Ideal and material models

The ambiguity of the term "model," the vast number of modeling types, and their rapid development currently make it difficult to construct a logically complete and universally accepted classification of models. Any such classification is conditional because it reflects, on the one hand, the subjective viewpoint of its authors, and on the other, the limitations of their knowledge across a finite number of scientific fields.

This classification should be seen as an attempt to create a tool or model for studying the properties and characteristics of the modeling process itself. Modeling is considered a general scientific method of inquiry. The use of modeling at the empirical and theoretical levels of research leads to a conventional division of models into material and ideal.

Material modeling is a type of modeling in which the investigation of an object is carried out using its material analog, which reproduces the main physical, geometric, dynamic, and functional characteristics of that object. The main varieties of material modeling are physical and analog. Both types of modeling are based on the properties of geometric or physical similarity.

Ideal modeling differs from material modeling in that it is based not on a materialized analogy between the object and the model, but on an ideal, conceptual analogy, and is always theoretical in nature. Ideal modeling is primary in relation to material modeling. First, an ideal model is formed in the human mind, and then a material model is built based on it.

Material Modeling

The main varieties of material modeling are physical and analog. Both types of modeling are based on the properties of geometric or physical similarity. Two geometric figures are similar if the ratio of all corresponding lengths and angles is the same. If the coefficient of similarity—the scale—is known, the dimensions of another, similar geometric figure can be determined by simply multiplying the dimensions of the first figure by the scale factor. Two phenomena are physically similar if, given the characteristics of one, the characteristics of the other can be obtained through a simple recalculation, which is analogous to converting from one system of measurement units to another. The study of the conditions for the similarity of phenomena is the subject of similarity theory.

Physical modeling is a type of modeling in which a real object is represented by its scaled-up or scaled-down material analog, which allows for investigation (usually in laboratory conditions), with the subsequent transfer of the properties of the studied processes and phenomena from the model to the object based on similarity theory.

Analog modeling is modeling based on the analogy of processes and phenomena that have different physical natures but are described formally in the same way (by the same mathematical relationships, logical, and structural diagrams). The basis of analog modeling is the congruence of the mathematical descriptions of different objects.

Models of the physical and analog types are a material reflection of the real object and are closely linked to it by their geometric, physical, and other characteristics. In practice, the process of investigating these types of models comes down to conducting a series of physical experiments where the physical or analog model is used instead of the real object.

Ideal Modeling

Ideal modeling is divided into two main types: intuitive and scientific.

Intuitive modeling is modeling based on an intuitive (not justified from the standpoint of formal logic) understanding of the object of study, which either cannot be or does not need to be formalized. A prime example of an intuitive model of the surrounding world is the life experience of any person. Any empirical knowledge without an explanation of the causes and mechanisms of the observed phenomenon should also be considered intuitive.

Scientific modeling is always a logically justified form of modeling that uses a minimal number of assumptions, adopted as hypotheses based on observations of the modeling object.

The main difference between scientific and intuitive modeling lies not only in the ability to perform the necessary operations and actions for modeling itself but also in the knowledge of the "internal" mechanisms used in the process. It can be said that scientific modeling knows not only *how* to model but also *why* it should be done that way. It is crucial to emphasize the extremely important role of intuition and intuitive models in science, as no significant new knowledge can be achieved without them. The latter is unattainable through formal logic alone.

Intuitive and scientific (theoretical) modeling should in no way be set in opposition to each other. They complement each other well, each having its own domain of application.

Symbolic modeling is a type of modeling that uses symbolic representations of some kind as models: diagrams, graphs, drawings, sets of symbols, and also includes a set of laws and rules by which these symbolic formations and elements can be manipulated. Examples of such models include any language, such as spoken and written human communication, algorithmic languages, and so on. The symbolic form is used to convey both scientific and intuitive knowledge. Modeling using mathematical relationships is also an example of symbolic modeling.

Intuitive knowledge is a generator of new knowledge. However, not all hunches and ideas withstand subsequent verification by experiment and the methods of formal logic characteristic of the scientific approach, which acts as a kind of filter for extracting the most valuable knowledge.