One kind of harmony of nature is widely noted: laws of nature that hold at one place and time tend to hold everywhere else. This is a kind of horizontal harmony of nature.
But maybe there is also a vertical harmony of nature. Nature has multiple levels. There is the fundamental physics, the chemistry, the biology, the psychology and the sociology of the world; and also, along a parallel hierarchy starting with the chemistry of the world, the geology and astronomy of the world. The unity I am interested in between these levels is subtler: it is that essentially the same scientific methods yield truth at all these levels. Granted, there are modifications. But at all the levels, the same inductive techniques are used, and relatively simple mathematical models are made to fit reality.
Suppose that all the higher levels reduce to the fundamental physics. I think it is still surprising that the methods that work for the reducing level continue to work for the reduced level. And if there is no reduction, then the vertical unity is even more surprising.
There may be a teleological argument here. But I am worried about three flies in the ointment. The first is that perhaps I am exaggerating the unity of methods of investigation between the different levels. In school, we learn about "the scientific method". But in fact the methods of investigation in the different sciences are perhaps rather less similar than talk of "the scientific method" suggests.
The second is that the unity between the levels may simply be an artifact of the method. In other words, we have a certain method of mathematically and inductively modeling reality. And the levels that I am talking about are nothing but areas where the method works fairly well. And there is nothing that surprising that given an orderly fundamental level, among the infinitely many other "levels" (not all in a single hierarchy; just as above we had two separate hierarchies, one going up to sociology and another to astronomy) of description of reality, there will be some that can be modeled using the same methods, and those are the levels we give names like "chemistry" and "geology". In other words, we have a selection bias when we set out the case for vertical order.
If this worry is right, then we should only be surprised by the order we find at the fundamental level. But, my, how surprised we should be by that!
And, further, if we see things in this way, we will see no reason to privilege scientific approaches epistemologically. For there is nothing that special about the sciences. There may be infinitely many levels of description of reality which can be better known using other methods.
The final fly in the ointment is that while there are a number of levels that can be known using the same methods, there seem to be areas where we have genuine knowledge, but the scientific methods do not work: ethics is a particularly important case.
So in the end, I do not know really what to make of the vertical harmony thesis. It bears more thought, I guess.