Well this is an interesting and often discussed topic.
I guess I should start off by saying that I like a task specific edge.
Let me give some examples. A local restaurant that I sharpen knives for I routinely had been doing 2-4k level edges, but his main concern was quick turnaround and I strongly suspected that his requirements were very low for an edge. Besides his knives came back horibly abused - chips, blunted tips, dull. Used on stainless countertops, scraping cast iron pans, etc. And most of his knives are cheap knives too. So I switched to using an 8-0 grit belt followed by a 220 belt. He never noticed a difference. Now I charge him a very low price and can get a stack of them back to him in no time at all.
My own knives - I use all kinds of edges and lately use a lot of natural stone edges of unspecified grits. And yes I do also use edges as high as 640k grit edges. Extra work - yes. Pleasurable to cut with - you bet! I have no problem with tomato cuts at that level of refinement. As a home cook, I can get away with a more extreme edge than someone doing high volume in a restaurant. I'm totally unapologetic about this. Some of my knives just get touchups on a Kangaroo strop with some 0.1 micron compound or higher - 160K+. My straight razors get 0.025 micron touchups routinely and I don't complain about my shaves
Now if I'm using a knife like a European chef's knife - the steel limits the practical amount of refinement, so BDL and I aren't too far off. And if you are touching up an edge with a steel, especially a ribbed one, then yes a refined edge is a waste of time since the steel is wiping it off on the first swipe.
I'm always amazed at the idea that using a steel to realign an edge is OK where you are continuing to use weakened steel for your edge, yet somehow it is assumed that a highly refined edge is a wire edge of some sort.
"If you aren't drawing a burr, deburring, and revealing a fresh metal edge you're polishing and not sharpening. "
Here BDL and I do part ways substantially. I often specifically DON'T draw a burr or make wire edge to deburr. I feel this method of sharpening is a deeply flawed but commonly stated concept. When you sharpen, the goal is to get the two sides of a knife to meet in a perfect union. Once the two sides have met, if you continue to sharpen, you generate an unnecessary burr. Then you break off this weakened metal which you have CREATED by going past this point of union. Now you have two sides that no longer meet, but instead have an exposed fracture plane of work hardened steel as your edge, with the high probability that you have additional fractures extending back into the very steel you are going to use as your edge. This yields a weaker edge than if you had not generated the weakened steel to begin with. And creating a wire edge on purpose to break the entire wire off is an even more excessive case of generating even more weakened steel. Instead I suggest generating the smallest possible burr - if you need to - at an 8k or higher grit level and not earlier. The idea of making burrs at each grit and breaking them off reminds me of Sisyphus, endless condemned to push a rock up a hill over and over.http://1.bp.blogspot.com/-IdMARwCE-AM/U ... syphus.jpg
I'd also like to point out the confused use of the term stropping, which I've mentioned in the past. It is best to think of simply the grit level and the stone or piece of leather or other substrate that the grit is on. So for instance, stropping on a 4 micron CBN strop is often a good enough edge preceded by a 1k stone. And this is far coarser than a 30k stone, even though it is a 'strop'. Stones strops, belts, etc should be considered as a continuum, where you simply pick the grit level and abrasive type suitable for the edge you wish to produce. The distinction between sharpening and polishing is an equally false premise and should be obvious to anyone who has seen an edge under magnification.
While I do have additional points of disagreement with other points raised, I figured that just going over one sentence's worth of disagreement is enough for starters
"As a side note, it's always fun for me to see where Ken Schwartz and I come to fundamental agreement and then veer off. " +1