langdon politely refrained from telling busoni that he was well aware of the fact that they were admiring fakes , and that in actuality , these copies were the second set of `` fake '' ghiberti doors langdon had encountered-the first set quite by accident while he was researching the labyrinths at grace cathedral in san francisco and discovered that replicas of ghiberti 's gates of paradise had served as the cathedral 's front doors since the mid-twentieth century .