Chips & Chips
Junior Member level 3
Jeffrey,
I think you are missing the point of my use of the word "model". I am saying that ANY description of a real world phenomenon is a model. If you are talking about a rough analogy, like the water-electricity comparison or a seemingly rock solid theory, like Newton and gravity, or just a set of equations that you use to design something, it IS a model. I am talking about a more general use of the word than anyone else here seems to be understanding. In this sense, the use of numbers, including imaginary or complex numbers, is part of a mathematical model of the system that is being designed or studied. Numbers, even the simple counting numbers, are abstractions, not physical things. Apples and oranges and bees and skyscrapers and electronic components in a circuit are real, physical things. We only use abstract numbers to try to predict the behavior of these and other real objects. And we only use these numbers and the mathematical manipulation of them WHEN THEY ACTUALLY WORK; that is work in the sense that they produce correct or near correct answers about that real world behavior.
In the sense of the word that I am using, you and I and all scientists and engineers are constantly using models. Almost everything they and we do is via models.
I think you are missing the point of my use of the word "model". I am saying that ANY description of a real world phenomenon is a model. If you are talking about a rough analogy, like the water-electricity comparison or a seemingly rock solid theory, like Newton and gravity, or just a set of equations that you use to design something, it IS a model. I am talking about a more general use of the word than anyone else here seems to be understanding. In this sense, the use of numbers, including imaginary or complex numbers, is part of a mathematical model of the system that is being designed or studied. Numbers, even the simple counting numbers, are abstractions, not physical things. Apples and oranges and bees and skyscrapers and electronic components in a circuit are real, physical things. We only use abstract numbers to try to predict the behavior of these and other real objects. And we only use these numbers and the mathematical manipulation of them WHEN THEY ACTUALLY WORK; that is work in the sense that they produce correct or near correct answers about that real world behavior.
In the sense of the word that I am using, you and I and all scientists and engineers are constantly using models. Almost everything they and we do is via models.