The interesting thing about the stream is that it is different each day. The stream I live near is a tidal stream, since I live by the ocean. Sometimes the tide is high when I go, so the water is brackish. At those times, I can see puffer fish and some kind of long narrow fish with large eyes and fins that look a bit like wings. When the tide is low, the carp swim from upstream along with the turtles. Blue herons stand in the shallower sections trying to catch the endless minnows that skip through the pebbles in the river bed.
I have often thought to record the stream by taking pictures, or video. But then, to what end? What time shall I go? And in what season? And, if I diligently point out the numerous animals that fill the stream, will I not deprive the viewer of the greatest pleasure -- that of discovering an amazing world where one would think that nothing existed?
I think your stream of consciousness is similar. The value is not in the individual thoughts and ideas, but in the experience of those ideas rushing from one place to another. While it is important to spend time to reflect on and view this wonder, it is not necessary to preserve a snapshot of it. Doing so will only distract you from what is happening now.
A person's life is too short to do all the things he or she imagines even in a single day. Do not waste your lifetime by chasing few ephemeral ideas.