Analog sound and dreams

So I had a dream last night about vinyl LP's and CD's and why CD's don't sound as good. In my dream I came up with a possible solution, since the future will definitely be digital.

Instead of turning the stream into a bunch of discrete data, why not just match the wave forms with equations? Then, as the processing hardware gets better and better it can just go for smaller and smaller time deltas in recreating the levels, instead of there being actual data lost in the storage medium. When I can play a CD and a record on the same equipment (well, the players are different, but the rest is the same) and hear a distinct difference, there is a problem.

I'm not an audio expert, so there might be a fundamental reason why this approach would fail, but I'm thinking that it's just a space thing. I can imagine the files getting enormous, but it seems like this could be a way to really fake it.

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Excuse the quality of writing, since I'm just trying to spit out the mental imagery as quickly as possible since I know I'll forget the stuff within half an hour.

In another dream, I started off in a sort of execution arena with 3 sandy areas. It was similar to the arena near the end of Attack of the Clones, if that were separated into 3 areas. This arena was run by bad guys, similar in appearance to the archers on the backs of the oliphants in the Lord of the Rings movies. They had kidnapped some good guy "soldiers" (I was a good guy) and were executing them. The soldiers had their heads up through small holes in the wooden platform in one of the areas, and the executioners were hitting their skulls with pickaxes.

I ran over to my "city," which was right next to this bad guy land, where there was a celebration happening because the war was over. They obviously didn't know about the executions going on in bad-land. I shouted what was happening, and they all started running to save their guys. I had a brief chat with Captain Jean-Luc Picard of the USS Enterprise, who was some high-ranking official. We got into a sort of Star Wars-esque speeder and followed a few minutes after the last of our guys ran out.

When we got back to the arena, the wood was gone and all 3 areas were sandy. We drove the speeder in to 2 abandoned areas. In the third area, we found all of our people behind bars in some sort of large cell, and another door opened. A King Kong sized monster came out and was meant to kill myself and Picard, I think. We evaded him in the speeder a bit, and I was taking quick shots at his eyes on each pass with an aerosol can of liquid nitrogen. (I do not think that this would be possible to make, but that's what it was in the dream.)

A serpentine beast joined the mix, and we maneuvered our way out of the arena. We were heading back to find some reinforcements, but who else was there?

The dream ended with a TV interview of one of the bad guys and a lot of evil chuckling.