Perpendicular Parallel
My friend Kent is evaluating a new knife sharpening system. It works in a way similar to the familiar Lansky system where the knife is clamped into a fixture and the abrasive “stone” is attached to a rod that slides through a hole in the fixture such that the abrasive is always in contact with the edge at the proper angle. This system allows the abrasive to stroke either parallel or perpendicular to the edge. His question to me was how the edge would perform with the scratches running in one orientation or another.
This issue has come up before. There is some concern expressed by woodworkers that side-to-side sharpening will weaken the edge as it introduces parallel scratches. Those scratches, it is feared, will cause the edge to break off along the scratch-line. While this may be the case with very coarse grits, by the time you’ve polished to a proper woodworking edge, abrasive scratches are difficult to detect even with an electron microscope (see pages 218 – 219 of The Perfect Edge for micrographs of edges honed with various abrasives). I can’t imagine an edge failure caused by half-micron scratches. I use a side-to-side motion when I hand-hone a blade, and a to-and-fro motion when I use a honing guide. With either method I hone to 8000-grit and remove the last little burr with a chromium oxide-charged strop. The cutting actions of the resultant glassy-smooth edges are indistinguishable.
The Perfect Edge (page 179)
But all that is about an edge for a hand-held woodworking tool. An edge that gets pushed into the wood, shearing the fibers in its path. The aforementioned knife sharpening system is designed for knives of the hunting-, fishing-, kitchen varieties. The requirements for a knife edge differ considerably from those for, say, a chisel. A knife is much less often pushed into that which it is cutting. Usually the edge of a knife is being slid through it with a sawing motion. There are some kitchen prep cutting actions where the knife is simply pushed through the food: chopping celery or broccoli, slicing cheese, for example. But a ripe tomato, raw meat or a loaf of French bread require an edge with some “tooth” on it to allow it to dig in. A polished edge (8000-grit or so) will glide over a ripe tomato skin without cutting but one that was honed to about 1200-grit will cut like crazy. And that soft French bread will need a serrated knife — an actual saw — or you’ll just mash it flat in the effort.
The point to all this is simply that the edge you need depends entirely on what you intend to cut. Ultimate sharpness and practical sharpness are not necessarily the same thing.
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I frequently peruse the blog links at Joseph Sellers’ Unplugged Shop and was pleasantly surprised to see three sharpening posts listed today. Matthew at Workshop Heaven describes how to sharpen a shoulder rebate plane, Jon Mac at Spoon Carving First Steps teaches about sharpening the hook knives he uses for carving spoons, and Ralph Beaumonot at the Accidental Woodworker shares his thoughts on sharpening chisels and plane irons.
And, of course, Joel at Tools for Working Wood came through once again with his most excellent piece on The Tools of Stropping. 
