Not to say I disagree with your post, but it's it more accurate to say that the natural sciences today explore models for the world in which we live? The models tend to be fairly obvious for things on the human scale, but when you talk about systems on the atomic scale, or on the cosmic scale, the immediacy of the models tends to break down. The result is that, just as for the abstract sciences (math, CS, etc), the usefulness of the models has to be justified. So, I feel that the line between purely abstract sciences and "natural sciences" is not quite as fine and well-defined as your post makes it to be.