Consider these examples:
Mr. Johnson has been the janitor for God knows how long.
Right behind this park is the new bridge that cost God knows how much.
You can replace "God knows how" with "I don't know how" or "who knows how" without really changing the meaning. (In Finnish I would use "ties vaikka kuinka", but I have no idea how to translate that into any other language, but I remark that it has to do with knowing, too.) You could replace it with "very" or drop it altogether, but that would certainly change the nuance.
Is there a similar intensifier in Latin that I could use to tell (in exaggeration) that no one knows the real extent? The God is irrelevant here; the idiom can refer to some divine entities or not. An attested classical idiom would be great.
For example, I might write something like the following in Latin:
Hora tertia postmeridiana Professor Smith nescio quam vetus acroasim faciet de lingua Latina.
I don't know how idiomatic the bold part is and how to replace it with something more suitable. Of course I could use vetustissimus or valde vetus, but I prefer indicating (jokingly) somehow that no one knows how old he is. Is nescio quam an idiomatic way to put this?