Computer REM sleep mode

My Mac just told me that it would go to sleep if I didn't connect it to a power supply. Obviously, I've connected it to a power supply so I can post this idea.

It strikes me that, when my Mac shuts down, it isn't really sleeping. I mean, it's fairly dormant and probably running a few low-level routines (like a human sleeper), but it certainly doesn't do all the things that the human brain does when it's asleep. In particular, I don't think my Mac does REM sleep; it doesn't seem to dream, which I think is sad.

Many famous people - such as Kekulé and others too numerous to remember - have been inspired by dreams. Even the average Joe or Joan can awake from a dream with one or two new ideas in their head.

What's needed, therefore, is computer REM sleep. In this mode, the computer would do a variety of random but somewhat self-consistent things with data and software it was working on while it was awake. For instance, it might put copies of all that day's emails into an Excel spreadsheet (duplicating the one that mentioned ostriches to fill a complete column), and use the result to modify a couple of TIFF files. Or it might search iTunes for music by Adobe produced by a record label called Python (or vice versa), and use the resulting music tracks to modulate some graphs in PowerPoint.

Obviously, the results of these bumbling, sleep-ridden actions would not be allowed to overwrite real data. Instead, they would be dumped into a dream-folder. For greater verisimilitude, the dream-folder's contents would be constantly deleted, so that only the results from the last few moments before waking were available for subsequent examination.