“…the supporting structure can only withstand the forces if the interfaces between the ten individual segments of the central rings, which weighs several tonnes, are built with a level of precision of less than 100 millionths of a metre…” - and they found a small family business in the north of Italy capable of doing this!
thus, 100 millionths of a meter = 0.1mm, or ~4 thou in American units. Easily achievable by hobbyists, let alone by serious, professional equipment.
Sure, that is a pretty exacting specification for what I suppose is a big machine, but I'm pretty sure very normal things like say, car engines get made to far tighter tolerances.
millionths of a meter are known as micron so most people would call this '100 micron' (or '100 micrometers') which is indeed close to 4 thou, as you calculated, and is the level of accuracy of my ~$500 3d printer.
1 thou was achievable in routine shops in the 1940s and a tenth of a thou (2.54 micron) is a common accuracy to target these days. Obviously it depends on the context and the size of the object, at some point you move away from cutting to using grinding and lapping to achieve your results, which is ultra-timeconsuming.
What usually matters more than absolute tolerances is relative tolerance, aka ppm. 100 micron / 4 thou tolerance can be achieved with hand tools and a bit of patience on the benchtop scale, say a 4" part. That's about 1000 ppm, or 0.1%. If I gave you a meter stick, you could probably eyeball marking something +/- 1mm.
Getting the same finish on a 120"/3m coil is 33 ppm. 100 ppm / 0.01% for any operation or process tends to be where things start to get really challenging. Deflection goes up by the length cubed, so increasing the size of all the tooling relative to the tolerance gets really challenging really fast.
“…the supporting structure can only withstand the forces if the interfaces between the ten individual segments of the central rings, which weighs several tonnes, are built with a level of precision of less than 100 millionths of a metre…” - and they found a small family business in the north of Italy capable of doing this!