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As a child I remember reading a book set in the future where Britain had been split into 2, I think with a wall down the middle. On the one side they embraced high technology and nothing was done manually, whereas the other side were totally against technology. The story is based around a boy from the technological side who somehow ends up on the other side of the "wall", I think driven by a fascination for reading "proper" books.

This may be Arthur C. Clarke's The City and the Stars as per Story where everyone lives in a walled city run by machines; another part of the planet has "non technology" people and Story about an intelligent, walled city; people are reproduced by machines, protagonist rebels and tries to leave.

The City and the Stars takes place one billion years in the future, in the city of Diaspar. By this time, the Earth is so old that the oceans have gone and humanity has all but left. As far as the people of Diaspar know, theirs is the only city left on the planet. The city of Diaspar is completely enclosed. Nobody has come in or left the city for as long as anybody can remember, and everybody in Diaspar has an instinctive insular conservatism. The story behind this fear of venturing outside the city tells of a race of ruthless invaders which beat humanity back from the stars to Earth, and then made a deal that humanity could live—if they never left the planet.

In Diaspar, the entire city is run by the Central Computer. Not only is the city repaired by machines, but the people themselves are created by the machines as well. The computer creates bodies for the people of Diaspar to live in and stores their minds in its memory at the end of their lives. At any time, only a small number of these people are actually living in Diaspar; the rest are retained in the computer's memory banks.

All the currently existent people of Diaspar have had past "lives" within Diaspar except one person—Alvin, the main character of this story. He is one of only a very small number of "Uniques", different from everybody else in Diaspar, not only because he does not have any past lives to remember, but because instead of fearing the outside, he feels compelled to leave. Alvin has just come to the age where he is considered grown up, and is putting all his energies into trying to find a way out. Eventually, a character called Khedron the Jester helps Alvin use the central computer to find a way out of the city of Diaspar. This involves the discovery that in the remote past, Diaspar was linked to other cities by an underground transport system. This system still exists although its terminal was covered over and sealed with only a secret entrance left.

Once out of Diaspar, Alvin finds that one other human habitation remains on Earth. In contrast to technological Diaspar, Lys is a vast green oasis shielded by mountains from the worldwide desert. Its people are not stored and recreated technologically, but naturally conceive, are born, age, and die. They have rejected the hyper-advanced technology of Diaspar in favor of an almost agrarian existence, with machines used only for labor-saving purposes. The people of Lys have instead worked to perfect the arts of the mind; they are telepaths, capable of communicating with each other over great distances and without words....

It is a rewrite of Against the Fall of Night. I remembered seeing someone posting about it before, and located the old question.