Cassia's Compact (Symbol)
Cassia's compact, like all artifacts, is a symbol of her individuality; for her personally, it symbolizes her connection to her grandfather. Once her father destroys her grandfather's tissue preservation sample, it becomes her last remaining tie to him. Not only was it his gift to her, but it was also the artifact that hid the forbidden poems that she ultimately comes to love so much. The Society taking it from her symbolizes their desire to erase what makes Cassia different from any other citizen, as well as their unknowing attempt to remove her grandfather's memory from her life. Cassia refuses to allow this to happen even after she is made to give the compact up.
The Story of Sisyphus (Allegory)
In many ways, the tale of Sisyphus that Ky tells Cassia represents the kind of lives that they and all citizens live. The Society's sentencing Sisyphus to push a rock up a hill but never reach the top symbolizes their desire to keep their citizens too busy with vocations and limited lives to ever accomplish anything for themselves, in the same way that Cassia felt no sense of accomplishment in having planted the beds of newroses because the Society designed and sanctioned every piece of the task. Ky can also personally identify with Sisyphus because they are both Aberrations, who desire to rebel against their totalitarian cages but are instead stuck in the Society's unfulfilling monotony.
The Green Tablet (Symbol)
Cassia's unwillingness to ever take a green tablet symbolizes her unwillingness to give in to the Society. To take the green tablet would be to allow the Society to dim her rage, sorrow, and true emotions, regulating them in order to keep her in line and unproblematic. By refusing to do this, she maintains her rebellious mindset. The fact that both Em and Cassia's mother take the tablet at different points in the book symbolizes their complicity in the Society's machinations, complicity that Cassia doesn't wish to share.
Statistical Probability (Motif)
As part of the Society's trust in data, numbers, and predicted outcomes, statistical probability and improbability play a huge role in the citizens' lives, including Cassia's. The whole idea of Matching life partners together, the book's main premise, is founded on statistical models that predict the best possible outcomes for future Matchees. The fact that Ky was accidentally Matched to someone from his own Province was statistically improbable enough that the Society allowed he and Cassia's relationship to flower in an attempt to see where it would go. In every aspect of Cassia's world, numerical calculations of this kind run the show.
The Top of the Hill (Symbol)
For Cassia and Ky, reaching the top of the Hill symbolizes many things: it is their acceptance of their own desires to fight for freedom; it is the peak of their relationship, where they finally betray the Society's rules by sharing their first kiss; it is the consecration of their societal defiance. Cassia hoped for most of the book that she would get to see the top of it, but when she realized that she would hiking a different hill and was instructed to focus on obstacles along its lower slopes, it became clear that the only way she was going to see the top was on her own terms. This parallels her desire to form a relationship with Ky, understanding that she would only be able to do so by defying the Society.
