In American History X, the key determinant ideal is the "capacity of oneself to change". That is, our behavior is a result of environmentally deterministic events, and thus we have the ability to change our thoughts, our behavior, and our life situation. In doing so, we hold a virtually limitless power to determine the circumstances surrounding our lives and the consequences of those circumstances.
The focus of the story centers around the primary character, Derrick, as we witness his tremendous psychological transformation from radical, racist skinhead to enlightened, mature leader against the very hate that he previously wrought. His miraculous, 180% transformation is a result of two aspects in his life - his experiences with both skinheads and blacks in prison as well as his interaction with his former high school mentor, Dr. Sweeney. Both Derrick and Sweeney believe in the potential of self-determinism. Even prior to his arrest, Derrick relays his view that people are responsible for their actions.
In talking about the riots after the Rodney King incident, Derrick states, "They're (blacks) not products of their environments...that's crap."
The second, though no less important, story of the movie intertwines with Derrick's story. Derrick's little brother, Danny, has followed, or is attempting to follow in his brother's footsteps, and subscribes wholly to the propaganda of the skinhead movement. Through his involvement with Dr. Sweeney and, later Derrick, Danny is forced to re-think the validity of the skinhead agenda. Again, we see the influence of Sweeney's confidence in the belief in self-determinism. In discussing Danny's seemingly adopted racist doctrine, Sweeney tells Murray, "He learned this, Murray. This racist propaganda...this Mien Kampf psychobabble. And he can unlearn it, too." Against the pressure he has been facing for the last three years from Cameron and the like, Danny evolves over the course of the story into a younger model of Derrick; liberated from the burden of hatred and bigotry that has consumed his existence up till then.
To the director's credit, this movie contains an incredible array of subtle, yet very powerful, messages. One of the most interesting of these aspects in this story is the idea that it actually takes place over the course of just a single day. While Derrick's transformation into the man that he becomes takes several years, Danny's de-programming actually only takes place over night. From his confrontation with the young black men in the morning, to his meeting with Sweeney, to the fight at the skinhead party, and through his talk afterwards with Derrick, the director illustrates an incredible aspect of human potential - the capability to alter an entire belief system in the relative "blink of an eye".
One of the most significant scenes in the movie with respect to environmental determinism is one that is often overlooked. As Derrick gets out of the shower and is looking at himself in the mirror, the scene changes to a glimpse of himself and Danny as toddlers on the beach. This single scene is one of the most powerful scenes in the entire movie, particularly in regard to environmental determinism. We see the boys as young toddlers and we feel Derrick's pain in remembering the days of innocence. We see young Derrick marvel at the sight of a simple seagull and we remember life before being corrupted by the evils of hatred. At this point, we feel Derrick's pain in realizing the tremendous time and energy he has wasted in his life on a false cause. Perhaps even more so, we feel the overwhelming guilt of realizing the pain and torture he has brought upon those who loved him most.
Again to the director's credit, we experience one of the greatest ironic tragedies in modern film. In seeing and feeling the pressure and turmoil of Danny experiences, we (the audience) feel the greatest relief with him as he realizes the error of his ways and puts his resolve down on paper. As the young black man fires upon Danny in the final scene, we feel the great despair in the tragedy of both of their plights.