Which is grammatically correct? Or are these both OK?

(1) You can write honestly and risk not being nice.

(2) You can write honestly and risk being not nice.

Hi Taka

To me, your first sentence is the more idiomatic one.

In your second sentence, I think native speakers of English would be more likely to choose a negative adjective such as "unkind" rather than use "not nice".

What book is telling you that, Taka?
Just take a look at the corpora. You'll find loads of usage examples for "not+being+adjective".

It seems to me there will often be differences in meaning or focus depending on where you put the word "not", and also whether or not it is an adjective or something else that follows the ing-form of a verb. I also think the use of "being" will tend to be different from most other verbs since it is so frequently used to describe a state. Here are some sample sentences.

- Mary's trying not to giggle (but that's not easy).  => Mary feels like giggling, but is not doing that.
- Trying not to giggle, Mary attempted to explain what the student's sentence actually meant.

I would interpret the sentences above to mean that Mary probably did not giggle, but that it was difficult to avoid doing that.

- Mary's not trying to giggle -- she simply can't help it. => Mary is doing something (probably giggling), but she is not doing it intentionally.
- Not trying to giggle,... (I really can't think of any good way to finish this sentence.)

Now look at these "being" examples:

- It is important not to be overly critical.
- Not being overly critical is important. => "Not being" suggests a way of acting/behaving.

- It is important to be not overly critical. (I would reject this word order.)
- Being not overly critical is important.  (I would reject this word order.)

In the following two sentences, I think the meaning is the same -- they both refer to the non-existence of too much differentiation.  However, to me the first sentence has a bit more stress on the idea of "non-existence" and the second one puts more focus/stress on the idea of degree ("not too much"):

- Obviously the result is dependent on there not being too much differentiation.
- Obviously the result is dependent on there being not too much differentiation.

In the two sentences above, I would accept "being not" in order to stress the degree (not too much), but I still prefer the first sentence.

Those are just some thoughts, Taka. I hope they help to answer your question.  Maybe someone else will have more input for you.

Taka

“Amy, is it not so rare for you native speakers to use 'doing not/being not' as negation of gerunds?”

I can add nothing important to Amy's reply; just the fact that in her sentence

Mary's trying not to giggle

"trying" isn't a gerund. It's a present participle. The negation would be: Mary's not trying to giggle. Therefore the not in the sentence actually makes the infinitive (to giggle) negative. Placing not before an infinitive is the usual way to make an infinitive negative:

To be or not to be, that is the question. | I would not go there.

CB