The City and the Stars ~ Arthur C. Clarke
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On a world decimated by apocalypse, two isolated city--nations stand alone. Long millennia ago, their leaders determined that the only way to avoid absolute destruction would be to cut off all communication between them. But in one city of ten million people--utterly unaware of the other's existence--lives a restless young man named Alvin whose curiosity and perseverance are about to lead him to a startling discovery. It may take only one person to topple the conventions his society is built on--and to end a carefully insulated way of life forever.