Eleven young people with unusual abilities travel aboard the floating ship Norn, bound for an organization called The World that has kept the Earth at peace. Among them are Koharu, who can call up a fire she barely controls; Mikoto Kuga, who raises the barriers that shield the ship; and Nanami Shiranui, trained to erase memories. Their voyage turns when Sorata Suzuhara, an elementary-schooler pulled back in time, appears on board and the passengers start asking what The World wants with them.