Ivan Seeking said:
Do you have any references for this; that they are indeed not random? I have read just the opposite.
Yes. May I ask where you read "just the opposite"? By any chance, here? http://www.medical-hypotheses.com/article/S0306-9877(05)00114-3/abstract
For every "tit" of this there is a "tat" http://www.medical-hypotheses.com/article/S0306-9877(07)00480-X/abstract
Here is one well accepted view which partially agrees with you:
"After a brief period of Stage 4 sleep, and to prevent us from falling into a deep coma, our brain partially arouses us: Our brainstem, the most primitive part of our brain, stimulates the higher levels of our brain with random impulses and returns us to Stage 2 sleep, associated with REM’s and dreams. We stay in the REM dream stage for a while and then again return to deeper stages."
The thing is... you COULD try and measure those random impulses, but while they TRIGGER dreams, they have nothing to do with content. Dreams themselves are highly patterned, much as the response to sensory deprivation is. You can predict many aspects of both, and the brain-stem does seem to be... spastic... during that time. That said, the "random" firings do not result in random dreams. Your dreams are formed from what you experience, what you can imagine, and some would say basic archetypes (I don't necessarily agree with that), and even if the trigger is random, that's it.
I'm not pawing through old JAMA archives to find a dozen studies, each contradicting the other. There are endless examples of studies which contradict each other in this field. I should point out that dreams are not exactly a perfectly understood quantity, nor is sleep in general. I can imagine differing points of view, but I'd be interested to see medical evidence of human random number generation. "Listening" to the brain-stem is not arguably more effective than radioactive decay, or atmospheric noise + keystrokes.
It would seem to be contrary to the nature of human decision making, if we experienced random ANYTHING above the level of the brain-stem. I am yet to see a study which proves that random activity (although it is widely accepted). So, again, I'm curious as to what exactly you've been reading.