Telling time in different languages

I was telling a friend about the article How To Be on Time in Estonia by Alex Bellos (Atlas Obscura) and its accompanying solution (PDF).

“[…] in Estonian, a “quarter past the hour” is instead described as “a quarter of an hour on the way to the next hour,” “half past the hour” is described as “half an hour on the way to the next hour,” and “three quarters past the hour” is described as “three quarters of an hour on the way to the next hour.””

Our conversation was as follows:

Me: Estonians say “one quarter of the way to four”
Me: We say “quarter after four”
Me: Some Germans say “¾ four”
Me: Don’t roll your eyes. It’s all arbitrary anyway.
Her: I know. But that one’s just dumb.

😂

It is pretty arbitrary, though.

• In English, we say “half past seven” to mean 07:30.
• In German, we say “half seven” (halb Sieben) to mean 06:30.
• In Ireland, they say “half seven” to mean 07:30.

English uses a preposition to indicate what to do with the two numbers: the “quarter” is always before (or to or ‘til) or after the indicated hour. The example above doesn’t have a preposition, but the “half” is past “seven”, indicating position. In French, it’s similar, where they either “add” (plus) a “quarter” (quart) or “subtract” it (moins).