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Mimesis
Mimesis is the act of creating in someone's mind, through artistic representation, an idea or ideas that the person will associate with past experience. Roughly translatable as "imitation," mimesis in poetry is the act of telling stories that are set in the real world. The events in the story need not have taken place, but the telling of the story will help the listener or viewer to imagine the events taking place in the real world.
Hamartia
This word translates almost directly as "error," though it is often rendered more elaborately as "tragic flaw." Tragedy, according to Aristotle, involves the downfall of a hero, and this downfall is effected by some error on the part of the hero. This error need not be an overarching moral failing: it could be a simple matter of not knowing something or forgetting something.
Anagnorisis
Anagnorisis translates as "recognition" or "discovery." In tragedy, it describes the moment where the hero, or some other character, passes from ignorance to knowledge. This could be a recognition of a long lost friend or family member, or it could be a sudden recognition of some fact about oneself, as is the case with Oedipus. Anagnorisis often occurs at the climax of a tragedy in tandem with peripeteia.
Mythos
When dealing with tragedy, this word is usually translated as "plot," but unlike "plot," mythos can be applied to all works of art. Not so much a matter of what happens and in what order, mythos deals with how the elements of a tragedy (or a painting, sculpture, etc.) come together to form a coherent and unified whole. The overall message or impression that we come away with is what is conveyed to us by the mythos of a piece.
Katharsis
Katharsis was normally used in ancient Greece by doctors to mean "purgation" or by priests to mean "purification." In the context of tragedy, Aristotle uses it to talk about a purgation or purification of emotions. Presumably, this means that katharsis is a release of built up emotional energy, much like a good cry. After katharsis, we reach a more stable and neutral emotional state.
Peripeteia
A reversal, either from good to bad or bad to good. Peripeteia often occurs at the climax of a story, often prompted by anagnorisis. Indeed, we might say that the peripeteia is the climax of a story: it is the turning point in the action, where things begin to move toward a conclusion.
Lusis
Literally "untying," the lusis is all the action in a tragedy from the climax onward, or the denouement. All the plot threads that have been woven together in the desis are slowly unraveled until we reach the conclusion of the play.
Desis
Literally "tying," the desis is all the action in a tragedy leading up to the climax. Plot threads are craftily woven together to form a more and more complex mess. At the peripeteia, or turning point, these plot threads begin to unravel in what is called the lusis, or denouement.
