Dmitch
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According to Wikipedia:
"In Hinduism, Brahman is "the unchanging reality amidst and beyond the world", which "cannot be exactly defined". It has been described in Sanskrit as Sat-cit-ananda and as the highest reality... According to Advaita, a liberated human being ... has realised Brahman as his or her own true self."
People who have had realizations of the ultimate reality, Brahman, experience themselves as the consciousness that creates all reality. They see themselves as all things and they see all beings are one. They see that ordinary reality is an illusion projected by the mind. They understand the Buddhist concept of emptiness: all is illusion, individual self is an illusion, material reality is an illusion, separate (other) beings are illusions. There is only Brahman. Even the unity of self and other is still illusion because there is no self, there is no other, there is only Brahman.
This realization cannot come to you as a thought or as a logical understanding. The analytical mind is no help here, in fact it is the problem. The realization is going to come to you as an experience when you stop using the mind, stop thinking about the world through the mind and stop thinking of yourself through the mind. The mind only projects illusion, the illusion of self, the illusion of things, the illusion of other separate beings. To attain realization, you have to turn your attention inward so far inward that you go inward to a point before all conceiving of or thinking of.
There are various ways to free yourself from the illusions projected by your own mind. One is through insight / mindfulness practices in which you observe how the mind produces illusions. Another is meditation where you still the mind by thinking of one thing, meditating with a single pointed, focused mind, until there are no other thoughts, then let go of that one thing. Another is working with a koan such as Who am I, What am I, or What is this?
It's really difficult to wrap the mind around this realization thing, intellectually speaking. Who is doing the realization?