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I "must not" write about Grammar
It may seem the low point of a boring life when you begin to post about grammar, and if you do not share my fascination for hidden structures within everyday life you will probably want to skip this. But I have recently come across an interesting simple explanation behind a translational mismatch between English and German, that has bothered bilinguals for ages: The classic "must not" vs. "muss nicht" false friend. Both are identical when taken word by word: must = muss, and not = nicht. However, together both mean entirely different things. While "must not" is roughly equivalent to "not permitted", "muss nicht" on the other hand means "do not have to". So why do we have this strange difference, and is one more correct than the other? Read on to find out.
After doing some research on a similar phenomenon, which we shall get to later, it recently dawned on me how the two semantics of the "must not" expression can be explained: It all comes down to what the "not" refers to. In German it refers to the verb whereas in English it refers to the rest of the sentence. So in English the sentence structure of "I must not work" can be seen as:

Whereas in German the false friend "Ich muss nicht arbeiten" could be visualized like this:

The interesting thing is, that this pattern applies to other auxiliary verbs such as "may" and "can" (and even non-auxiliary verbs, such as "like" or in German "mag"). Take "may" for instance. In English the structure of a sentence involving "may" could be "may [not work]" whereas it is "[may not] work" ("darf nicht arbeiten") in German. Two completely different statements!
Maybe the most interesting case is "can", where we reach the boundaries of both English and German very quickly. It was this very word that caused me headaches when it appeared in a document I was writing, and led me to the investigation which has now turned into the dry blog-post you are currently reading. So what is the difference between "can [not work]" and "[can not] work" ("kann nicht arbeiten")? Well, the first means that although you are able to "not work", you are capable of working as well. The second however means that you are not able to work - period. Interestingly enough, English has an equivalent for that, and that is "cannot". German however, does not seem to have a real equivalent for the English "can not". The only one I can think of is to split the "can" from the "not" using a separator word, such as "also": "Ich kann auch nicht arbeiten." ("I can also not work"). This is a desperate attempt by the German language to stress that the "not work" is separate from the "can", and that we do not mean "cannot". When you start looking at even more complex combinations of "can" and "not" both languages run out of breath rather quickly, and have to use more complex structures, such as: "I am incapable of not loving you", "Mir ist es unmöglich dich nicht zu lieben."
Anyway for the real geeks, I have summarized the semantical interpretations of the discussed words for a statement 's' in the table below:

In the end, I guess what fascinates me about this is that I had always found the English interpretation of these words non-intuitive, while now they seem at least as consistent and logical as their German counterparts. It has also given me a fresh view on how sentences are interpreted in both languages, and how my brain has interpreted them correctly all along without me actually realizing the underlying fundamental differences. Those of you that speak one of these languages only by learning it in school, please leave your experiences in the comments. I would be interested to hear what your thoughts are on this.
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Our English teacher pointed out the false friends when we learned those things at school. Back then I asked myself: Gosh, English isn't intuitive at all, how to remember this?? Then I quickly realised that must means you are "forced" to do something. And that it would not be weird at all, if "must not" meant force in the opposite direction. I've never thought this through though - like you did. So thanks dude, today I learned something new!
Thanks for making my post sound interesting ;-). Anyway, I think you hit the heart of the problem: The special rule for "must not" English teachers give is in fact a bit misleading. There is no "must not" really. There is only "must", and whatever follows it is "forced". Therefore "must [do sth.]" indicates a hard requirement of doing that something, just as much as "must [not do sth]." indicates the requirement of not doing something.