I sharpen my knives on a grinder that uses 2" x 72" belts. For that kind of aburdly sharp edge, I grinder sharpen a Moran edge (basically an appleseed profile vs a "v" bevel that a lansky creates) using a 600 grit belt, then hand hone with 800-1200 grit papers. You do this by mounting the paper on a mousepad. The "give" the mousepad offers helps the paper follow the moran edge. When its razor sharp, I then strop using a mounted leather "stick" strop until the edge is almost a mirror polish.
This kind of absurd surgical edge is fun but not as practical. A good old convex moran edge is, IMHO, the best edge profile out there if maintained correctly. This image demonstrates why:
As you can see, maintaining a convex edge means you take material off the whole blade surface as you sharpen, so it will always cut with the same ability. With a lansky, after a few sharpenings, the cutting bevel is still the same angle but the "meat" behind it gets thicker with each sharpening.
In addition, the convex edge will "slip" through materials easier than the V profile. This comes into play most often in heavy chopping when you need to tread a fine line between a thin blade that wants to deform under heavy stress and a thick, strong blade that must force the wood apart more and results in less cutting ability.
ABS cutting competitions try to force makers to have the best of all worlds by having different tests in sucession. First fine cutting like paper tube slicing (sharpness), then timed 2X4 chopping (edge strength, proper heat treating), then rope cutting (edge geometry)....at the end, any deformations of the edge, chipping or even dulling of the knife are automatic disqualifications.
