I'm reading this thread with css adjustments from the Dark Reader Firefox extension that I just learned about a few weeks ago, and damn, I am soooo happy with it.
Not closely related, but the topic reminds me of this gem of a question from math.SE: Why does "Turn! Turn! Turn!" equal 241217.524881? (It's because of the calculator, but not in an obvious way.)
It has quite a few details that give a sense of the engineering challenges involved.
- The Kibble balance has a weighing mode, and a calibration mode; the two are used to cancel out a significant portion of the systematic error introduced by the mechanical system
- Measurements are made in a vacuum to eliminate effects of air buoyancy, which are significant at the desired level of precision.
- One advantage of the wheel configuration is that it allows the supporting cables to move the coil exactly vertically, thereby avoiding the undesirable sideways motion that a coil suspended from a beam balance can experience.
I could go on, but this gives an idea and you can go read it yourself ;)
I think the story is told as a sort of cultural marker of what a Big F-ing Deal this discovery was/is. Mathematics, collectively, struggled for a long time to find a way to make 3-dimensional numbers into an algebra in a way that extends the algebra of complex numbers. (The cross and dot products are unsatisfying, because they don't have division.) The shock that this can be done in four, -- not three -- dimensions is still sort of reverberating, and that's what I think this story marks. It's a short stand-in for the longer story I've just summarized, and it evokes (or is meant to evoke) the mind-shattering thrill of discovery.
I don't necessarily think the story accomplishes this -- your question is but one piece of evidence that it doesn't -- but I think for those who spend a good amount of time with these kinds of algebra questions, it comes to take on that role, and that's why I think it's repeated.
(Teaser -- if you want to know more about these kinds of questions, Google for "real division algebras". There are not very many, and they way they are organized is not, I think, something one would expect.)