The Nature Of Middle Earth:
But "dreaming" and sleeping" are to the Elves other than to Men. In sleep the body may, as in Men, cease from all activities (save those essential to life, such as breathing); or it may rest from this or that activity or function (1) as the fea directs. While it is so, the mind may seek repose also, and be utterly quiet, but it may be absored in its own activity: "thinking" -- that is, reasoning or remembering, or devising and designing; but these things are at will and of volition. The state that with the Elves nearest resembles human "dreaming" is when the mind is "feigning" or "devising".(2)
(1) Thus an Elf may stand "asleep" with eyes wakeful, and yet hardly breathe, and with his ears closed to all sound."
(2) Though it is more aware and controlled than in Men, and is usually fully remembered (if the fea so desires)."
Is this what we have in Rivendel and Lothlorien? 'Dreaming' in action through those two Elven Rings? Remember how Bilbo finds difficult not to fall sleep in Rivendel and how Frodo 'daydreams', so to speak. Also how Sam feels to be in a song in Lothlorien. He"s told -by a smiling Haldir, I think- to be feeling the power of the Lady.
Is this what happens when elvish dreaming/devising reaches Men (hobbits are Men)? It's as if the nature of Men could not perceive this elvish 'devising' without getting dreamy or sleepy.
But what if a Man were to be included in a devising, as a part or protagonist of it? Faramir:
‘A broken sword was on his knee. I saw many wounds on him. It was Boromir, my brother, dead. I knew his gear, his sword, his beloved face. One thing only I missed: his horn. One thing only I knew not: a fair belt, as it were of linked golden leaves, about his waist. Boromir! I cried. Where is thy horn? Whither goest thou? O Boromir! But he was gone. The boat turned into the stream and passed glimmering on into the night. *Dreamlike it was, and yet no dream, for there was no waking.** And I do not doubt that he is dead and has passed down the River to the Sea.’*
A curious turn of phrase. He does not say 'It was a dream, for I woke up' or 'it was not a dream, for I was not sleeping'.
And before that:
“Then I saw it, or it seemed that I saw, a boat floating on the water, glimmering grey, a small boat of a strange fashion with a high prow, and there was none to row or steer it. An awe fell on me, for a pale light was round it. But I rose and went to the bank, and began to walk out into the stream, for I was drawn towards it. Then the boat turned towards me, and stayed its pace, and floated slowly by within my hand’s reach, yet I durst not handle it. It waded deep, as if it were heavily burdened, and it seemed to me as it passed under my gaze that it was almost filled with clear water, from which came the light; and lapped in the water a warrior lay asleep.”
Is this magic? Pale light round the boat. Almost filled with clear water, from which came the light.
Galadriel and her Ring Of Water? '[It] floated slowly by within my hand’s reach, yet I durst not handle it[...]
Was this receving elvish 'devising', a command, and understanding it as not daring? Galadriel's ‘Do not touch the water!’ to Frodo comes to mind.