Hari OM
'Text-days' are for delving into the words and theory of Advaita Vedanta.
In talking of non-duality, how is it that we perceive our existence and that of the world around us? Does not this physical presence deny that idea of 'singularity'? We could extend our questioning to 'how can a changing world arise from something said to be changeless? Does not the very existence of the changing require change within the 'changeless'? Does this not, then, repudiate what is called here as Truth?
icNmaÇEkrsE iv:[aE äüaTmEKySvêpke,
æme[Ev jg¾at< rJJva< spRæmae ywa.24.
Chinmaatraikarase vishnau brhamaatmaikya-svaruupake,
Bhramanaiva jagaj-jaatam rajjvaam sarpa-bhramo yathaa ||24||
Just as there arises the delusion of the snake on the rope, so too owing to delusion alone has the world arisen in the homogenous Pure Consciousness, which is all-pervading and of the nature of one-ness between Truth and Self.

First, we do not apprehend the rope (aavarana shakti), then we compound our error by mis-apprehending the snake (vikshepa shakti). If we had but apprehended correctly at first, the misapprehension could not have arisen. By 'not seeing' the rope, we superimposed the snake. However, the snake delusion could not have occurred without the substratum of the 'unseen' rope. This is what Maya does to us at all times. The substratum does not change, only perception. The vikshepa came about due to the similarity of the snake to a rope. However, for someone who does not have snakes as part of their lives, it is unlikely they will make a mistake and they will see the rope only as a rope.
Further, there must be a negative expectation within the perceiver - that is to say, they are likely to be fearful of snakes and all too ready to believe the delusion. The conditions in which the rope lies may also play a part in the aavarana and vikshepa. Had the rope been in full daylight and if our eyesight is up to scratch, it is much less likely we would make a mistake. What is more, there is a knowledge of the substratum (the rope in this example) - the perceiver knows there something there, but not being clear about what that is, created something familiar out of it.
The illusion of the world is due to our senses not being sufficiently tuned to the substratum, thus creating the world around us through projection from our vaasanas and the lives of the jiiva. We all know "I am" but we do not know exactly who that "I" is. "I" am the substratum upon which we lay our version of existence. Due to non-access to a valid means of Knowledge (as in Vedanta), the illusion continues unchallenged.