That sounds like a cool project. Do you know of any transcendental number that does admit an intuitive proof of irrationality (or, more generally, of not being algebraic to any specific degree)?
My gut feeling is that this shouldn't typically be the case, but I'm tired and struggling to convey why without descending into downright criminal levels of vagueness. I'd be more hopeful about an algebraic number of degree >1 having a 'nice' reason for specifically being irrational.
If it's even odds then I expect it's a losing bet no matter what anyone writes down - that's why in the imagined scenario it's forced. The pertinent question isn't whether you expect to lose money by playing, it's whether you expect to lose less money by including non-motorised vehicles in your write-up than by excluding them.
Personally my instinct is that I'd lose more money by specifying skateboards and bikes as I've usually seen those addressed by their own signs rather than being included under "vehicle".
I agree 100% with the spirit of your point and I think imagining a forced bet scenario can help to clarify things. There are three main concepts we want to interpret within the context of the phrasing of the rule: (1) the intended referrent of 'vehicle'; (2) the intended meaning of 'in' the park; (3) the actual intention of the rule regarding emergency vehicles.
This is the scenario: imagine you're forced to wager a nontrivial sum of money on the following bet. You have to write down how you interpreted (1), (2), and (3). Then we randomly pick a real park that has this exact rule phrased in this exact way (I'm hopeful there'll be at least one out there), find the person who wrote the rule, give them your written interpretation, and ask if they agree. You lose if they don't. Notice we're not asking them to also write down a longer interpretation and comparing word-for-word. Just whether they think you got the gist of it.
I would write down that 'vehicle' was intended to refer to motorized passenger vehicles, 'in' was intended to mean that the vehicles shouldn't be in/on water or land within park boundaries, and that the rule wasn't intended to restrict passage to emergency vehicles responding to emergency situations. I expect most people would write something similar if they had real money on the line.
The trouble with the horrible website is it's trying to prove that nebulosity makes content moderation difficult by forcing people to disagree, but this disagreement almost entirely pertains to a point that has nothing to do with nebulosity: the park rule would only ever be written within a wider legal framework and doesn't make sense in isolation.
If I take my answers to (1) and (2), I'm forced to conclude that the emergency vehicles were violating the rule within the ridiculously artificial scenario presented. However, I'm also confident that this rule would only have been written verbatim within a wider legal framework that provided exceptions for emergency vehicles.
Consider self-defence in the context of murder or manslaughter. In the UK at least, the first thing the court does is establish whether the defendant would fit the criteria for murder / manslaughter ignoring the self-defence aspect, because otherwise it's a moot point. Once this is done, they would then establish whether the defence of self-defence also applies, which would then negate the conviction. If you wanted to prove that law is complex because it's hard to define words, would you really make a website that says "Ignore everything else you know and suppose that murder is only defined as killing a person" and then think you're being really smart when people disagree on the scenario involving clear self-defence? Hopefully not, because they're really only disagreeing with being forced to invoke your artificially-restricted definition.
That said, the website demonstrates the real reason why online moderation is hard: because it disproportionately attracts the sorts of people who answered 'yes' to the ISS question in this quiz. So you often end up with lots of users sharing a reasonable consensus on what the rules mean being moderated by a tiny group of... we'll say 'non-representative' moderators. It's a common problem with any banal form of authority, and isn't specific to website moderation at all.
Learning names for the sake of learning names is never helpful. However the history of mathematics can help to contextualise the material and its motivation. For example, group theory has myriad modern applications. It can be (and usually is) presented in the standard mathematically-polished form, beginning with the axioms and perhaps using matrix groups or simple geometric symmetries as examples. For many learners this is a perfectly sensible way of approaching it and they wouldn't be interested to know more, yet I found it rather clinical and dry.
