mirror was about chidhood, memory,russia in the 20th century,family,(tarkovsky's)he wanted to show his parents that he loved them,a very personal film,and a masterpiece i don't think it is necessary to understand a film for that film to be a masterwork,but i think i understand mirror well
as it shfts from one era to another an appreciation of russian history  helps which i have in spades,ah tarkovsky what a visionary!
