
- A computer model is a mathematical model that can be analyzed due to its complexity and / or to the sheer number of degrees of freedom with only one computer.
- In computer graphics and related areas 3D models are generated by bodies with the help of geometric modeling.
- A Digital Terrain Model (DTM ) or Digital Elevation Model (DEM ) is a digital, numerical model of terrain heights and shapes. A DGM or DEM is in contrast to the digital surface model (DSM ) no objects on the ground point (eg, trees or buildings).
Science: Chemistry and Physics
In chemistry models are used in particular to illustrate the smallest particles, such as atoms and molecules, and to the explanation and interpretation of chemical reactions, which are often also simulated. Model experiments often represent the function of technical processes
In physics models play similar in chemistry to illustrate and understanding of atoms and elementary particles a major role. Physical theories and models are closely linked and determine the thinking in models for gaining knowledge and understanding of relations and structures. Examples of theories are the atomic theory, the kinetic theory of gases, the wave theory of light and the theory of relativity. For modeling includes the mathematization of physical laws. In the educational field models are often used in the sense of analogies between the examined object region and already explored areas. In addition, demonstration models are used as simplified images (eg, the planetary model). Simulations are used not only to illustrate physical relationships of the testing of hypotheses. Experiments not only in physics classes often a model by simplifying the complex reality and be limited in the inductive derivation of laws on the essentials. Function models, for example, have a meaning to clarify the function of simple machines.
Specific approaches
Modellplatonismus
The term was coined by Hans Albert. It identifies critical deviation of the neo-classical style in the economics of the methodology of empirical social science. For example, that the law of demand, the quantity theory and the theory of growth.
Although the neoclassical theory is directed with their model considerations are evident on the economic actions of people, the social causation of human action, as it provides some empirical social science in different ways into account, mostly off. Some theorists deny even the intention to provide causal explanations and content themselves instead of statements that hold information content because they can fail on empirical data, with statements that have nothing more than a reference to reality (ie real things to mention ). This approach is connected with the tendency to make the statements so that they are true already, due to their logical structure. This is achieved by tautological formulations or the use of conventionalist strategies ( immunization strategy ), including for example the use of an explicit or implicit ceteris paribus clause expects. This is not always overlooked by their followers in their practical consequences for the applicability of the analytical results methodical style of thinking in models that are consciously or unconsciously cut off from any empirical evidence, runs on a novel form of Platonism addition. Plato was convinced that the reality might be known by purely logical thinking; place to observe the stars, we should explore the laws of motion by thought.
In the German political economy at that time dominated the doctrinal dispute between conceptual realism ( essentialism ) and Modellplatonismus. This front-line position holds for Albert missed for methodological reasons; he is instead a of Economics, understood as an empirical social science. In this sense, he also speaks of market sociology or a " sociology of commercial relations."