(For English readers: The word "model" corresponds to "モデル" and "模型" in Japanese.)

Fig: Real car and its model

Next, we will dig into the word "model." The word "model" is sometimes translated as "模型" especially in the field of natural sciences. For example, "標準模型"(standard model) of elementary particles.

A toy car which a child plays is also called "模型." The toy car is not equal to a real car. However, it is a toy which has important parts extracted from real car to achieve the purpose of running a car and playing. *30

The model in science is a simplified expression to explain the mechanism of the real world. Because the phenomenon in the real world is complicated, we make them simple so that we can handle them with our limited cognitive ability.

For example, in high school physics, we ignore air resistance or friction.

The air resistance and friction exist in the real world. Ignoring them, we simplify the problem and make it possible for high school students to handle it.

Since the model extracts a part of the reality, it does not exactly match the reality. The words "all models are wrong" (*31) means to this.

The value of the model is not the degree of fitness with the reality. It is how much the model is lower in operation cost than directly manipulating the reality.

Especially the model expressed using mathematical expressions is called "mathematical model." Making a model in the form of a mathematical expression or program makes experiments easier. It is because there is no need for physical experimental equipment.

A good programmer sometimes predicts the cause of the problem without having to look at the actual source code. Why is it possible? There is a model of the program in his brain. He can experiment in the brain that he breaks various parts of the program and observe what happens in the case. Then, he picks the cause which bring the similar result with the observed in the real world.

*30: Which part is important depends on the purpose. Toy cars have batteries and motors rather than gasoline engines, but the difference is not important to play. On the other hand, if you are researching to make a gasoline engine with good fuel economy, having gasoline engines is important. On the contrary, the design of the exterior is not important.

*31: Box, G. E. (1976). "Science and statistics." Journal of the American Statistical Association, 71 (356), 791-799.

*32: Physicist Ernst Mach thought that describing many facts with few concepts and saving the thinking effort was the fundamental principle of science. It is called Denkökonomie (thought economy.) The unit of speed "Mach" named after him.