Abstract
Dictionaries tell us that the word “model” originates from the Latin word “modulus” which means “measure, template, norm”. This term was used in proceedings on civil engineering several centuries BC. Currently, it relates to an enormously wide range of material objects, symbolic structures and ideal images ranging from models of clothes, small copies of ships and aeroplanes, different pictures and plots to mathematical equations and computational algorithms. Starting to define the concept of “model”, we would like to remind about the difficulty to give strict definitions of basic concepts. Thus, when university professors define “oscillations” and “waves” in their lectures on this subject, it is common for many of them to repeat the joke of Russian academician L.I. Mandel’shtam, who illustrated the problem with the example of the term “heap”: How many objects, and of which kind, deserve such a name? As well, he compared strict definitions at the beginning of studying any topic to “swaddling oneself with barbed wire”. Among classical examples of impossibility to give exhaustive formulations, one can mention the terms “bald spot”, “forest”, etc. Therefore, we will not consider variety of existing definitions of “model” and “modelling” in detail. Any of them relates to the purposes and subjective preferences of an author and is valid in a certain sense. However, it is restricted since it ignores some objects or properties that deserve attention from other points of view.
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Notes
- 1.
Along with the concept of systematisation, one uses the concept of classification. The latter is stricter since it implies that there are strict boundaries distinguishing different classes. The base for both concepts is some set of properties. For example, buttons can be classified based on their colour, shape, number of holes, way of attaching to clothes, etc.
- 2.
There is an opinion that less general meaning of the term “model” is more reasonable. Namely, it is suggested to call “model” only such things that are not covered by the terms “theory”, “hypotheses”, “formalism”.
- 3.
Does logical model reflect the “rules” of nature? Based on that the species “Homo sapiens” has successfully competed with other biological species depleted of mind and logic, extended over all continents and reached oceanic depths and cosmos, one can believe that H. sapiens correctly assesses the rules of evolution and interrelations among natural objects. Hence, logical models make objective sense.
- 4.
This statement can be attributed more readily to people whose “left” hemisphere of the brain is developed better, i.e. perception dominates over logic.
- 5.
In particular, when two equally strong stretched strings, one of them being twice as long as the other one, oscillate, the interval between their tones is equal to an octave.
- 6.
The variables are complementary if each of them can be specified more precisely at the expense of lower certainty in the value of the other one.
- 7.
It is appropriate to recall here the words of L.I. Mandel’shtam about the concept of “clear” as something habitual and perceptible.
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Bezruchko, B.P., Smirnov, D.A. (2010). The Concept of Model. What is Remarkable in Mathematical Models. In: Extracting Knowledge From Time Series. Springer Series in Synergetics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12601-7_1
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