A good translator can find a comparable idiom that neatly replaces it in the target language, but it is rare to have idioms that match exactly in their applicable scope. It depends on the context, on the tone of voice, on the age of the speaker, on other visible or hidden social classifiers, even on the region the original speaker hails from.

This is something humans (i.e., experienced translators) excel at. It is something computers cannot do except at a very basic level — they lack the cultural knowledge and autonomous connection making capability needed.

In Dutch I could translate 'not my cup of tea' in many ways depending on the context. Some examples:

Neutral translation in lieu of additional context: „Dit is niet naar mijn smaak.”

Young person in a social context: „Dit is niet echt mijn ding, nee.”

Middle age manager in a white collar office environment: „Nee, dit is 'not my cup of tea', zeg maar.”¹

Ironic and/or cynical down-to-earth jocular fellow: „Dit is niet mijn kopje thee.”²

1: Note the literal borrowing of English. 2: A literal translation used humorously, knowing full well that this is not 'correct'.

If human language reflect human culture, and NLPs are trained on written text, is it impossible that they can have the cultural context to make such a translation? Is it impossible that an NLP can get a query like "translate this phrase into informal slang Arabic" and the NLP properly does so?

I find it improbable at this state, because 'understanding human culture' and bridging the gaps between two languages without compromising the quality of the prose depends not just on written text, but also decades of experience in being a human being in that society/language, and being able to make connections which may not be apparent from texts. A computer would also miss the final step: our monitoring function that accepts or rejects translations as silly, down-right anti-social, or totally apt — that well honed Fingerspitzengefühl that comes from the total sum of your experience and maturity.

You would, in effect, have to train an artificial intelligence with a brain capable of mimicking ours by raising it as a child in our society (sometimes cheerfully acknowledged by sci-fi writers who employ such characters), and even then you would need to have a brain that processes certain events, happenings, and subtle hints the way a human being roughly does.

Perhaps someone will manage to train one in a suitable manner one day (far far away — not in our lifetime), but I wouldn't want to be responsible for debugging it.

Someone will manage to make one that is good enough for some purposes though. Plenty of semi-gibberish manuals included with products that strongly reek of machine translation these days.

Nice examples! Please also do "Nu komt de aap uit de mouw!"

Don't forget the evergreen "Unfortunately peanut butter!".

You can always find a good-enough substitute, but the original nuance will be lost. The native speaker can choose between "dislike", "would not prefer" or "not my cup of tea". The target language may have an even wider arsenal of phrases suited for different social occasions and across varying levels of politeness. Essentially, mapping the input to the output is a lossy process.

Obviously. That was the commenters point.

The commenter's point was that there is information that can be expressed in one language but not another (they're not all essentially the same). The fact that you can't translate a figure of speech doesn't evidence this.

I don't want to put words into their mouth, but I think the comment was more about how we think depending on the language we use rather than the concept we're able to express or not.