When we are talking at the (sub) micron level, isn't the goal to create an edge that is as even as possible, both at the edge and the edge of the edge? So to smooth out scratches from previous stones and, ultimately (but this is a dream ) see no molecule raises and drops at all anymore?
It's a cliff hanger, I know! I've got a couple of things on my plate keeping me from writing up the blogs at the moment - I've got a new website that we're trying to launch on Friday!
That answer is "it depends". The smoother the edge of the edge becomes, the less aggressive it is for tearing, and it slices more. Good for shaving and unzipping hides, but due to the relative thinness of the edge of the edge, it can easily loose that freshness, much like a newly sharpened pencil. Geometry is used to support the edge of the edge. But ultimately, the point of the edge is still approaching 0 width no matter what the angle.
Conversely, a less refined edge has larger serrations in the edge (more refined still has serrations, just a lot of very small ones), and that helps for sawing and ripping power, although the coarser the serrations, the more likely they are to break off during use. Butchers like rougher edges in general since they are more concerned with removing the meat from the bone aggressively rather than making a beautifully presented slice cut.
Anyway, all of this will be explained in due time with the pictures
Therefore I'd be interested to know what the difference is between polishing and creating consistent scratches.
Again, it boils down to Aesthetic vs. Function, and are two different philosophies in sharpening. I prefer the function over the aesthetic in general, but lots of other guys prefer aesthetic over the functional. The Shapton and Chosera 2K stones leave a very similar scratch pattern, but their resulting edges are tangibly different.
I'm in total agreement here with the added caveat that the polish level (when considering function) should be dictated by the type of cutting to be done. In the most simplistic view, if you're push-cutting, as you would to shave or to carve wood, then you'll want as polished a bevel and edge as possible and if you're slice cutting, then some level of micro-serration is desirable, the exact size of the serrations is dependent on the material you're cutting. I've tried to cut zip ties with with a super polished edge and the knife just kind of slides across the surface, so I've found that a relatively coarse finish is good for cutting hard plastics. If you're slashing rope, toothier is better. If you're cutting rope by pressing it against a board and push cutting, then smooth is better. Materials that have a tough shell and soft interior like tomatoes and baguettes benefit from a slightly toothy edge (unless the angle is super acute and then you can push cut right through that stuff with a super polished edge ) When I'm first starting out with a knife, I like to polish as much as possible and then try to use it on whatever it's intended for. Then I start going backwards in coarseness until I find the right finish level for the job and then I keep it there.