Since her father disappeared, Anna lives alone with her overprotective mother, who bans books, friends, and the outside world. Determined to escape, Anna climbs a vine in the family greenhouse, 4 cm a day. Along the way, she befriends Marionnette and meets Bob and Lucie, an endearing bookseller duo. Their journey leads to the bizarre hole factory of Mr. Flanagan. To rescue her father and understand this strange world, Anna will need courage, cleverness, and perhaps a magical scientific theory.