Fred,
Excellent answer.
I realize that the natural world obeys different laws than the atomic world.
However, given the proper tools, would man ever be able to construct, say, one ball bearing that was absolutely identical to a second ball bearing?
The requirement that every diameter even of something weighing on the order of as little as a gram must be the same to within 1 atom is literally an astronomically difficult requirement.
A ball-bearing the size of a BB pellet has on the order of 10^21 atoms. If you started counting those atoms now, it would take you north of 100 trillion years just to account for them all. That is about 1000 times the age of the universe. Machining a 1 gram ball-bearing to within an Angstrom (which is around the size of an iron atom) on every diameter? Possible in pure principle. Impractical in every sense.