Please note that there's no real evidence that single-hemisphere sleep is a thing in humans. Some sleep researchers suggest that a brain hemisphere can spontaneously be awake during ordinary sleep in "unfamiliar" places, and that this can be a cause of poor quality sleep - but that's a very different thing from what Ziz claims to be able to do.
Also, to the best of my knowledge, Gwern has never written anything on his site about this purported single-hemisphere sleep, see https://gwern.net/doc/zeo/index for the details of what he has written about.
Gwen, not Gwern. Gwen Danielson, if he is still alive, is wanted for his possible involvement in multiple homicides related to the Ziz cult. Not Gwern.
And unihemispheric sleep (Gwen’s word for what they do; they like to invent their own terms) is one of the techniques the Ziz cult uses.
Thanks for correcting that mixup! So there's no source whatsoever for this bizarre notion other than the Zizian death cult itself. That makes it even crazier that some people (whether here or in the news media) seem to be taking it at face value, though.
I am uninvolved (thankfully, not many people have been confused) but on the topic of the meditation practice: years ago when reading the zizian.info writeup, I found the unihemispheric sleep part to be the most alarming & interesting part.
There are many strange altered states of consciousness found by experimentation, and I can totally believe that some form of auto-hypnosis + sleep deprivation - which would parallel many well-attested mind-altering practices in many different cultures & religions - could have bizarre effects or induce psychosis and hallucinating demonic entities, and turn an activist vegan into a murderer. (Their specific interpretation of 'unihemispheric' sleep may or may not be true. I would say that it's worth checking... except I'm not sure how one could either prudently or ethically investigate it, given the apparent consequences.)
And it would answer the question many people have been asking about how these unlikely-seeming murderers were made, in a way that the rest of it all does not.
Generally I think it's good to take people's reports of their unusual mental experiences at face value, even when they're crazy. Not that they never lie, but that you learn more by assuming they're probably telling the truth.
I haven't attempted unihemispheric sleep, and it sounds like a phenomenon that isn't represented in the literature, but it also sounds like it wouldn't get past an IRB anytime in the last decades, so I assume it's probably real.
Also, to the best of my knowledge, Gwern has never written anything on his site about this purported single-hemisphere sleep, see https://gwern.net/doc/zeo/index for the details of what he has written about.