"See the edge" is rather imprecise. I can "see" my finger, even though I can't see the individual cells. Circle of confusion for normal human vision at close range is about 0.2 mm, so we can pick out individual lines down to about 5 lines per mm. A fairly modern APS-C digital sensor can only do about ten times better, but would have to do 1,000 time better than the eye to see if the knife was optimally sharp. What this means is that, roughly, any feature smaller than 0.2 mm will appear to be a point, with any finer detail being lost. We can, of course, see the edge of the knife. But that depends on how you mean "see." We cannot see irregularities. If we consider an ideal blade as a plane with an edge ending in a theoretical line, we cannot see divergences from that theoretical perfection that are less than 0.2 mm. Even dull blades appear to form a perfect line against the background.
But what we are interested in is the thickness of the blade at the point where the sides effectively turn inward toward each other, creating a blunted edge. To judge if the arbitrarily chosen goal of 2,800 nm for that thickness had been achieved, we would need magnification. Remember, even with magnification, we cannot judge sharpness unless we look down on the edge itself from some angle. We can't see it by looking at the side of the blade. And looking down, we could not tell any difference between a width of 0.0028 mm (2,800 nm) and a width of 0.2 mm, ten times as thick. Any flaw we can see is truly gross damage.
What's also interesting is that we cannot, then, see the burr that inevitably forms while sharpening, the thinest edge of steel that is so thin that it can't stand up to the stone. But we can feel it easily as drag if we run a finger toward the edge and off the blade. Since few of us use the finest stone to finish or a strop, we always have that burr left after sharpening. Of course, absence of burr doesn't imply a sharp blade. Only when the edge becomes thin can the burr form, and most people use some device that is subject to the blade held in the hand wobbling against the stone so that little of the edge actually gets to become that thin.
"Kitchen duty is awarded only to those of manifest excellence..." - The Master, Dogen