If they are able to think, that means they are conscious no? My favorite type of sleep is the sort that precludes conscious mental activity, since I tend to think of work or other mentally fatiguing subject matter and physical sensations like pain and tension. I'd like my sleep to exclude that sort of suffering. Maybe there should be more than one word for sleep. We could distinguish certain aspects, maybe name them or something? Course I'm probably asleep right now and dreaming I typed this.
Before I went to sleep, my inability to prove it had been bugging me all day long, and I suspected it'd be featured on the next morning's (way too early) final exam for my university course. I solved it in my dream, woke up, wrote on my whiteboard what I remembered and sure enough, it was correct. I worked it a few more times to cram it into my memory before running to my exam.
To my great delight, the ability to prove that theorem was featured heavily in one of the exam's questions, and helped me do quite well on the exam overall.
This happens sometimes, but thoughts occurring in dreams are more likely to make no sense when you're awake.
If I wake up remembering a dream, I write it down. Last entry... I voluntarily went for some experimental blood draw procedure secretly running in an abandoned building accessed by going past the end of a train station platform. Most people who take this procedure are kidnapped and forced to. The desk nurse was surprised I was there voluntarily. Does that mean this actually happens? No...
Entry before that: Passed by a contest on the way to some other stuff. Contestants were trying to most quickly free a live snake by chiseling it out of a frozen burger.
It's the same type of nonsense you can get by playing with LLM randomness settings if your LLM isn't fine tuned to delve and to apologize.
When dreaming, if I try to do math or anything difficult, my mind does a nifty trick where it just skips all the hard steps and gives me a result.
I must usually accept these results, but occasionally, I don't, and that's often when I realize I'm dreaming - I literally cannot conjure up those steps at all, they simply don't exist.