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+- Gattaca represents an oppressive society.
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+Several key examples of oppressive societies exist in modern day humanity, and the oppression within these societies exists in a broad range of ways. These methods include privilege, racism, sexism, class oppression, sexuality oppression, etc. *Gattaca* introduces the idea of a new kind of oppression - genetic oppression. This discrimination is blindingly obvious in some ways, but is sometimes also presented in more subtle detail. From the beginning of the movie, the idea of the "invalids" is a significant theme and becomes the focus of Vincent's struggles. Genetic discrimination, a form of societal oppression, causes leaders at Gattaca Corporation to effectively ignore Vincent's interest in space exploration despite his considerable potential. This is a great contrast to Vincent's brother Eugene, who "never suffered from the routine discrimination of a 'utero'". This theme of oppression can also be generalised to the rest of the society represented in *Gattaca*, as is evident through the society's control over individuals. The leaders have caused society to look "so hard for any flaw that after a while that's all you see", another example of oppression. This makes it clear that beneath the clean and futuristic setting of *Gattaca* is a sinister, discriminating society which has fell into its own trap of oppression.
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+Gattaca shows how individuals suffer within an oppressive regime.
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+Oppression in *Gattaca* is clearly an integral theme, as is shown by Vincent's struggle against discrimination from almost all parts of society, including his own brother. Following the journey of Vincent allows the movie to reveal an aspect of oppression which is alien to most people, showing the reality of suffering genetic discrimination. Clearly the main character Vincent suffers greatly from the oppressive regime of his society, admitting that "I'll never understand what possessed my mother to put her faith in God's hands". This decision by Vincent's mother would not have negative consequences if it were not for the prejudiced society, but this causes Vincent great trouble throughout his life. Further, Vincent shows his discontent that he "was never meant for this world", exemplifying how he feels displaced and ignored by society. These feelings that Vincent experiences are clearly direct consequences of an oppressive regime implemented by a discriminating society, and encourage us to be cautious in our own societies.
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+Gattaca reveals how and why people rebel against oppression.
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+There are several different types of rebellion, and *Gattaca* encourages viewers to consider potential causes for it and the way in which it is executed. The protagonist, Vincent, is the most "rebellious" character in the movie - he describes himself as "someone who was never meant for this world", a feeling which causes much unrest in Vincent and the people around him. This results in Vincent pursuing his goal of space flight, rather than accepting his imperfections and society's discrimination against them. This progression of events allows the film to explicitly portray how oppression can lead to rebellion, causing a feedback loop in which everyone sees each other's acts as wrong. This phenomenon reaches a zenith towards the end of the movie, with the murder investigation and the risk of Vincent's methods being uncovered. Also, Vincent's colleague Irene is presented as playing a part in his rebellion, and marks an important point in which Vincent becomes a mentor for someone in a situation similar to what he experienced initially. The couple then empower each other, and the film foreshadows a larger widespread rebellion. These various factors of rebellion mentioned are contrasted against each other in *Gattaca* and are intended to display the complex path of events that is inevitable in such societies.
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+Gattaca depicts the consequences of individual rebellion.
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+Whilst the film emphasises the effect of Irene on Vincent's rebellion, it is very much a "solo effort" for Vincent until this point. Importantly, the time at which he frees Irene from the "routine discrimination" strictly correlates with the beginning of Vincent's success - having fallen in love and being granted inclusion in the space mission, viewers suddenly feel less disappointed and more tense. Not only is this a strong filmic technique, it also shows how hard it is for Vincent to succeed on his own. Once he becomes familiar with Irene, he starts to feel less isolated and this enables him to focus more on the practical aspects of his success - "everything he needed to get into Gattaca" - rather than being distracted by emotional uncertainty. This reveals the effects of connections between individuals who rebel, and contains a rich allegory about communities and unity.
As $\quad f(x) \rightarrow \pm \infty,\quad {1 \over f(x)} \rightarrow 0^\pm$ (vert asymptote at $f(x)=0$)
-As $\quad x \rightarrow \pm \infty,\quad {-1 \over x}$
+<!-- As $\quad x \rightarrow \pm \infty,\quad {-1 \over x}$ -->
- reciprocal functions are always on the same side of $x=0$
- if $y=f(x)$ has a local max|min at $x=1$, then $y={1 \over f(x)}$ has a local max|min at $x=a$