As I'm sure you know, group theory arose as a novel yet natural way of investigating the conditions under which polynomials can have closed-form solutions, and when Galois began to sniff this out it allowed him to get to grips with the impossibility of a closed-form solution to the general quintic polynomial: a problem which had beguiled mathematicians for centuries, solved by a theory which crystallised a more structural way of approaching abstract mathematics. Even though Galois theory is a relatively niche topic within the broad context of academia, for me it draws out the true character of group theory in a way that matrix groups don't, and neither do contrived examples formed from the natural numbers under various quotients. And it clearly solves a problem that required a new way of thinking.
There's certainly a balance to be struck here. If you fixate on historical origins then you aren't engaging with the reasons why the topic is still relevant today, so you risk missing the point. It also slows down the pace at which you can absorb the tools needed for applications. But if you only engage with the modern approach you risk building a disconnected, lifeless archipelago of knowledge, unable to see the beautiful links that unify so much of mathematics.
I grew up with the Times crossword over dinner. We're not the most talkative family so a puzzle gives us something to do together while we're eating. A few observations, learned from introducing various other people to the hobby over the years:
1) The number one problem for new people is simply absorbing the rules of how to parse a clue. The linked article does a good job of going through these. Try to avoid the sense of learned hopelessness that often sets in early on.
2) The second most common isue is not managing in practice to get away from a literal reading. You need to take every word in isolation and try to escape the inevitable misdirection. For example, if the word 'rose' is in a clue that also contains the word 'flower', it's very unlikely that you're supposed to read 'flower' to mean something with petals. You need to think of any possible interpretation other than the obvious one. The classic second meaning here would be to read it as 'something that flows', which will mean the name of a river. Which brings us neatly onto the third difficulty:
3) Cryptic crosswords are heavily grounded in old-fashioned English culture. A reference to a river could mean a major international river or an obscure one from the British Isles, but it would be considered unfair to refer to an obscure river from another country. There are also some incredibly dusty references: 'sailor' could mean 'tar' (an archaic english slang that now exists only in crosswords) or 'AB' for 'able-bodied [seaman]'. 'Men' could refer to 'RA' (Royal Artillery) or 'RE' (Royal Engineers) among other things. One of the worst is 'posh' (or synonyms of it) to clue the letter 'u', which comes from high-society slang in the early-mid 20th century. 'Home counties' would be SE for South East [of England]. Cockney rhyming slang also often features, among many other things.
Problem 3 is the most insurmountable. It's also largely unfixable. If the range of acceptable references were broadened, it would become almost impossible for anyone to finish any given puzzle. But the references were fixed at a time that is no longer relevant and provides a huge barrier to entry for new people, which is why I expect these puzzles will largely die out over the next generation.
The bottom line is that if you feel like you struggle with cryptic crosswords, it's probably not because you're being stupid. There's a surprising amount of domain-specific knowledge you have to absorb, and in the best of cases any given puzzle will typically contain one or two absolute stinkers.
A few references to help:
4) I haven't seen squarepursuit before (linked by tclancy) but it looks like an excellent resource.
A few random tips:
1) Try to get the clues from the first row and the first column early on, as these give you starting letters for other clues
2) Get used to looking for anagram indicators. 'drunk', 'rotten', 'altered', anything like that. The other anagram indicator is always from adding up letters: if the answer is nine letters, look for combinations of words that add up to nine letters. Once you identify them, anagrams are a solid place to start once you've looked at the first row/column.
3) If possible, crosswords are best done with company. Everyone thinks in different ways.
4) Be wary of fish references. These can be incredibly obscure, and often indicate that setter was struggling to clue the last few letters so just googled them and found some vietnamese river fish that fit the bill.
5) If you're truly fed up, you can use a thesaurus on the word that you think is the definition. This is a bad habit, but if it lets you open up the puzzle a bit then it might be the right course of action.
My gut feeling is that this shouldn't typically be the case, but I'm tired and struggling to convey why without descending into downright criminal levels of vagueness. I'd be more hopeful about an algebraic number of degree >1 having a 'nice' reason for specifically being irrational.