'It' (most of 17th, 18th and 19th and some early 20th century mathematics, chemistry and physics) is clearly a lot more abstract than the failed alchemies.
The point is that 'just keep trying' would not have been a good strategy.
Are you sure it's not using static data generated by a car which has driven the same roads and then has had speed limit sign detection run on the captured video?
However, as far as I can tell, the GPS data, in at least some cases, comes from Streetview-type camera cars which drive along the roads and capture the roadsigns.
On French highways there are context-dependent speed limit signs which look exactly like normal signs but with a small additional panel below which tells you when they apply. Eg, big 70 in a round red circle, with a small picture of a car towing a trailer below. Eg https://external-content.duckduckgo.com/iu/?u=https%3A%2F%2F... which obviously only applies to cars with trailers.
Google maps (on my phone, not built-in to the car in any way) would constantly tell me that the speed limit of the road was that of the last such sign regardless of the specificity.
If you Google the name of a UK car insurer with some likely keyword like 'claim' or 'accident', you get paid listing from people offering two 'services'. a) 'call connection', which means that you call their premium-rate number and they just put the call through to the right company's phone line while charging you per-minute. b) 'claim management', you fill out a form on their website, they submit it to the actual company's website, and take a percentage of your claim. Neither of these are illegal, Google has promised to not take ad money from the first type, but in practice don't remove ads fast enough to make it unviable.
Consumer-facing companies now, ludicrously, have to do their own SEO to make sure they appear top of search results for their own name, and some even pay Google for ads to themselves. But clicks are more valuable to scammers than to legit businesses, so the former can always outbid the latter.
However, the analogy is still accurate, because the right approach involved several steps which no one thought were conceivably part of the solution: "understand how forces work at macro scales", "understand electricity", "understand magnetism", "develop a mathematical framework for summing tiny localized effects over large and irregular shapes", "develop a mathematical framework for understanding how continuous distributions evolve based on simple rules", "learn to look accurately at extremely small things", "learn to distinguish between approximate and exact numerical relationships", "develop a mathematical framework for understanding the large-scale interaction of huge numbers of tiny components", and so on.
If you went back in time to an age where people were working hard on changing lead into gold and your mission was to help them succeed as soon as possible, your best bet would probably be something like teaching them the decimal place value system, or how to express algebraic problems as geometric ones. But if you also told people that this knowledge was the key to solving the two problems they were working on, "how to make very pure versions of a substance", and "how to understand what makes specific types of matter different" you would reasonably have been regarded as deluded.
You have pointed out that when the machine locks out, there is an actual reason behind it. I don't think anyone claimed that it's simply triggered by an RNG or a timer.
However, why are the machines this opaque and difficult to keep running? I think the point has been clearly made, that an incentive structure optimises for low reliability. Nothing you said contradicts this.
Perhaps it is, but if there had been credible evidence of a theft 'I would not have been able to spend all that money in cash' is not the basis of a solid defense.
There have been genuine cases where accountants, bank managers, and so on have embezzled large sums of money, including in cash, and spent it all untraceably on things like feeding a gambling addiction.
It would be an extremely good solution if it worked as intended. In fact Openreach were not fully independent from BT for most of their existence, and they operated the network in a way which was extremely favorable to BT for a long time.
Thus, the two companies extracted an exorbitant rent for the formerly public goods they controlled. The fact that some of this rent went to inefficiencies of running two separate companies on an illusionary arm's length basis does not really improve matters.
It was an extremely complex case which was very hard to prove, against companies which belong to the establishment and had been shown the benefit of the doubt by the legal system on multiple occasions.
Post Offices handle a large amount of cash, much more than any other business of their size. Many of the sub-post offices in question would be paying out pensions and welfare benefits in cash to a large proportion of local customers. If someone was stealing from the post office, they could easily do so in cash.
The point is that 'just keep trying' would not have been a good strategy.