Although long and containing many silent scenes, Lee Chang-Dong's Burning gripped me when I first saw it in a theater. I formed an immediate impression of the "solution" to the mystery as it is presented, which is fairly clear and unambiguous. Afterward, I was surprised to read in various reviews and comments that many people felt that the solution is equivocal. On second viewing, it became clear why I felt so certain instinctively.
Below I'm going to focus only on explaining the mystery of Hae-mi's disappearance but not the artistic and poetic choices of the film, which are abundant and beautiful regardless.
Despite the artistic pedigree of Lee, he clearly employed genre techniques and elements in Burning, and centered the plot around a mystery: Hae-mi's vanishing. (I'm using the word "vanishing" to recall the Dutch movie "The Vanishing", which left a deep impression on me, and I'd be damned if Lee had not seen it.) If we look at this movie purely as a thriller/mystery, the question boils down to this:
Was she murdered by Ben?
And the possible answers are only two:
1) Yes, Ben murdered her and hid her body somewhere that cannot be found.
2) No, Ben has done nothing to her, and she disappeared for some other reason.
Why do I believe that the answer has to be 1)? Because all clues given in the movie support 1), and there is nothing in the movie that supports 2). In fact, there are almost too many clues to point to 1). In a conventional murder mystery, the author would provide some red herrings in addition to the "real" solution or culprit. Here, there is no red herring to suggest an alternative theory. Every little clue always points to Ben's crime.
For everyone who believes that the movie still leaves open the possibility that Ben did not kill Hae-mi, the next question is inevitably "Then where is she?" The only possible answer is that she is hiding from the debt collectors, which Lee Chang-Dong tosses out there in one scene, and she has told no one, including Jong-su and Ben, anything about her escape. Keep in mind that this is a theory from an acquaintance. There are no other scenes to suggest that Lee has any interest in this possibility. We don't see Hae-mi talking about fearing the debt collectors or being threatened. We don't hear about anyone else being disappeared by debt collectors (not even a news fragment). We don't see anyone harassing Hae-mi for her debt or threaten to kidnap her or break her legs.
That is the heart of the matter. This is not a true-crime documentary, where the truth may or may not conform to the clues presented in the movie. This is fiction, in which all the characters and scenes are the creations of Lee Chang-Dong's mind. What could have happened to Hae-mi outside of what Lee shows us is immaterial. All we care about is the author's intention for the story. And his intention cannot be more apparent.
Of course, I am fully aware of Durrenmatt's "The Pledge", which argues for the unknowability of real life occurrences, and the indifference of the universe toward a person's perception or knowledge. That's valid, but Burning is obviously not that story. Even The Pledge came out of one man's mind with a point --- Durrenmatt's point. Lee too had a point to make, and he made this movie to support his point. He gave us no indication that the point is nihilism. As the audience, it is our responsibility to try to receive his signals and understand his intention. Otherwise we might as well write our own stories.
So yes, what I should and do care about is his version of the truth, and he is obviously telling us that Ben murdered Hae-mi.
In addition to the physical evidence of Ben's collection of cheap trinkets and the cat who answers to the name of "Boil," the more decisive clues are in the portrayal of the character. Early in the movie, before we suspect any criminal behaviors, Ben would drop lines that suggest his psychopathic personality, like "I don't remember ever shedding a tear" and "You have a stone in your heart; that's why you can't feel anything" (paraphrases). The latter line is transparently talking about himself, even though he is saying it to Hae-mi, who obviously does not have a stone in her heart. The exact same contempt (yawn) he shows to both Hae-mi and the subsequent girlfriend (ie, victim) is clearly a demonstration of his game, as he clearly is not interested in these women as individuals.
Many commentators made a point of questioning the veracity of Hae-mi. Is she a liar? Why does no one remember the past events she mentions? Is the cat real? Did she really fall into a well in childhood? She is so good at eating a nonexistent tangerine, perhaps the cat and her memory of the well are both fake as well? And, by extension, maybe her disappearance (or existence) is fake too?
Here we are again faced with two possibilities:
1) Hae-mi has lied about or imagined some or all of the things.
2) Hae-mi is telling the truth about everything.
If 1) is true, then we can allow ourselves to discount everything she says and does, including her disappearance. Maybe her obsession with the "little hunger and great hunger" and her dance in the sunset are a performance or delusion. Both JS and Ben are fooled. There is never a tangerine or cat or anything else there. The most charitable reading is that she has no grasp on reality, so much so that she never bothers to contact JS after running away from the debt collectors. A less charitable interpretation is that she is just like JS's mother, who disappears and shows up 16 years later asking for money.
If 2) is true, her story in this movie is about the erasure of a young woman, full of yearning, loneliness, spirit, and life. When she was a child, she fell into a well and no one even noticed. She did not tell her family after being rescued and her family did not care enough to ask where she had been. It is one of many signs of her family's indifference toward her, consistent with the exchange in the eatery ("tell her not to come home until she's paid off her credit card debts") and Ben's casual slip that she had no contact with her family (note that both corroborate each other). In the context of the movie, she has figuratively "fallen into a well" and disappeared again, and, again, the only person who cares is Jong-su. The rest of the world just moves on as if nothing has happened. She tries to express her yearning for the meaning of life and her sense of beauty (the trash-filled parking lot in Africa where she was moved to tears by the sunset), and others look at her with awkward chuckles and yawns.
Which one do you think is Lee Chang-Dong's intention? I have seen one other film by Lee ("Secret Sunshine"). Between these two films, I sense zero cynicism from him. Instead, I feel a barrage of humanism, as in, he loves human beings in their natural state of existence. What is the probability of such a humanist devising Scenario 1? I'd say it hovers right about zero.
Some people watch Hae-mi's pantomime and infer that she invents things and events that do not exist and perhaps cannot tell the difference. I think the pantomime has an entirely different meaning. It's about poverty, deprivation, and the absence of the things you need. Obviously, this is a feeling that Hae-mi and Jung-su share but Ben knows nothing about --- except that Ben too has the same feeling. We cannot pretend that what's lacking in HM's and JS's lives is not money. Their despair and shame and isolation, and their reluctance to engage in a full-blown romantic relationship, all have to do with their poverty in a city of casual wealth. And yet there is so much more missing, not the least family, not the least a meaning. JS's yearning for mother, and HM's yearning for anyone. Their most basic needs are not met, and the only way to keep life going is to "forget that it's not there."
Ben has his own missing piece in life, and we can surmise that he too has a yearning for it. This absence is intolerable to him, and he refuses to tolerate it, unlike how HM and JS tolerate their unmet needs. Hence he burns greenhouses. In both the source materials (Faulkner and Murakami), it is barns that are burned, and barns symbolize food and wealth. Here, however, it is greenhouses, which symbolize life. Not quite the same thing.
As a co-owner of two cats, I just want to make a note about the "Schrodinger's cat" here. Is the cat a part of Hae-mi's imagination? Compare the two parallel scenes depicting its absence: When JS goes to feed it when HM is in Africa, he sees that the food and water bowls are empty, and the litterbox contains cat poop. When he goes back to the apartment after HM's disappearance, there were no bowls and no litterbox at all.
If there is poop, trust me, the cat is real.