What is the difference between 「だと」 and 「であること・なの」


I was looking at example sentences for 「気づく」 to determine which particle it
uses and I found that it takes 「に」. For example: 「彼はそれ **に** 間もなく気づくだろう」.
However, I also found these sentences: 「私は彼が有名人 **だと** 気づく」 and 「自分が一人
**であるのに** 気づく」.

Firstly, I'm struggling to analyse 「一人であるのに気づく」; 一人 (noun) + であるの
(nominaliser) + に気づく is this correct? I thought that you only used である with こと
(e.g. 先生であること), but you use な with の (e.g. 先生なの).

Secondly, I have no clue what 「だと」 means in the other example. Again, it looks
like a nominalised sentence to me, but I'm not sure how 「だと」 is used. Even if
it was nominalised, why is と used and not に?




There are a few (probably more than I'm thinking of) cases where に and と can
be used interchangeably, such as に比べて/と比べて, and I think that's the case with
気づく also.

私は彼が有名人だと気づく

There's an implicit nominalization here: 彼が有名人だ (the fact that he is famous)
と気づく (I realize). It's similar (probably related) to when you use と as the
quoting particle without using quotation marks.

As for 一人であること, I don't think the rule you learned about when the の
nominalizer is required is correct. 一人なのに気づく sounds like you're saying, "I
realize it **despite the fact** that I am alone."

**Edit:** Just thought of a more obvious analogy. I trust that nothing seems
odd about the だと combination in this sentence:

有名人だと思う。

