We can do complexor arithmetic [quaternions] ... and curiously we can compute great arithmetic products, even continuing without interruption while waking-up: suggesting the waking process is a continuum, though we do not recall falling asleep.
We may append that the typical dream relates to a different sort of place than the obvious Earth: terminal velocity is about 4mph faster than the dream-aether may carry you about - which is neither a stand-still [as the sleeper is motionless in bed] nor fast [as in the day] - we can also vigor-swim-fly [taking some vigorous effort, but is possible] - so an atmospheric aether exists thick-enough to manipulate: perhap a small factor thicker than Earth's - though we also find we can breathe yet apparently 'underwater' ... this all may have ramifications beyond having your feet kick-out when you try to dash-run.
In dreams there is some measure of [mental] desire-assertion spatial-control: [at least] enough to glide-about the floor 'at-will'. [not enough to fly - this mental assertion has much the feeling of the mental concentration used when exercising mathematical test-taking [mental] mechanisms, therefor suggesting aether-redirection-control - but the ability to dream-jump with no apparent regard for placement or depth suggests a multitude of compatible identity-tendrils - but this is beyond the usual arithmo-mathematical content]
Most importantly there seems a fairly regular self-consistency to these dream parameters, though the dreams range from sublime to hilarious, exactly repetitious to astonishingly interpretable.
[a 'lambhorn' article]
[under construction, and arithmetic needs re-checking]