Artificial and Natural Classifications

There are two types of classifications: artificial and natural.

In artificial classification, the division into classes is made “as is necessary”, that is, based on the purpose,—as many classes and with as many boundaries as is dictated by the purpose of modeling. For example, peasant families in the 20s of the 20th century in Siberia they differed in prosperity q according to the “bell-shaped” distribution (Figure 3.8). For some purposes, the division of peasants into three classes was introduced: poor, middle-class, and reach kulaks, which oversimplified the description of their diversity. On the basis of this model, the Bolsheviks set the task of “eliminating kulaks as a class” and realized this goal. It is characteristic that the boundaries between the classes were not clearly defined, which only increased the injustice. No wonder artificial classification is also called arbitrary.

A slightly different classification is achieved when the considered set is clearly inhomogeneous (Figure 3.9). Natural groupings (called clusters in statistics) seem to suggest being defined as classes, as shown in Figure 3.9 (hence the name of the classification natural).

However, it should be borne in mind that the natural classification is also only a simplified, coarsened model of reality. For example, the seemingly obvious division of objects into “living” and “dead” faces difficulties in determining the legality of the removal of organs from the deceased person for their transplantation to the living: it is not always obvious that the victim cannot be returned to life. Another example is the “obvious” division of people into men and women, as well as those born as hermaphrodites; sometimes (according to statistics 4%) individuals, because of the entanglement in their bio-chemo-psychological processes, are not able to uniquely identify their own sex. The Olympic Committee had to introduce a genetic test in a female power sports as one of the absolute champions of the world was found to be a man (with all the external signs of a women, though crude).

Artificial, or arbitrary, subjective classification

FIGURE 3.8 Artificial, or arbitrary, subjective classification.

Natural or objective classification

FIGURE 3.9 Natural or objective classification.

As the simplest model, classification underlies other, more complex abstract models. This is achieved both by increasing the number of classes and by introducing more and more relationships between classes.

In some cases, the disadvantages of unambiguous classification become unacceptable. Two types of classification generalization are developed: statistical and vague.

When classifying random objects or quantities, the concept of overlapping distributions is introduced and classification errors are associated with this overlap. For example, in Figure 3.10, the boundary C divides the set X into two classes, A, and X2, associated with density distributions, pfx) and p2(x). (The shaded regions equal the probabilities of errors.)

Another type of classification uncertainty is described by the theory of vague (fuzzy) sets. This theory is based on the assumption that one object belongs to different classes at the same time. In this model, there is no clear boundary between classes. We can only talk about the degree of belonging of the object to a particular class. This degree is expressed by the membership function, which takes a value from 0 (“certainly does not belong”) to 1 (“certainly belongs”). For example, consider the classification of numbers into “small”, “medium”, and “large”, a number can belong to all classes simultaneously, although to different degrees (i.e., with different values of the membership function NA(n)) (Figure 3.11).

This concludes the consideration of abstract models as limited knowledge of them is enough for us to present the subsequent material.

Statistical classification

FIGURE 3.10 Statistical classification.

Fuzzy classification

FIGURE 3.11 Fuzzy classification.

Real Models

The second class of models form real objects used as models of considered system. The analytical technique of classification by the origin of similarity between the model and the original leads to three types of real models.

The first type is called direct similarity models. Direct similarity between the model and the original is established by their direct interaction (traces, fingerprint, printing, etc.) or due to a chain of such interactions (photo, building layout, toys, etc.).

The second type is the models of indirect similarity, or analogy. Analogy, the similarity of the two phenomena, is explained by the coincidence of the natural laws they obey. Abstract models (theories) of two phenomena can “overlap”, which leads to the similarities of these phenomena. Therefore, by watching one of them, you can make a judgment about the other (see Figure 3.12: О — “object”, M — “model”). For example, consider the electromechanical analogy, Newton’s law F = m • a and Ohm’s law U = R • 1 are structurally identical. This allows us to model mechanical systems by electrical ones, which are more convenient to work with. In many buildings and structures (bridges, towers), piezoelectric sensors are connected to the electrical model of the structure. This allows you to judge its condition and decide on its maintenance. Other examples of analogies include subordination to Kirchhoff’s law of currents in power networks, water flow in pipelines, information in communication networks, and transport flow on city streets. It is possible to work out optimal structures and processes for the corresponding networks in the electric model. Models of indirect similarity include analog computers, investigative experiments in criminology, historical parallels, the life of separated twins, and experimental animals in medicine.

However, you should carefully use analogies because, in addition to the same patterns, different phenomena have different features as well. Therefore, not all conclusions about the model can be transferred to the original, and not all features of the original are present in the analog model. Sometimes the concept of “degree of analogy” is introduced associated with the extent of “overlap” of the compared theories.

