Why many scientists use the term mathematical model ?
If you have a certain phenomenon and you want to model it, you will describe its, more or less, approximate behaviour by applying to it laws which can be physical, chemical, economical, geometrical and so on, depending on the phenomenon.
Mathematics is only a tool to describe these laws, so you should speak of physical, chemical, economical, geometrical ... models and not of mathematical ones.
Most of the models I encounter in my research are physical models because, to build them up, the laws of physics are used.
Each time I hear the term mathematical model, my nose gets wrinkled.
What is your opinion ?
Dear Prof. Carlomagno!
I may have misunderstood, but when I use the expression "mathematical model" or "mathematical modeling, I am guided by the following considerations.
A mathematical model is a mathematical representation of reality, one of the variants of the model as a system study which allows to obtain information about some other system.
The process of building and studying mathematical models is a mathematical modeling.
All the natural and social Sciences that use mathematical tools, essentially doing mathematical modeling: replace the object of study of its mathematical model and then study the latter. Communication of the mathematical model to reality is carried out with a chain of hypotheses, idealizations and simplifications. Using the mathematical methods described are, as a rule, the ideal object, built on stage meaningful modeling.
Although, perhaps better to talk about the mathematical model of any physical or other process? But we try to speak briefly, often without thinking about the meaning, considering it is obvious and the reader will understand us.
Best regards, Leonid Skvortsov
Dear Dr. Skvortsov,
what you call
chain of hypotheses, idealizations and simplifications
is nothing else that the process of modelling the object of study that, in your particular field, you perform by means of physical laws.
You may use mathematics just to express such laws.
Best regards. Giovanni Maria Carlomagno
Dear Prof. Carlomagno!
The world around us is matematika. After all, what is quantum mechanics? It's just a convenient mathematical description of the microworld. A mathematical model of the world that is not given to us in sensation. But this does not mean that he is, as we described in the model... So whether or not "break" the spear?
Best regards, Leonid Skvortsov
Dear Prof. Carlomagno!
Perhaps the fact that the physical model implies a physical representation of a system, object or process with the goal of their research, that is, this view with other physical, real object that has in some aspect similar dynamics behavior. At the same time means the similarity (or identity) of a mathematical model of the research object and the object model. By measuring parameters of the object model, the researchers can obtain the values of parameters of object of research. In turn, the model object is created by mathematical modelling, i.e. using a mathematical model.
Best regards, Leonid Skvortsov
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