In the natural sciences, this system happens to be the world in which we live
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.
> isn't it more accurate to say that the natural sciences today explore models for the world in which we live?
This is entirely true, and there are absolutely areas of natural science where the "right models" are pretty unclear, such as theoretical physics, as you mention. In this sense my distinction is somewhat fuzzy.
I am likely biased to perceive a large gulf because I work in molecular genetics, a field in which the there is a lot we are certain about; much of what we do is filling in holes and fleshing out the details of overarching models that are known to be largely correct.
I really like knowing that there are people dedicated to thinking deep thoughts. There was a recent potential proof published on a tough math problem, and apparently the author had gone dark for 15 years creating a fantastic mathematical universe and vocabulary all on his own. Thats worthwhile. Maybe not for everyone to go off doing it, but definitely for some.
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.