The third type of real models is based on similarity, which is neither direct nor indirect. For example, letters — sound models; money — value models; various signs, signals, symbols, maps, and drawings contain relevant information. Compliance of such models with their originals is a result of agreement between their users, Let’s call such models conventional similarity models.

They work successfully but only as long as the agreements on their meaning (monetary reform, dead languages, secret signs, etc.) are known and respected.

Further analytical consideration of the set of all real models cannot be brought to define common elements: the variety of subjects used as models is too large.

It is possible, of course, to identify the elements of a specific real model (e.g., a geographical map), but the conclusions will be of a particular nature.

Synthetic Approach to the Concept of a Model

In accordance with the synthetic method, explaining the nature of models begins with defining a metasystem of which the model is a part. It is possible to begin the selection of the metasystem from the above definition of the model as the image of the original. This definition has already identified two elements of the metasystem: the model and the simulated original.

An important feature of the model is that it is never identical to the original (even when they are trying to achieve it — counterfeit banknotes, copies of works of art, and other fakes). Often this is simply not necessary: each model is needed for a specific purpose, which requires only some (far from all) information about the original.

The purposefulness of the models has a number of important consequences.

The first is that the purpose of modeling is determined by a certain subject, who, therefore, must be included as another element of the metasystem.

A variety of purposes leads to a plurality of different models for the same original. For example, we should not be puzzled by the existence of several different definitions of something, or by the different testimonies of witnesses to the same event. As an example of the multiplicity of models of one object, to describe the different relations between the subjects in the applied systems analysis, three types of ideologies are considered (see Chapter 1); and political scientist R. Epperson distinguished the following five types of a form of government in society:

Rule by no one: anarchy.

Rule by one man: a dictatorship or a monarchy.

Rule of the few: oligarchy.

Majority rule: democracy.

Rule of law: republic.

Models of the phenomenon can even contradict each other (e.g., the corpuscular and wave theory of light). Models can be distinguished by type of purposes. For example, it is useful to classify models into cognitive and pragmatic ones.

Cognitive models obtain information about the outside world, represent the obtained knowledge, and are subject to changes when new knowledge is added to them.

Cognitive models (Figure 3.13) do not pretend to finality or completeness: there is always something unknown. In cognitive practice, it is customary to tolerate differing and even contradictory opinions. Scientific models are constantly questioned and checked for accuracy, and are continuously refined and developed.

Continuing to consider the relationship between the model and the original, we will focus on the content of information in the model. The original and the model are

Scheme of cognitive modeling

FIGURE 3.13 Scheme of cognitive modeling.

different things. There are a lot of things in the original that are not included in the model for two reasons: first, not everything that is known about the original will need to be included in the model designed to achieve a specific goal (zone A in Figure 3.13 depicts the known but unnecessary, including the wrongly considered unnecessary and not included in the model); second, there is always something unknown in the original, which cannot be included in the model (zone В in Figure 3.13). Zone 2 in the figure shows information about the original included in the model. This is true information, something common in the model and the original, thanks to what the model can serve as its (partial, specific) substitute or a representative. Let’s pay attention to zone 3. It reflects the fact that the model always has its own properties that have nothing to do with the original, that is, false content. It is important to emphasize that this applies to any model, no matter how hard the model creator tries to include only true information in the model.

For example, the analytical function of time as a signal model reflects the fact that the signal is a certain time process. However, this model does not reflect the fact that the repeated signal does not carry new information as the first time. This model does not have the property of real signals to simultaneously occupy a finite time interval and a finite frequency band. In many (and if look closely, in all) theories, the feature of the model to contain false information manifests itself in the form of so-called paradoxes. For example, in the theories of electrostatics and gravity, infinity paradoxes occur at zero distances between interacting particles.

Pragmatic models transform reality in accordance with the objectives of the subject. They reflect the currently nonexistent, but desired (projects, plans, programs, algorithms, rules of law, etc.), and have a normative, directive character. This gives them the status of “the only true”, which is clearly expressed in ideologies, religions, morals, standards, technical drawings, technologies, etc. In contrast to cognitive models, “adjusted” to reality, in transformative activity, reality is “fitted” to the pragmatic model (Figure 3.14).

Let’s conclude the consideration of the relationship between the original and the model by emphasizing the inherent inaccuracy and approximation of the model. Even those aspects of the original that are intentionally displayed are described with some accuracy and approximation. Sometimes the approximation is forced by nature (lack of knowledge), and sometimes it is introduced deliberately for the simplicity of work with the model (e.g., linearization of nonlinear relations between variables).

Scheme of pragmatic modeling

FIGURE 3.14 Scheme of pragmatic modeling.

