realization of the forms is mirrored by the level of Understanding in the Ways of Thinking.The key to the struggle for knowledge is the reasoning skills acquired through mathematics as they are applied to understanding ourselves.The shadows on the cave wall change continually and are of little worth, but the reality out side the cave never changes and that makes it important. The ideals are mainly our concepts of courage, love, friendship, justice, and other unchanging qualities.I know this is a bit tricky, but it is how I see the allegory, and most of it is in the preceding and following books of the Republic. I think you should read those chapters, think about what I have said and zero in on what the allegory means to you.CAVEPlato, the most creative and influential of Socrates' disciples, wrote dialogues, in which he frequently used the figure of Socrates to espouse his own (Plato's) full-fledged philosophy. 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 ...