Lyric discussion by aguywholikesmusic 

I think the first verse and closing line of the song uses the metaphor of a broken thin (which for simplicity's sake I will refer to as a vase from here on out) for a relationship that's suddenly fallen apart, and in spite of what the singer (from this point forward referred to as "he" or "him") see's as the best interest of the song's subject (from this point forward referred to as "she" or "her"), it has been shoddily repaired, but no longer retains any value.

"I'm not knocking your want to carry that home" seems to refer to her remaining attached to a broken piece. The vase will never be repaired to it's original form, and the relationship is not salvageable.

"Took it with you when you moved and got it broke," I think in this line he's talking strictly about the literal meaning rather than the metaphorical meaning. How often when you box things up to move a fragile item, regardless of how much newspaper you throw in there, do you open the box at the new place to find that it's broke?

"Found the pieces, we counted them all alone. Didn't add up, forgot to carry a zero" She opens the box to find the broken vase, and even though theoretically every piece should be in the box, since it was intact the last time she saw it, she can't recreate it using the pieces in the box. It doesn't make sense why. Carrying a zero is absurd math. Saying that your forgot to carry a zero is not an explanation for why a math problem is wrong. It doesn't make sense why the relationship can't go back to the way it was. They're still the same people, but somehow there are pieces missing.

At this point the metaphor is dropped, and he responds to her clinging to the broken relationship, and he's not happy about it. He can't keep making excuses for (I can't be your apologist very long), he's surprised that she is being so irrational (I'm surprised you'd want to carry that on), and he remembers a time when she would ridicule others for doing what she's doing now (You have become what you thought was dumb).

And at the end he finally returns to the metaphor.

"And now we can't even touch it. Afraid it'll fall apart." Apparently, she has decided to go back to trying to make the failed relationship work, and like a vase that's been glued together with parts missing, it's so fragile you can't touch it.

I think you nailed it. People seem to be focused on the "blemishes" part and assuming this is somehow a song about "faking" or pretending to be someone one isn't. But that part of the song isn't really central to the theme, in my opinion. It's a minor digression compared to the fragile object metaphor. And becoming "a fraction of the sum" relates to "occupied with what other persons are occupied with and vice versa." She has stopped caring about putting the relationship back together (which they originally did "all alone") and become more concerned with the general concerns of...

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