The Concept of Adequacy

At times, it is possible to achieve the same purpose with the help of various models (e.g., hiking using maps of different scales). It turns out that different models of the same object provide different levels of success in achieving the goal. This property of models is called the extent of adequacy. Usually, two levels of adequacy are used: the model successfully achieving the goal is called adequate, while the other is called an inadequate model.

Discussing the relation between such properties of models as adequacy and accuracy (truth) is of interest as they are not always compatible.

For cognitive models, whose destination is an accumulation of knowledge about the surrounding reality, they are synonyms. This is not the case with pragmatic models. Every one of us has told lies. Lie was preferred to truth because achieving the goal with the help of the lie was easier than with truth. Therefore, in certain circumstances, false models may be adequate (otherwise, lie would not be needed).

The Coherence of the Model with the Culture

You cannot read a book written in an unfamiliar language; it is impossible to listen to a record on a gramophone record without a gramophone; a fifth-year student would not understand the special course without the knowledge gained earlier. Similar examples illustrate the fact that for a model to realize its model function, it is not enough just to have the model itself. It is necessary that the model is compatible and consistent with the environment, which for the model is the culture (world of models) of the user.

When considering the properties of systems, this condition is called inherence: the inherence of a model to culture of the subject is a necessary requirement for successful modeling. The degree of the model’s inherence may change, that is, increase (user training, the appearance of an adapter such as a Rosetta stone, etc.) or decrease (forgetting, degradation of culture) due to a change in the environment or the model itself.

Thus, another element should be included in the modeling metasystem — the culture of the subject.

General scheme of modeling as a metasystem

FIGURE 3.15 General scheme of modeling as a metasystem.

As a result, the scheme of the metasystem “modeling” can be represented as in Figure 3.15. In accordance with the synthesis methodology, to explain what a model is, it is necessary to discuss the relationship of the model with the remaining components of the modeling metasystem. This was the subject of the above reasoning. At the same time, we identified only those connections that are essential for the subsequent presentation of the technology of applied systems analysis.

The remaining links between the elements of the metasystem can be the subject of special consideration and are considered by various sciences.

Hierarchy of Models

Therefore, any activity of the subject is based on the use of models, that is, knowledge of what the subject is dealing with, and why he is performing the activity. In this case, models can describe both the real and the desired states of the system under consideration with varying degrees of detail. In this regard, it is useful to distinguish the levels of elaboration of information with which you have to deal. R. Ackoff proposed [1] the following classification (note the specific use of known terms):

Data — (what?) — description of the results of measurements and observations; experimental protocols; the original “raw” data.

Information — (composition?) — the result of a primary data processing; their ordering, classification, and grouping.

Knowledge — (structure?) — the result of secondary data processing; identifying links and patterns between groups and classes of data.

Understanding — (why?) — an explanation of the identified patterns; the construction of theories that give such an explanation.

Wisdom — (what for?) — information about why all this is necessary; is it good, should it be continued or stopped? that is, approach in terms of aesthetics, ethics, and ideologies.

In an attempt to emphasize the different significance of these levels of information, according to R. Ackoff, an ounce of this level is equal to the value of a pound of the previous one. It is possible to argue about quantitative relationships, but the qualitative difference is obvious. It is worth noting that in the existing education system, attention and training time is given to levels of information in inverse proportion to their actual importance.

Both above-discussed activities of a subject (cognitive and transformational) serve the external needs of interactions of the subject with the environment. However, there are other types of human behavior, neither cognitive nor practical, that serve the internal needs of a subject — arts and the eternal rest (especially, sleep dreams). They are also supported by modeling, but it’s a subject of another book.

Questions and Tasks

  • 1. Show that the cognitive and transformative activities of the subject are impossible without modeling.
  • 2. Describe the analysis algorithm and list which models it generates.
  • 3. Describe the synthesis algorithm and indicate which models it generates. Which one of them directly describes the object (phenomenon) under investigation?
  • 4. What is an “abstract model”? In addition to language, what other examples of abstract models can you give?
  • 5. What caused the diversity of languages?
  • 6. Which is the simplest abstract model of the diversity of the reality surrounding us?
  • 7. What is the difference between artificial and natural classifications?
  • 8. What is a “real model”? Give three types of real models (classification by origin of similarity of the model to the original).
  • 9. What is the difference between the use of cognitive and pragmatic models?
  • 10. Why any model, besides the true content, has and (necessarily and inevitably) untrue content?
  • 11. Which quality of a model is called adequacy?
  • 12. What is the environment for the model?
  • 13. Define the following terms:
    • - model;
    • - analysis;
    • - synthesis;
    • - abstract model;
    • - language model;
    • - real model;
    • - classification (artificial and natural);
    • - cognitive models;
    • - pragmatic models;
    • - the adequacy of the model;
    • - culture (of subject, organization, and nation of any social system).
 
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