As an example, the author mentions otsukaresama, which is the set phrase to use if you've been driving for a long time with guests and have reached your destination (and many, many other situations). But having the driver thank their guests for their patience is basically not a thing in English, so how do you translate that? The literal translation, "honorable tired lord" (~ thank you for your effort/patience), is completely incomprehensible.
Depending on the context, you'd want either explanation. If you're learning Japanese you'd probably want the explanation of how and when it's used, and the literal words that compose it.
But if you were translating a manga book and it used that phrase, you would probably just put "Ahh, we're finally here!"
I think there's just something of a bastardized use of the word "untranslatable". As long as a language can convey abstract concepts, you should be able to translate anything into it.
I don't know that I would say this is a bastardization of the word, but I see where you're coming from.
But regarding translating it as "we're finally here", that's not what it means: it's not an expression of satisfaction, it's acknowledging that to others that it's been a long trip for them.
This is also why at its best, translation is a skill and an art. The same text can have significantly differing impacts readers depending on who’s translating.
You can explain the meaning of a text, sure, and for technical texts that may be all you need, but if the goal is not simply the transfer of dry information and the result fails to trigger the intended associations and emotions, your job as a translator is not yet done.
Personally I prefer footnotes in those situations. I'd rather have a few sentences that explain the nuance an author was trying to convey with their word choice that a native speaker would have picked up on rather than have a phrase thrown out entirely and replaced with some alternative localization that might be familiar in an effort to try to capture the same "feel" but barely comes close to what was actually said (if you're lucky).
I get your irritation but I think it's also a way of signaling to the reader that the difficult word is heavily freighted with meaning that would be blindingly obvious to a native/fluent speaker but require a small essay to convey in English (and still wouldn't have the emotional impact) - linguistic operator overloading, if you will.
To declare something "untranslatable" is essentially to imply that a non-native speaker is incapable of understanding it no matter how much they study the language. It deals in "touchy feely unquantifiable nonsense".
Noticed that everyone in here who proclaims that some things are untranslatable have yet to provide actual concrete examples of them (SRC LANG, TGT LANG, SRC SENTENCE)
The fact that you can have legal documents translated from one language to another is all the proof you need that if you're a good enough translator, all languages are interchangeable. You might need a whole lot more words or a whole lot less words depending on the source and target language though.
Here's an easy one: nearly any pun is literally impossible to translate while still being a pun. You can explain the pun by talking about the original language, but it can't be adequately translated.
"You are shit" vs "You are the shit". Explaining "the shit" to someone who's fluent in English but not culturally fluent in American is almost impossible. There's a qualitative difference between "You are very good" or "You are the best" and "You are the shit". They're not exactly synonyms.
Another good example: Dude or Guy as used in Californian.
Or you skip all the context and just say it means "you're great", very easy translation.
"Eres el mejor" - I just translated it into Spanish
Different scenarios require different methods of translation, sometimes you'll want something literal, and sometimes you can just translate the intent behind the words. As long as you can do that, I would consider it "translatable".
A paragraph footnote might accurately convey the intended meaning but it won't evoke the same feelings. A good author or translator cares about both these things.
It's that emotional and cultural baggage layered on top of words that's hard to translate.
So for example in USA you can call someone "a benedict arnold". As an immigrant this means nothing to me. People tell me it means "bad". I understand the words, but there's no impact behind them because I lack the cultural background.
If somebody had first explained to you that Benedict Arnold was a well known traitor during the revolutionary war you'd have nearly the same context as your average American.
It's hardly what I would call untranslatable. I'm sure you could find some poor sod who the public education system failed so terribly that Benedict Arnold is as equally opaque in America.
Interestingly, Chinese colloquially refers to languages as the same as culture. For example, Chinese is 中文, literally Chinese culture; English 英文, English culture; Japanese 日文, Japanese culture. The suffix 文 signifies culture.
There is also the word 語 and 語言 to signify language; this is more formal but without the connotation of culture. But my point is culture is indelibly tied to language.
文 has a broad meaning. Here it would be
https://en.wiktionary.org/wiki/%E6%96%87#Pronunciation_1 8. (written) language.
(as opposed to spoken language, which is what 語 is)
My understanding is that 文 (in this context) refers to the written language, whereas 語 and 語言 refers to the spoken language. Which is why we say 寫中文 instead of 寫中語. 語 and 文 often gets mixed up, but the nitty-picky-correct way should be what I described.
FWIW here in Hong Kong we have a term "兩文三語" which means two written (Chinese and English) and three spoken languages (Cantonese, Mandarin and English).