Although I’ve never watched The Postman (not to be confused with Il Postino), I have read the original novel, written by David Brin. The book is pretty good, set in Oregon’s Willamette Valley, home of Eastchester.
The second part of the book revolves around the mysterious Cyclops–not a one-eyed, three-fingered creature, but a sentient artificial intelligence (AI) machine. Cyclops somehow survived the electromagnetic pulses and other man-made calamities that brought about the post-apocalyptic landscape of The Postman.
Cyclops dishes out advice and makes prophecies, giving hope for better days ahead, paralleling the postman’s efforts to rally survivors around his fabrication of a Restored United States of America. Where the postman uses the mail service to inspire, the Cyclops group sends its members to other towns to solicit food in exchange for repaired electronics and weather predictions.
For some time post-apocalypse, Cyclops was a source of inspiration for people trying to get by and rebuild, largely cut off from others. It turns out Cyclops is not AI, but instead is a human-controlled machination–much like the Wizard of Oz. The postman exposes Cyclops’ secret, then moves on to other regions to expand his mail service and continue his mission to restore civilization.