Very pin-pointed descriptions directing towards the insight of non-dual.
From "Living Nonduality: Enlightenment Teachings of Self-Realization" by Robert Wolfe, 2009
Duality, which has been referred to by many sages, basically defines a condition wherein exists "more than one" - generally, two (which, in Latin, is duo). In Buddhism it is usually synonymous with "manyness", multiplicity.
The two (or more) things which comprise duality can be any two (or more) things. The proposition that there is "good" at one extreme, and "bad" at another extreme, is an example of duality. If I say that there is "this" over here and "that" over there, two different or "separate" things, that would be a dualistic expression. If I say that "I" )"me") like spaghetti ("not-mine"), this is dualism. To hold the view that there is something identifiable as "me" and something identifiable (or unidentifiable) as "god" is dualistic.
However, even if I say that "I" am "god", I haven't yet exceeded the boundaries of duality. In the same way, if I say, "I feel fear", that is duality; if I say, "I am the fear that I feel", that is still duality.
The nature of normal human thought is divisive. A mother opens the door and steps into the room: all of the stillness and all of the motion in the room are summarized into one immediate, pertinent sentence in Mom's mind; observing little Andy holding a ruler, and hearing wee Carol crying, and Mother's initial thought is, "Andy hit Carol."
Typically, human thought finds its expression in sentences, and these sentences are composed of words. Each word "means" a "different" "thing": Andy is one thing, Carol is another thing, and hit is yet another thing.
Andy is the subject of the thought, Carol is the object, and hit is the action that connects the two, subject-versus-object, things.
Even in the shortest sentence (in the Bible) - "Jesus wept." - Jesus is one thing, his weeping is another thing... although "related".
Primary to all relational, or relative, thought is the self-conclusive thought, the "I" thought, which predicates the existence of the subject of the thought. The formulation of the thought "I am angry" presumes not only that such a specific entity as anger exists, but that there is a particular entity - I - that recognizes anger and has cause to consciously note its presence.
The unquestioned (and in some minds unquestionable) assumption, or conclusion, that there is in reality a separate "self" which exists, is the very foundation of all our common, relational thinking.
To whatever extent that one cannot (at least experimentally) suspend the "certainty" of the sense of self, one cannot appreciate the perspective which the sages have described as non-dual. This is referred to, in contemporary terms, as oneness or wholeness, and in Buddhism as suchness, in Taoism as tao (the way it is).
To minds limited to the mechanics of duality (self versus other, this as opposed to that), even to say that "all things are one" will not transcend the perspective of duality - because they envision that "one" (entity A) containing "all things" (entity B). Not-two implies that there is not ever, under any circumstances, more than (if any) one thing or entity: "all things", and the "one" thing that they are, are the same thing.
The yogi Patanjali is credited with saying, "It is the observer-observed phenomenon which is the cause of human suffering." Krishnamurti was known to have stated this more succinctly, in the equation form: "The observer is the observed."
This statement sometimes engenders confusion in a mind which cannot (even temporarily) suspend its attachment to the dualistic propensity of thought. Its first reaction may be, "If I - the observer - look at a tree - the observed - am I the tree?" To suggest, in response, the true implication that there is, quintessentially, no I (other than as an isolated, thought-created entity) and no tree (ditto) will likely be resisted.
I cannot truly be the tree and have my I-ness remain. And if I, the observer, am the observed tree, the tree is likewise the very same thing that the observer is - which is to say that it no longer retains exclusive tree-ness. My separate identity has vanished into the tree (the observer is the observed), in this manner of speaking; and the separate identity of the tree - both of which identities were only distinctive creations of thought - has vanished into me (the observed is likewise the observer). Two, separate, dualistic identities have evaporated. If we now feel compelled (as thought will) to find a name for what is no longer the observer/observed contradiction, we can call it suchness, oneness, "not-two, not-one", etc.
The mind which is enmeshed in duality is the psyche which is reluctant to surrender its sovereignty; that is, to re-examine the certainty that "I" - me, myself - exist as an entity which is independent and in a subject-object relationship to every other supposed entity.
To realize that the observer does not categorically exist (nor, by definition, that which he alleges to observe) is thoroughly to reorient one's entire mode of thinking. When the observer is actually the observed, there can be no "self" nor "other". Any such distinctions, however subtle, are the dualistic assertions of divisive thought.
"No self?! No right and wrong? No past and future!?." one exclaims. Is it any wonder that duality is a pattern of thought which man finds it exceedingly difficult to relinquish?
At death... or possibly before... that which thinks it is an independent, isolated entity (and that which it thinks it separately and "objectively" observes or identifies) - "self" and all "other" - will disappear: there is not any thing which stands apart from suchness, not one thing.
The No-Thought Experience
In terms of your query, I think we could say that there is a) unrecognized duality; b) recognized duality; and c) nonduality.
We could say that a) is the condition of the ignore-ant person: her perception is mired in a dualistic perspective; and she is not even aware that this is the case, because she has no inkling that any other perception is possible.
Let's say that, at some point, she becomes aware of her dualistic perception, and supposes that another perspective on the actuality of our existence is possible. She conceives of this as "oneness", which she equates with non-duality. But her comprehension of this is that "I am united with everything." Her conception is (despite herassumption) dualistic. There is an "I", on the one hand, and "everything" else, on the other. Item 1 and item 2 are "united". She is still impaled by her subject/object mindset.
Perhaps at some point - c) - the perception dawns that "non-dual" literally posits "not two;" no two "things." She has realized that the (conditioned) conception of "I" and (as opposed to) "other" is false. There being, in absolute actuality, no "this" and no "that," there is no reality that can be described as "uniting."
She has transmuted from not recognizing her dualistic mindset; to recognizing her dualistic mindset; to relinquishing her dualistic mindset (and the "I" who supposed that any of this pertained to her "self.") Her awareness is presently nondual.
In general, Dzogchen characterizes the a) condition as "ordinary" mind; the b) condition as "alaya" (oneness as an "experience"); and c) "rigpa" (nondual awareness which is beyond "experiencing").
In comparable terms, the Hindu savikalpa samadhi is analogous to b); and sahaja samadhi to c). In b), through disciplined concentration or fixation (meditation) on "not-self," she can nullify "self" so as to experience its "non-existence." But there is an experiencer. When the phenomenal experience ebbs (as all do), the "not-self" is no longer a present actuality and the "self" is again a conscious entity.
Attendant to b) is the notion that (first) she is apart from something (desirable); and (second) is driven, by ego motivation, to "attain" or "achieve" it. Subject proposes to "merge" with object. But subject does not comprehend that in a non-dual "merging" bothsubject and object dissolve. The subject, here, expects to remain an entity to which an (unusual) experience is to be added. It is a stultifying, frustrating pursuit, a deadening cycle of "arriving" and inevitably "departing". But because of the (temporary) suspension of "conceptual," egoic thought, it is sometimes presumed to be the "liberation" which is spoken about.
The true liberation is in that nondual awareness of c). Where the inspiration is that "there are not two things," there no longer is a "self" which is apart from the "One"! Thus, no condition such as b); or a). In point of fact, even c) - when conceived of as an entity(such as Self, Buddha-nature, etc) - no longer has any relevance. There is no subject self or desirable experience (such as "no thought") in rigpa or sahaja samadhi.