I believe the story is The Star Seekers, by Milton LesserThe Star Seekers, by Milton Lesser. I read it approximately 60 years ago. Great Storystory. II have forgotten some of the details, but whenever I see dinner trays with dirty dishes on a conveyor belt at a cafeteria, I think about the dinner trays on the conveyor in the story.
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Having worked in a few mega-corporation environments, I have often thought of some of my coworkersco-workers who worked as drones, never really knowing what was in the huge corporate environment around them, and never really knowing who used their output or who provided their inputs -- oblivious to what was really happening in the greater environment.