Hence the challenge (mentioned in the article) of defining the kilogram in a sensible way. The obvious method would be to say "1 kg = the mass of [###] of carbon atoms" or something like that. But counting 10^23 individual atoms is impossible for all practical purposes: it's still less precise than just weighing that reference lump of metal (despite the flaws of that approach).
The remarkable thing described in this article is that scientists are evidently at the verge of being able to count one electron at a time fast enough for use in calibrating actual, practical current measurement devices. That's pretty cool.
Using a cesium time standard and an atomic force microscope figure out the half life of individual atoms of 14C (or something more fun/shorter) then define a kilo of 14C as a pile of 14C generating X decay events per whatever interval calibrated by our cesium time standard.
(edited to add the point is you can watch individual atoms with the AFM and see which ones disintegrated in the past since the last scan, and its no great trick for a century or so to detect individual decays using a geiger counter. Also 14C is no fun for this task. Try a shorter halflife)
...almost as much of an embarrassment as...
The scientific soap opera of metrology (not meteorology) is interesting to read about. Computer science is hardly the only discipline to suffer from multiple standards.
One standard defined an amp as a certain mass of plated silver in a certain amount of time, so if that was still "cool" then you'd have mass defined indirectly solely from the quantum hall effect and Josephson junction effect and time aka cesium vibrations or whatever it is, which wanders into the whole "a kilo is a lump of metal in Paris" situation.
"At present, an ampere is defined as the amount of charge flowing per second through two infinitely long wires one metre apart"
If the wires are one metre apart, then how are they infinitely long?
The infinitely long part ensures the force is uniform through all parts of the wire.
Hope that helps.
Now the question to someone more knowledgeable in physics than me: if the described effort pans out, does that mean we can define kilogram as the mass that would accelerate at 1 m/s^2 if we apply the same force that affects two infinite wires one meter apart, with 1 ampere flowing through them?
This would then allow independent scientists to make their own spheres, calculate the number of silicon atoms in the sphere, and have their own reference benchmarks for the kilo without needing to check in with Paris.