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About 25 to 30 years ago I remember reading a short story in which the protagonist was in a society where, at a certain age, people's brains were replaced by an egg-like silver sphere.
The main character was very worried about this process, and even though others who'd had the procedure done said there was nothing to worry about, throughout the story the protagonist rebelled against the concept. I can't remember the ending or anything else about the story, except that the concepts of personal identity and losing oneself seemed to be central to the theme. I appreciate any help in identifying this!