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gwern comments on A Parable of Elites and Takeoffs - Less Wrong
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Pt 1: I don't know. The core of science is not so very complicated. Empiricism plus skepticism plus math. The hardest part of that is math, and of the three that is the most easily transmitted by book. Of the rest, that's a bit of sociology I can't judge. Lesotho isn't what I'm holding up as 'the most likely source of a rebound in the event of nuclear war' - it's an example of the spread of real science.
Pt 2: Sometimes... but even if acupuncture is a really reliable way of inducing a strong placebo effect on people even if they know it 'does nothing', that's useful.
Then why did it take so long?
The tradition of math is the most ancient & universal of the 3 parts you mention. Most regions of the world develop math, sometimes to fairly high levels like in India or China. Is that consistent with it being 'the hardest part'? In contrast, empiricism and skepticism are typically marginal and unpopular on the rare occasions they show up; the Greek Skeptics were one of the more minor traditions, the Carvaka of India were some heretics known from like one surviving text from the early BCs and were never a viable force, and offhand I don't even know of any Chinese philosophical tradition which could reasonably be described as either 'empirical' or 'skeptical'.
It's also not what they think they're measuring. Still diseased.
Because it's psychologically hard and unintuitive, not because it's complicated. Math is complicated and difficult, but it's not psychologically challenging like 'do your best to destroy your own clever explanations and cheer if someone else does'.
Acupuncture makes a great example. Here we have folks who are on to something that works. Yay! Case closed. ... except, not. Because they don't have the idea of science, the hard and unintuitive thing that says you should try to find all the times that that thing you rely on doesn't work, they can't find those boundaries.
...and if science is psychologically hard & unintuitive, all the easier for it to be substituted for something superficially similar but ineffective.
And how does that not make science harder than math?
Skepticism and empiricism are robust ideas, by which I mean there's nothing particularly similar to them. They are also very compact. You can fit them on a post-card. On the other hand, math is this enormous edifice.
The 'getting it wrong' that you see all over modern science is a failure, yes, but most of these scientist-failures are failing due to contingent local factors like conflicts of interest and grant proposals and muddy results and competition pressures... they're failing to fulfill the scientific ideal for sure, but it's not because they lack the scientific ideal. They can correctly teach science. If bad scientists were all we had, then science would have bad habits and that would be bad, but it could be solved much more easily than having to redesign the thing without knowing that it was possible, like we did the first time.
This is still the case even if all the scientists are under the thumbs of warlords who make them do stupid stuff. The idea is there, the light can spread. Not right away, likely, but we won't need to wait thousands of years for it to re-emerge.