His head was a city
Of paper buildings
And the echoes that remained
Of old friends and lovers
Their features bleeding
Together in his brain
And once it started was harder to
Tell them apart
He was always distracted
By the very mention
Of an open door
'Cause he had sworn not to be what he'd been before
To be a remain remain remain remainder
The television was snowing softly
As she hunted for her keys
She said she never envisioned him the type of person capable of such deceit
And they carried on like long division
And it was clear with every page
That they were further away from a solution that would play
Without a remain remain remain remainder
He had sworn not to be what he'd been before
To be the remain remain remain remainder
Of paper buildings
And the echoes that remained
Of old friends and lovers
Their features bleeding
Together in his brain
And once it started was harder to
Tell them apart
He was always distracted
By the very mention
Of an open door
'Cause he had sworn not to be what he'd been before
To be a remain remain remain remainder
The television was snowing softly
As she hunted for her keys
She said she never envisioned him the type of person capable of such deceit
And they carried on like long division
And it was clear with every page
That they were further away from a solution that would play
Without a remain remain remain remainder
He had sworn not to be what he'd been before
To be the remain remain remain remainder
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Kind of reminds me of being in love with a close friend who is in a relationship with someone else, and the complexities of having to work that relationship.
(This interpretation is obviously heavily inspired by my personal situation right now, but most stuff on this website is based off that kind of thing.)
The lyric relating to "old friends and lovers" and their features bleeding together in the speaker's brain seems to relate to this. The speaker is torn between his friendship with this person and his love for her, and is unsure how he can view the relationship objectively as a result.
"He was always distracted by the very mention of an open door." If the girl is unhappy with her relationship and speaks to the speaker about it, he becomes distracted by the opportunity to finally be with her.
"cause he had sworn not to be what he'd been before, to be a remainder" seems to refer to him wanting to change his situation with this girl. He wants to be an active part of her equation instead of just a remainder that is sidelined from her life. '
"She said she never envisioned him the type of person capable of such deceit" refers to the speaker finally confessing his feelings to the girl and her responding poorly. She only thought of him as a friend and feels like he had been deceitful towards her since he had ulterior motives in their relationship of wanting more.
"They carried on like long division, and it was clear with every page, they were further from a solution that would play without a remainder." It is clear to both of them that they cannot continue like this, no matter what will happen next. Either the girl leaves her boyfriend for the speaker, abandons the speaker and continue to be with her boyfriend, or somehow lose both of them and become a remainder herself.