> so this seems pretty irrelevant to whether there's a discontinuity in the first place
Have you proven there is one? Or are you just saying "sleep is really weird so that must be a 'conscious discontinuity.'" I'm pointing out the obvious flaws in this logic.
> you're just saying there may be multiple during a given night's sleep.
No, you're saying that, and I'm asking you to define it.
It's a pretty well understood part of sleep research. Sleep has different phases, only REM, the lightest part of sleep, is associated with dreaming. Also, it matches up with my experience of dreams and basically all the reports I've seen from others on dreams: there's not a continuous experience from falling asleep to dreams, there's being in the process of falling asleep, then there's being in a dream, and the experience is discontinuous, the transition between wakefullness and dreaming is not experienced, nor is the transition between different dreams.
(I've also personally experienced a very sharp discontinuity around sleep, once or twice, where I have literally 'blinked' while looking out my bedroom window and seen it go from dark to bright light, experiencing nothing of the hours in between. Though I suppose in many ways this is a much more continuous conscious experience than I normally have when sleeping, where waking up feels much more disjoint from falling asleep)
I mean personally I see continuity as mostly being about the hardware with the process running on it only being secondary at best and disjointed, though not completely irrelevant.
So funnily, I'm "perpendicular" to the issue of if continuous consciousness is needed -- i think the only relevant question is following the original structure and processes every "tick" of the universe to see what happened.
E.g. to me if the structure is wholly or nearly-wholly preserved, "teleporting" by the mechanism of particles having an uncertain position is non destructive and retains continuity, stasis is the same, becoming part of a hivemind is the same -- though leaving one or being quickly ship-of-theseus'd would likely impair continuity, but less in a manner of "death" and merely making the question meaningless, because two new entities are born descended from the same source, akin to how who we were as children never dies, only undergoes a process of growth/change/refinement until it's something not only different but significantly more than the "original".
I think a very interesting line of thought is actually if severe brain damage essentially kills continuity / "the original", in context of how we can absolutely disable or impair parts of the brain with magnetism or drugs but then have the hardware return to original function along with apparent return of the original process. It actually feels much closer to the self-evidently wrong assertion that any mere identical copy would equally be the original, suggesting to me that damaging the original too far past a point may actively kill that thread of consciousness in a way I wouldn't consider to be the case from sleep / stasis / joining-but-not-leaving a hivemind / etc.
What do you base this assertion on?
> so this seems pretty irrelevant to whether there's a discontinuity in the first place
Have you proven there is one? Or are you just saying "sleep is really weird so that must be a 'conscious discontinuity.'" I'm pointing out the obvious flaws in this logic.
> you're just saying there may be multiple during a given night's sleep.
No, you're saying that, and I'm asking you to define it.