Be very careful: discrimination (viveka) between Ātma and Māyā, or the Real and illusory, is a good deal trickier than you may have realized. It’s easy to make the mistake of supposing that the two terms are somehow parallel and thus equally real, even though this is precisely what the distinction is meant to help us avoid. “It’s not that the One became two, but that these two are One,” to use a formulation favored by Coomaraswamy—taken, if I recall correctly, from the Corpus Hermeticum.
We’re all of us subject at one level or another to what Coleridge called the “despotism of the eye”, which means among other things that we’re inclined to think in pictures or diagrams, or rather to extend the usefulness of such pictures and diagrams beyond their legitimate range, making of them something more than provocations to insight. And thus we end up, if we’re not vigilant, replacing the conjunction “and” by a mental line, with Ātma positioned on one side and Māyā on the other. In truth, of course, there is no such line, no conjunction (that is, no actual joining of two different things), and—by definition—no Māyā.
Part of the problem can be traced to the analogies traditionally used to facilitate discrimination. Ātma is sometimes compared to the sun and Māyā to the sun’s reflection on water, but the analogy misleads us as soon as we go looking for the metaphysical equivalent of the physical water; to suppose there’s a third thing in addition to Ātma and Māyā, situated as it were along the interface between them, is only to reinforce the error of thinking there are already two things. The analogy of a rope that’s mistaken for a snake is doubtless less problematic, though here again there’s a misleading third entity, namely, the observer who makes the mistake. Better perhaps to visualize a man (Ātma) looking at his image (Māyā) in a mirror—though now you must beware of reifying the mirror!
From a certain point of view, the best—because least deceiving—analogy may be that of the dreaming man and his dream, since he himself is the one upon whom the dream is overlaid. This comparison also deceives, however, if the unreality of a dream is carried too far. For it’s clearly no solution to conclude that there’s really “nothing there”—there in that something-shaped hole where there might have been something but in fact there’s just Māyā. By calling into question our misguided efforts to imagine Māyā as if it were separate from Ātma, we mustn’t fall to the opposite side of this dialectical tight-rope. Māyā is illusion, not hallucination, which means that something real, indeed the only Real, is truly “there”, not that a nothing has been turned into an apparently real. Advaitists are neither solipsists nor subjective idealists.