Figuring Out Plato’s Divided Line

Plato’s Divided Line ranks mathematical thinking above empirical perception. But readers today know that the Line’s technical specifications entail equality between the segments representing these two types of mental experience. Was Socrates even aware of this paradox? What was his understanding of the Line? My answers to these and other questions are based on the first interpretation of this passage conducted in real dramatic time and accompanied by rigorous, historically feasible geometrical proofs.