Use of prepositions in all languages is, AFAIK, totally chaotic and not subject to usable rules. You just learn from long experience. Can you explain why New Yorkers stand on line, while in all other dialects of English I am aware of we stand in line. Or why you go to college, but go to university (at least in the US). In the US, an illness might land you in the hospital, while in Canada it lands you in hospital (okay that is not a variation in the preposition).
For what its worth, probably not much, it seems to me that you use in only for something that surrounds you. In earth would suggest you are underground, while on earth suggests it is below you. On third ave suggests you are outside it, while in the Empire State Building suggests you are inside it. But I know from my daily life that there is simply no correspondence between prepositions in English and French.
The Canadian (and UK) usage is actually consistent with a wide variety of other phrases common to all English-speaking countries. It’s just that English, for some reason, doesn’t use that usage for “hospital” specifically. Basically, you drop the article if you’re in a place as a “client”, so to speak (and apropos to this thread, the preposition might also change).
For instance: When you’re visiting a sick friend, you’re at the hospital. When you’re lying in bed in one of the wards, you’re in hospital. When you’re meeting with the PTA, you’re at the school. When you’re making excuses to the teacher for your late work, you’re at school. When you’re helping to set up for the parish rummage sale, you’re at the church. When you’re sitting in the pews praying, you’re at church.
Hispanics have a similar problem with those English prepositions: in and on both correspond to our en, at corresponds either to our en or to cerca de (nearby). And yes, a lot of Hispanics eventually learn that “in” is for larger spaces or periods of time than “on”.
If whatever is “large enough” that you could say things are (happening) inside, it’s in. In a week (meaning “taking up seven days”), in February (as short as February is, it still is large enough for events to take place “inside” February).
If it’s smaller, it’s on. On Tuesday (one day: smaller than seven days).
If it’s not exactly there but can be in the neighborhood, at. “Meet me at the train station”: it can be inside the train station or outside (at the door of the station, which again doesn’t mean that you’re standing exactly in the door, you’re near the door). “Meet me in the train station”: you’re actually going to be inside.
Part of the issue is that the in/on division is relative, and that different scales (and, as this thread shows, different speakers) place the limit between “in” and “on” at different points. I’ve been speaking English for 40 years and those two still trip me when I’m tired, but practice makes better even if never perfect.
You’re confusing two different things: preposition usage and one-to-one word correspondence between languages. And one of the languages you happen to know is notorious for having more exceptions than rules. Several languages solve the in/on conundrum by a very simple method: there’s no in/on conundrum, as there is a single preposition for both “in” and “on”.
No, ‘in heat’ is the correct formation. Because it is within a bounded space or time: the dogs heat cycle lasts only for a limited time of the month. Just like we say ‘in the evening’ because that is a bounded time period out of the 24 hour day.
I’d agree with Sage Rat’s formulation. You would say::
I live in the state of Illinois.
I live on (the shore of) Lake Michigan.
I live at 123 Lakeshore Drive.
or
We’ll meet in the afternoon.
We’ll meet at 4pm.
Long ago I attended a lecture by an AI prof once where the key issue at hand was the difference between “on” and “in”. I.e., you can put an apple on a plate or you can put an apple in a bowl. But imagine deforming the bowl and making it flatter and flatter. At some point it becomes a plate. When do you switch from “on” to “in”?
This is something people generally aren’t conscious of and intuitively understand (or so they think). How do you get an AI program to imitate such nuances?
The examples in the OP are similar. You can be “in” something if there is a perceived boundary. It could be physical like a fence or mental like a state/national border. But it’s all very fluid. Esp. when it basically becomes idiomatic like “on a base”. “In a base” would make better sense but somehow “on” is the expectation.
People are idiosyncratic. So their languages are idiosyncratic.
The original concept of “base” is from geometry, and it refers to a line or a flat surface, never to a volume; you can’t be “in” something which has no volume.
I used to teach SAT prep classes; in training, we were told that while the SAT does (or at least did back then) specifically test usage of the correct preposition, there are no rules we can give our students to help them out. Native English speakers pick up the correct usages in childhood, and non-native English speakers are basically screwed for those questions.