In the third season TNG episode "Deja Q", Q has his powers stripped by the Q Continuum and is exiled to the Enterprise in human form. Q has a discussion with Data about humans and comes out with this line:
Q: Humans are such commonplace little creatures. They roam the galaxy looking for something, they know not what.
Now, this "know not what" business is quite an archaism. Usually in modern English we don't follow verbs with not except modals (can, would, do) and negatives are usually formed with such constructions (Cannot/can't, would not/wouldn't, do not/don't, did not/didn't etc.) Colloquially, you would probably say "Humans roam the galaxy looking for something and they don't even know what they're looking for."
Is this a reference to something or just some weird affectation the writers imposed on Q here? Why? Has Q spoken like this at other times?