I'm slightly confused over this concept and hope to gain some understanding from all my seniors over here. I'm thinking this confusion is a result of me mixing two concepts of "different frequencies" together and as a result failing to piece two sets of understandings together, so I hope I could be brought back to the right tracks again. 
Quote from DPReview:
I've also noticed that in macro photography — which is an application that often requires shallow DOF if I'm not wrong — it is preferred to shoot at the telephoto end. Putting aside the more practical/execution issues such as wanting to shoot from a distance to prevent scaring the insects and animals (or if it helps, imagine the case that I want to shoot an inanimate object for practice/abstract purposes), does telephoto also help to give that desired DOF?
My train of thought is as such: consider the case that I wanted to take a picture of a subject at a given size with a shallow DOF. By basic principle of DOF, if I want to have a greater blurring of the background, I should decrease the distance between the subject and my camera, as well as increase the distance between the subject and the background, keeping all other things constant.
However, after I "zoom in" on my subject, I have to move back further than if I were to shoot the same subject at the wider end, in order to obtain that same given size. Doing so effectively violates my basic understanding of obtaining a shallow DOF as stated in the previous photograph. So why is shooting telephoto preferred?
Having said that, to complicate matters further: some lens have higher F-numbers when at their telephoto ends. So using telephoto would mean using a larger F-number while at the same time increasing subject-camera distance.
To give a concrete example with figures: would shooting at 35mm f/2.8 or 140mm f/4 be better to give the desired shallow DOF?
Granted, in this case the F-numbers are different so it's no longer about the focal length only, but since shorter focal lengths (35mm in this case) provide greater DOF, does the f/2.8 of 35mm more than compensate to give a shallow DOF compared to f/4 at 140mm? Don't really know how to phrase this, hope it isn't too confusing!
Sorry for the long read, I thought it was better to describe my question in greater detail.
Quote from DPReview:
I've also noticed that in macro photography — which is an application that often requires shallow DOF if I'm not wrong — it is preferred to shoot at the telephoto end. Putting aside the more practical/execution issues such as wanting to shoot from a distance to prevent scaring the insects and animals (or if it helps, imagine the case that I want to shoot an inanimate object for practice/abstract purposes), does telephoto also help to give that desired DOF?
My train of thought is as such: consider the case that I wanted to take a picture of a subject at a given size with a shallow DOF. By basic principle of DOF, if I want to have a greater blurring of the background, I should decrease the distance between the subject and my camera, as well as increase the distance between the subject and the background, keeping all other things constant.
However, after I "zoom in" on my subject, I have to move back further than if I were to shoot the same subject at the wider end, in order to obtain that same given size. Doing so effectively violates my basic understanding of obtaining a shallow DOF as stated in the previous photograph. So why is shooting telephoto preferred?
Having said that, to complicate matters further: some lens have higher F-numbers when at their telephoto ends. So using telephoto would mean using a larger F-number while at the same time increasing subject-camera distance.
To give a concrete example with figures: would shooting at 35mm f/2.8 or 140mm f/4 be better to give the desired shallow DOF?
Granted, in this case the F-numbers are different so it's no longer about the focal length only, but since shorter focal lengths (35mm in this case) provide greater DOF, does the f/2.8 of 35mm more than compensate to give a shallow DOF compared to f/4 at 140mm? Don't really know how to phrase this, hope it isn't too confusing!
Sorry for the long read, I thought it was better to describe my question in greater detail.
