Finally, I've gotten around to Tarkovsky.
With Andrei Rublev, I tried to watch the movie with all my thoughts filled in. I didn't "get" it until half way into the movie (In a movie about a painter, he is not even shown painting? What is this movie about? What is "The Raid" doing here? etc., etc.,)
With Solayris, I took constant breaks, tried to make sense of it and in the end, couldn't make sense of everything.
With Stalker, I sat there with an empty mind without any expectations. I put myself in the position of the camera and just watched it unfold. At the end of the movie, I still won't say I understood all of it. But there's a sense of calmness that I don't experience often. Coming off any movie, I have my thoughts filled to the brim. Today, I am not eager to read other's interpretations, I am not even thinking about my own interpretation.
Just another opinion in a sea of opinions - I've read some of the posts on IMDB boards of Tarkovsky's movies. There's seems to be a constant battle on whether his films are 'pretentious & boring' or 'works of art'. There's also this constant effort to pigeonhole the intellectual capability of those who "get" it and those who don't. I really do not think it is based on intellectual capability or having appreciation for art films, because most people tend to like other movies generally considered as 'art films' or even somewhat understand Tarkovsky, but still find his movies boring and pointless. I do not count myself among either group - intellectuals or the art movie lovers. But, I think the key may be the will to 'surrender and just watch' that separates people who like Tarkovsky and those who do not. Otherwise, they may be just a series of long, "boring" but often beautiful shots where nothing ever happens.