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The janitor, Purdeep, is involved with six scenes, but makes appearances in only five. Notice the progression.
Scene 1: Rhoda enters the janitors' room. Purdeep sits at a desk, fiddling with a spray bottle that's labeled "ammonia". Nothing is said.
Scene 2: Rhoda and Purdeep sit in an empty classroom together, eating their lunches. Nothing is said.
Scene 3: Rhoda is cleaning in the hall, hears tapping, looks. Purdeep is moving along the hallway, toward Rhoda (but not at Rhoda), using a broom as a blind man does a cane. Nothing is said.
Scene 4: Rhoda and Purdeep are cleaning the hallway. Purdeep is sweeping, struggling at sweeping because he can't really see that well, so Rhoda tries to help him, guides the broom. Purdeep touches her. He speaks. "Listen to me, keep your mind clear, and that's it. You will have peace of mind. My dear, don't worry, learn to adjust yourself." Rhoda stares at him, mouth agape.
Scene 5: Rhoda enters the janitors' room. Purdeep isn't there. Another janitor is, a younger man: Federico. Rhoda asks where Purdeep is. "Checked out," is Federico's response. When's he coming back, Rhoda asks.
"I don't think he is. He poured bleach in his ears."
"Why would he do that?"
"Look, I don't know. Why would he pour bleach in his eyes?"
Rhoda says, "He blinded himself??"
"You didn't know? He said he was tired of seeing himself everywhere."
Scene 6: Rhoda goes to the hospital. The nurse informs her that Purdeep can't see or hear. She puts a hand on Purdeep's shoulder. "Rhoda," he says. She curls up next to him. "You are wondering why." She doesn't respond. "No. No. No. You know why." Rhoda takes Purdeep's hand. She traces in the palm. First the letter "F". Then, in this order. "O" "R" "G" "I" "V" "E". FORGIVE. Purdeep cries.
And that's the last we see of Purdeep.
What's the point?
As I see it, the key to understanding the importance of the character, thematically, is in Scene 5. He poured bleach in his eyes because he was "tired of seeing himself everywhere." This kind of action in a movie with voice-overs that discuss the philosophical implications of meeting yourself. In a movie where the main character is disgusted with herself and doesn't know what to do with her life because she doesn't think she deserves to do anything with her life (which is why she strips her bedroom and makes it look like a jail cell, why she tries to commit suicide in the snow, why she is working as a janitor to begin with).
Can you hate yourself so much that the mere sight of yourself causes you to blind yourself?
We see Purdeep silent three times. Then he finally speaks, for the first time as far as we're concerned (and maybe for the first time Rhoda's heard, because she looks amazed (though you can argue she was amazed that he touched her and spoke such prolific words)). Then he deafens himself.
Maybe his reason for deafening himself is different than his reason for blinding himself. But in the logical realm of story structure, we can only assume the reason is the same: he was tired of hearing himself. Which explains why he didn't speak before. He waited and waited and waited as long as he could, but Rhoda wasn't getting better, and he wanted to help her. Then he poured the bleach in his ears (tired of hearing himself). We can look at his words as a sacrifice.
Rhoda and Purdeep both suffer from acute self-loathing. Rhoda for the car accident. Purdeep for unexplained reasons. Both are working as janitors. We can make a case that Purdeep is a sort of Ghost of Christmas Future. If Rhoda can't forgive herself, if she can't clear her head, if she can't find the redemption she refuses to seek: she'll end up as Purdeep--a person who hates himself so completely he eradicates his own voice and image.
When Rhoda writes in Purdeep's hand the message "Forgive", Purdeep cries because he has never been able to forgive himself, and Rhoda understands this. The advice Purdeep gave Rhoda, to "keep your mind clear", was not a means of healing but a way to avoid the confrontation of self that is necessary for redemption, for forgiveness. There's a huge difference between keeping your mind clear and clearing your mind. One implies avoidance, the other cleaning.
Another Earth is showing us people who do not want to deal with their problems: Rhoda with her guilt, John Burroughs with what he's lost (what Rhoda has taken from him), and Purdeep with who he is. If Rhoda and John represent Offender and Victim, respectively, then Purdeep represents, thanks to his lack of backstory, the Every-Loather. It doesn't matter WHY he loathes himself, just that he does. And if any of us who self-loath allow this to go on for so long, we will self-destruct like Purdeep. Maybe not in such a calculated way. Instead, a casual mental, emotional, and physical decay. Which is what we're seeing with Rhoda and John, before they begin to save one another.
We can then transition the conversation into "how" to forgive. And that's the question Another Earth attempts to answer through the characters Rhoda and John.