the mind and the activity state that creates the conscious mind would always be there.
It is (until death). Again, stop with the binary thinking. And "activity state," as your previous graphic demonstrated, is a
wavelength that is ever oscillating and changing in a dynamic manner. It is NOT some rigidly defined repetitive pattern that never alters.
It is more like a song, with component instrumental and vocal parts all working together in harmony (or not, as the case may be). Why is this such a difficult concept for you to grasp?
It's like you're saying, "Only the guitar is the song. Anything else is 'different activity'."
Well, yeah, no shit. The bass line is "different activity" than the rhythm guitar, which is "different activity" than the drums, which is "different activity" than the trumpet. and the song as a whole is "different activity" than its component parts, etc.
Just picture every musician station to be a neuron and every instrument to be a "different activity potential" and the simple action of each of the musician/neurons moving their bows or strumming their strings or hitting their drums, etc., in other words,
firing all being orchestrated/managed by the Conductor who is using the orchestra to create a piece of
never ending (until death) music that ebbs and flows and has moments of pianissimo and crescendo and fortissimo, etc., and all manner of wavelengths in between:
What you are referring to as "sleep" is pianissimo and "wake" is fortissimo or the like, but it's ALL one continuous never ending song, ultimately, regardless of the many times there may be musicians at rest or playing solos or all working together or some playing discordantly, etc.,etc., etc.
Iow, the conductor--the brain--starts conducting at birth and doesn't stop playing the song until brain death and the song has many "different activities" (even those nested within others), etc.