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Lens grinding and Avogadro's number

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A bunch of scientists are working on defining the kilogram using fundamental constants of physics, rather than the weight of a particular chunk of metal, as it is now.  But before they can do that, they've got to determine Avogadro's number—the number of atoms in a particular mass of an element, 6.022 x 10^23 if I'm not mistaken—to unprecedented precision.  One strategy is to make a sphere weighing exactly one kilogram, and then count the number of atoms, thereby reverse-engineering the kilogram.  The trouble is, the sphere has to be as close to perfect as humanly possible.  How is the world's most perfect sphere created?  By hand.  No, really:
To improve on the precision of his result from the 1970s and ’80s, Becker needed to reduce the irregularity of his silicon surfaces. He commissioned one of the world’s most renowned lensmakers — a German immigrant in Australia named Achim Leistner — to craft the most perfect sphere ever created, a flawless orb honed precisely to the mass of Le Grand K.
Leistner describes his job as “massaging atoms.” He works by hand because he believes — and the most advanced computer imaging has confirmed — that no machine can match his touch. Taking a 1.01-kilogram silicon ball crudely cut on a 3-D lathe to within 10 micrometers of sphericity, Leistner spends several months polishing the surface by spinning the object inside a pair of funnels — like a scoop of ice cream held between two cones — until he can feel the molecular structure of the cubic silicon crystal itself with his fingertips, 12 edges and eight corners barely protruding from the rounded surface. Then the hard work begins. Without letting the mass of the sphere drop below the 1-kilogram mass of the international prototype, Leistner must polish each of the nearly imperceptible edges and corners, removing mere nanometers of material per week. Since a several-atom layer of silicon dioxide (more familiarly known as quartz) forms on the surface whenever he stops spinning the sphere, and since quartz is much harder than pure silicon, he can spend as many as six hours a day carefully buffing off the oxide layer before reaching the silicon atoms to be shaved.
 Unbelievable.
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