Humans are model-builders. We create models of the world to manage complexity and to help us understand problems we're trying to solve. You see models all the time. Maps are models of roadways. Globes are models of the Earth. Chemical symbols are models of chemical interactions. Atomic models are representations of the interaction of sub-atomic particles.
Models are simplifications. There is little point to a model that is as complex as the object in the problem domain. If you had a map of the United States that had every rock, blade of grass, and bit of dirt in the entire country, the map would have to be as big as the country itself.[1] Your road atlas of the U.S. eschews all sorts of irrelevant detail, focusing only on those aspects of the problem domain (e.g., the country's roads) that are important to solving the problem (e.g., getting from one place to another). If you want to drive from Boston to New York City, you don't care where the trees are; you care where the exits and interchanges are located. Therefore, the network of roads is what appears on the atlas.
[1] To borrow a joke from comedian Steven Wright: "I have a map of the world. One inch equals one inch. I live at E5."
Albert Einstein once said, "Things should be made as simple as possible, but not any simpler." A model must be faithful to those aspects of the problem domain that are relevant. For example, a road map must provide accurate relative distances. The distance from Boston to New York must be proportional to the actual driving distance. If one inch represents 25 miles at the start of the trip, it must represent 25 miles throughout the trip, or the map will be unusable.
A good object-oriented design is an accurate model of the problem you are trying to solve. Your design choices will influence not only how you solve the problem, but in fact they will influence how you think about the problem. A good design, like a good model, allows you to examine the relevant details of the problem without confusion.
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