Sankara talks of the knowledge of having been in a state of deep dreamless sleep (d.s.) as a memory in his commentary on Brh.Up. IV.iii.6:
We see also that the purpose of a light is served in dreams, as, for instance, meeting and parting from friends, and going to other places, etc.; and we awake from deep sleep with the remembrance that we slept happily and knew nothing. Therefore there exists some extraneous light.
Evan Thompson in his paper #37 open mind papers (commentary by Jennifer Windt and E.T's reply_ in epub and pdf)
on the neuroscientific implications of the knowledge that we have been in a state of deep sleep concludes that being in a state of deep sleep is experiental because it is a memory. You cannot have a memory which is veridical without there having been a prior experience. If you remember something e.g. posting a letter, there are not two elements one a letter being posted and two, you being the poster of that letter. That seems an epistemological bedrock.
c.f Brh.Up. IV.iii.6: Similarly, in the case of remembrance, he who remembers being also the one who saw, the two are identical.
So what then are the experiential aspects of the deep dreamless sleep experience asks Professor Thompson? Here I believe that Thompson has gone astray, forgetting the automatic and characteristic M.O. of the advaitin. When Sankara talks of ‘memory’ in opening the discussion he is using ‘memory’ as a handy shelf to park the ‘experience’ on. It is typical adhiropa/apavada or attribution followed by retraction. It is a method of continuous approximation or correction and refinement. In Western terms it is dialectic, Socratic, maiuetic. As the development of the teaching proceeds the real nature of what I have called a protophaenomenon
is made clear. In that post I quote at length from Chapter II of Upadesa Sahasri. Sankara says that ‘the knowledge of the knower can never be lost’. There is no experiencer to have an experience in the state of deep dreamless sleep yet nevertheless there is knowledge. That is the whole point of the insight.
Thompson’s discussion of the neuroscientific implications of d.s. is interesting but his account of the Advaitic position is not correct in my view. It would render Sankara’s thesis self contradictory. Jennifer Windt in her commentary paper writes about spatio-temporal apprehension in normal, lucid, and white, dreams. I will write more about that later. However she too bounces between experience and memory in her account of d.s.