Space colonization generation ship book

Question

Someone asked a question like this recently, but didn’t have as many details about the book, and none of the answers seemed right to me. In the 1970s I read a book that was probably at least 10 years old by that time, if not much older.

It told the story of a teenage boy who, along with one or two of his friends, was going through the annual ritual of leaving his "world" and traveling through those of others. He went through a trapdoor into a farming world, where people were putting food onto conveyor belts that were feeding the rest of the worlds that, nobody remembered but the boy eventually learned, made up a ship that was traveling from Earth to another planet. The boy passed into a third “world” where people just sat around on electronic wheelchairs, growing fat while they did nothing but watch entertainment programs on TVs, and then finally to a fourth world where the scientists knew it was a spaceship and were wondering why the first world was not getting ready for the imminent landing.

Answer 1

This sounds very much like The Star Seekers, a novel by Milton Lesser first published in 1953. It deals with a generation ship hollowed out of an asteroid, making its way to Alpha Centuari. From review on Goodreads:

They have segregated the settlers into engineers, farmers, artists and scientists. Each of these occupy their own unique spheres, each with their own functions. However, over the 200 years it takes to travel to our nearest star, their travels and functions get lost. It was forgotten, only to become a Authorian myth of a bygone era.

The central character is a boy named Mikal. He lives in a society where on their 18th birthday boys are obliged to make the "Journey of the Four Circles", and visit the other societies. He lives in "Astrosphere" and has aspirations of becoming an Engineer. On his trip he first goes to the "Jungle", then to "The Place of the Revelers" (where they indeed have television, but in three dimensions), and finally to Far Labry, "the center of the world and somehow holds the secret of magic both black and white.". This turns out to be a laboratory, and the inhabitants know of the ship's mission:

"This starship left Earth just a few days short of two hundred years ago. Which reminds me, your people in Astrosphere should even now be slowing the starship, preparing to put it in an orbit around one of the Centaurian planets. How is the work progressing?"