note, by other people
I think Krishnamurti spoke beautifully about the observer and the observed. He uses a very logical expression, but I found also ramana maharshi also expressed it well, although typically through actions, I loved that he would teach through silence.
I think the observer and the observed can be understood directly through serious mindful meditation, but also understood intellectually... I think of things like color, or perceptions of beauty... if I look out over the ocean and *observe* a beautiful blue sunset, is the thing observed separate or independent of my mind? Both the "blue" and the "beauty" are qualities created in my mind, created by the observer, and when I think about what is observed, what is separate, if I think very deeply and seriously about this question-- then I realize there is no difference. The "observer" can only exist in relation to what is observed, and that which is "observed" only exists in relation to the observer.
If you try to draw a line between you as the observer and what was observed you'll find there is no place to draw the line. If you think about yourself as separate, as a soul independent of the rest of the cosmos, and try to draw a line between "you" and everything else, you'll find yourself contemplating the ends of the universe looking for where "you" stop and "not-you" begins.
And likewise if you imagine everything that is separate from you, distant galaxies and so forth, and try to narrow in on where "not-you" stops and "you" begin, you'll shrink any sense of "you" and realize there is just one universe, that all the elements and energy of your body and mind are part of the universe at large.
Many Buddhist traditions teach the latter approach of renunciation, of abiding without "self". Of letting go of ego, which is just the perception of "you" as separate from the universe.
Likewise other traditions, like some in Hinduism, use the former method to teach that there is only the universal Self, and that the manifestations of our minds imagine us to be separate and different from the Self, living in the illusion (maya) of separation, while reality is the universal Self.
I think both approaches reach the same place, the metaphors to express are just metaphors and not to be confused with the transcendent truth. Sometimes we get stuck in the metaphors and get confused, you'll see this when people argue about nirvana vs samadhi, or about different levels of enlightenment, this is where a piercing intellect like Krishnamurti could break through, but also the blissful silence of ramana maharshi could dissolve the confusion and reach an untainted truth.