You can watch yourself waking up in the morning. First there is darkness. Then there is awareness without thought or words, or even the world or self. Then you come fully alive because you remember where you are in bed and what is happening in your life.
This final state is the arising of the I Am sense that you exist, and simultaneously, you are aware of the existence of the world.
Robert says seek the source of the I-thought. If you carefully watch your awakening, the source lies in what Robert calls the "gap," that brief period of time that awareness arises, a state without thought or mind, and from which arises the sense of I and of Am, I exist.
Simultaneously arises the awareness of a separate world.
Now, if you sit in meditation, or quietly in a chair or while lying in bed, you can be simultaneously aware of both the I Am sense, and the world, They are both watched as "objects" by the watcher. You are aware there is a witness watching both the I Am and the world of objects embedded in space, and changing through time.
However, because the waking and I Am appear to happen within the body, and the world appears to be observed as existing outside the body. But if you are quiet and do not think or label, you will recognize that not only are you aware of the I Am as separate from the witness, but so too obviously is the observed world. We do not take the world to be us. But exactly in the same way, we can observe and also feel the (our) bodies as being objects no different from the I Am sensation and the external world.
So, what do we realize from this? We realize that the Witness is separate from the observed existence of the body, the world, and the I Am sensation, and all of that observed consciousness is added onto it.
This is why Robert says you do not exist and that the world is unreal. Both the I Am and the world come and go.
Consciousness comes and goes; it arises and subsides.
Consciousness is just temporary and changeable, and we are separate from it, witnessing it. Only the witness does not change, yet it is Consciousness itself that understands and articulates that Consciousness is only temporary and unreal.
It arises, and from it comes the sense of I, of separate existence, and the world, both at the same time.
Play with this understanding. Lie in bed each morning and watch the coming and going of consciousness. Noting that you are watching the coming and going of consciousness.
Then notice that you are aware of the coming and going of consciousness, and therefore you are not consciousness, your body, or the world, or the mind.