What is the difference between noch nie and noch nicht and simply nie?
Is this related to whether I expect the negation to change in the future or not?
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Adding to this... The difference is akin to that between grammatical tenses.
"nie" is an unqualified never. At the time in question, the action has not previously occurred.
Ich habe nie geraucht. (I never smoked)
You'd use this form to plainly state a fact.
"noch nie" is a stronger statement than the above, never before.
Ich habe noch nie geraucht. (I haven't smoked ever before)
Just like in English, this is slightly ambiguous. It can either be an emphatic denial of having smoked ever before, or you'd say it to make a point that while you've never smoked before, you may be about to now.
"noch nicht" means not yet. During the time period in question, the action has not been performed. It could have happened prior to it, and it could very well happen later. In fact, there is an implication that one is amenable to performing the action.
Ich habe noch nicht geraucht. (I haven't yet smoked)
This is what you'd use to express that you haven't yet smoked this morning (say). You're almost certainly a smoker, and you'll probably smoke again.
For the sake of completeness:
Ich rauche nicht (I don't smoke)
A negation; you may or may not have smoked in the (distant) past, but you don't (want to) now.
"nie nicht" or "noch nie nicht"
This means you're a Bavarian. I've always taken it for granted that you just ignore the nie, but perhaps the Bavarian dialect is more subtle than that.
It's the difference between "I have never" and "I haven't yet".
If you have never, for instance, been to Brazil, you can say both:
"Ich war noch nicht in Brasilien."
"Ich war noch nie in Brasilien."
Both work fine. "Noch nie" places more emphasis on the fact that you've never been there.
If, however, you make a statement that is true only for a given scope of time, you can't use "noch nie":
"Ich habe (heute) noch nicht gefrühstückt."
"Ich war (dieses Jahr) noch nicht in Brasilien."