Why did plato write the allegory of the cave?

Plato, In "The Republic," Plato sums up his views in an image of ignorant humanity, trapped in the depths and not even aware of its own limited perspective. The rare individual escapes the limitations of that cave and, through a long, tortuous intellectual journey, discovers a higher realm, a true reality, with a final, almost mystical awareness of Goodness as the origin of everything that exists. Such a person is then the best equipped to govern in society, having a knowledge of what is ultimately most worthwhile in life and not just a knowledge of techniques; but that person will frequently be misunderstood by those ordinary folks back in the cave who haven't shared in the intellectual insight. If he were living today, Plato might replace his rather awkward cave metaphor with a movie theater, with the projector replacing the fire, the film replacing the objects which cast shadows, the shadows on the cave wall with the projected movie on the screen, and the echo with the loudspeakers behind the screen. The essential point is that the prisoners in the cave are not seeing reality, but only a shadowy representation of it. The importance of the allegory lies in Plato's belief that there are invisible truths lying under the apparent surface of things which only the most enlightened can grasp. Used to the world of illusion in the cave, the prisoners at first resist enlightenment, as students resist education. But those who can achieve enlightenment deserve to be the leaders and rulers of all the rest. At the end of the passage, Plato expresses another of his favorite ideas: that education is not a process of putting knowledge into empty minds, but of making people realize that which they already know. This notion that truth is somehow embedded in our minds was also powerfully influential for many centuries. 

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Cherokee  removal, part of the trail of tears, refers to the  forced  relocation between 1836 and 1839 of thecherokee  nation from  their lands ingeorgia, south carolina, north carolina, tennessee, texas, and alabama to the indian territory (present day oklahoma)  in  the thenwestern united states, and the resultant deaths