@iakov98 Glad I could help! I however feel like my comment is only posing problems for you rather than helping you forward. So let me briefly suggest some comments and distinctions that may help you interpret the many wonderful comments here.
I start with your Visualisation (V) process, which is characterized by the presence of 'mental imagery'.
Let's say mental imagery is 'conscious experience decoupled from sensory input', or something like that. We next should make an important distinction within this concept: a distinction between *voluntary* mental imagery and *involuntary* mental imagery. Voluntary mental imagery is when we deliberately conjure up a mental image - this could be called 'pure visualisation'. For example: you deliberately visualise a pink elephant just because you want to. By contrast, involuntary mental imagery is when mental images 'present themselves' automatically and associatively (on the basis of relevant memories) in some situation. For example: if I say to you "DONT visualise an elephant", images of elephants will nonetheless often come to you if you have many vivid memories of elephants readily available, and if I say to you "Ruy Lopez", you might automatically make a rough visualisation of a Ruy Lopez on the board.
With this distinction between voluntary and involuntary mental imagery, I think we can understand e.g. the comment from
@Denkischerz that his opening play is almost entirely visualization based --- I would say: a lot of involuntary mental imagery presents itself because the positions are so familiar and there are so many relevant vivid memories to draw from --- and that it becomes harder to visualize once they get deeper into the game --- I would say: now fewer involuntary mental images present themselves, and they must resort to voluntary visualisation, which requires more effort.
We also see many comments that their visualisation of the chessboard is 'fragmented', i.e. that they only visualise parts of the board rather than the whole grid, or 'relative', in the sense that they see mostly the relation between pieces rather than the whole set-up of individual pieces. This is true and important, I think. Again, I would say this can be partly explained by the distinction between voluntary and involuntary visualisation: we are more familiar with the relations between pieces rather than with these pieces as individual things on independent squares (because the relations are relatively stable across different games, and actually 'more important' for winning a game than, say, the appearance or location of an individual piece), and so mental imagery of pieces-in-relation-to-each-other may present itself more easily than mental imagery of individual pieces or mental imagery of a complete set-up.
Next, your M process. I would suggest that you indeed regard this as a more 'cluster of *factual* imagination / memory / reason' rather than a 'memory as opposed to visualisation' process. The distinction between 'sensory versus factual (or even propositional)' is much more clear than the distinction between visualisation and memory. In the comments here, it seems that (i) this factual process takes over once we lose the capacity for (involuntary) visualisation, but also that (ii) this factual process is often used to assist voluntary and involuntary visualisations, e.g. in the sense that you deliberately, factually recall the position of a part of the board, and then, on the basis of this deliberate factual recollection, involuntary visualisations present themselves again and voluntary visualisation can proceed with some sense of 'security' that the visualisations match the actual board. Many comment write that it is hard to do this for the whole board and they can only do it for a part of the board, which makes sense in many ways. One important way in which this makes sense is that not all pieces on the board stand in equally important relations to each other, so you only visualize the most important relations between the most important/relevant pieces (these are typically, but not always, also close to each other spatially).
Two final comment before I should stop this too-lengthy comment.
Firstly, I love the suggestion from
@PureImprov to include a third category alongside visualisation versus 'factual memory/reasoning': Spatial reasoning. This makes sense because, alongside *sensory* processing mechanisms in the brain we also have *motory* processing mechanisms, which are responsible for sensing, predicting and processing our (somehwat mysterious) 'inner sense' of body position and body movement. A key term here is *mental modeling*, other key terms are *kinaesthesia* and *proprioception*. It is true that alongside sensory perception/imagination/memory (and factual reason/imagination/memory) we also have *motory perception/imagination/memory*. Imagine, for example, *reaching* for an apple. Sports athletes can exploit this capacity to robustly improve athletic performance just through mental simulation. It is a very interesting question to what extent this capacity is relevant for chess, where spatial relations are definitely important to some extent, but not to the fullest extent, because *playing* chess is surely not as an 'embodied' activity as, say, playing football or snowboarding --- the spatial awareness of our bodies is intuitively more relevant in these sports than in chess.
Secondly, about your question of aphantasia. I do not know much about aphantasia, but I do know that the term has been coined only very recently and that the phenomenon is still very mysterious, although many seem to agree that it really is a thing. A big question is: (a) do people with aphantasia not *have* mental imagery, or (b) do they have mental imagery but are they not *aware* of it (or they would call it something else than mental imagery). Recent research suggests that (a) is the case, see e.g.
www.sciencedirect.com/science/article/abs/pii/S0010945217303581 . I also found this elegant article, which might be easier to read:
www.sciencedirect.com/science/article/abs/pii/S0010945217303568 . This is very interesting, especially given that mental imagery plays such an important role for most of us. The main thing to explain here, then, is: how are people with aphantasia capable of having normal lives and even being brilliant scientists or (blindfold) chess players? I'm speculating here, but I think this harks back to the last paragraph in my previous comment: what seems to do the 'real work' in visualisation etc, e.g. what makes us play actually good moves, is not the visualisations itself (of which we may or may not be capable) but rather the associations and expectations that accompany the topic of a visualisation. In other words, perhaps you need not actually *see* some image of a Ruy Lopez in the mind and still get all the cognitive benefits of *expecting to see a Ruy Lopez*. In this way, having an actual imagine in the mind would be somewhat irrelevant for being able to play blindfold: it's all about memories and expectations. But, then, not the visual nor the factual kind... A new Pandora's box opens!
[Edit. Now I am curious: those do identify as having aphantasia, do you feel capable of *motory imagination* as I described it? Do you feel like you are substantially imagining something if you try to imagine the feeling of reaching for an apple, or the feeling of being in a downwards accelerating elevator or a car that is taking a turn too fast, or the sense of vertigo you feel when you stand on a glass floor on the roof of a skyscraper? ]
[Edit: Also this general article on imagination might be a good starting point for getting into the science of visualisation (you can skip the detailed science parts and still learn a lot):
www.nature.com/articles/s41583-019-0202-9 ]
I hope this is helpful in any way. Maybe I got carried away a bit. Please push me if anything is unclear. All this stuff about imagination is always rather controversial and speculative to some extent..
