Zero Sail

'Zero Sail' dive through Imaginary Number Space by the Shadow Border

Imaginary Number Space (虚数空間, Kyosū Kūkan?) is a type of alternative space in the Nasuverse, apart from normal space and reality.[1]


It is possible to travel through Imaginary Number Space in specialized craft such as the Imaginary Numbers Submersible Shadow Border, with the use of the Imaginary Numbers Observation Device Paper Moon, though the method is difficult and inherently dangerous.[1][2] In performing a 'Zero Sail' dive in this way, the craft departs from normal reality and dives into the 'sea' of imaginary numbers, and requires a connection or bond to be formed to an existence within the normal reality in order to surface.[1][2]

Imaginary Number Space has 'tides' which can cause a time difference between vessels passing through it and normal reality.[1][2]

The Far Side of the Moon is an instance of Imaginary Number Space,[3] and BB is capable of utilizing Imaginary Number Space.[4][5][6][7] Passionlip's Breast Valley is an imaginary number space pocket.[8][9]


Fate/Extra CCCEdit

After Tamamo-no-Mae was forced to regrow her tails in order to save Hakuno Kishinami from the Moon Cell, she severed them and sealed them in Imaginary Number Space. However they attained sentience, becoming the Tamamo Nine, and managed to escape.[10]

BB made use of Imaginary Number Space during the C.C.C. incident.[11][4]

Fate/Grand OrderEdit

Goetia's temple, formed through Ars Paulina, was located in Imaginary Number Space.[12] Tiamat was previously sealed within the world of imaginary numbers.[13]

Following the destruction of Chaldea at the hands of invaders from the Lostbelts, the survivors were forced to dive into Imaginary Number Space in the Shadow Border to escape the Oprichniki overwhelming the Antarctic coastline. After a week in Imaginary Number Space, they formed a connection to their attackers and managed to resurface in the Russian Lostbelt, with three months having passed for the planet.[1][2]

The Shadow Border performed another short dive to enter the Norse Lostbelt, during which there were signs of something else nearby within Imaginary Number Space.[14]


  1. 1.0 1.1 1.2 1.3 1.4 Fate/Grand Order: Cosmos in the Lostbelt Prologue
  2. 2.0 2.1 2.2 2.3 Fate/Grand Order: Cosmos in the Lostbelt - Anastasia: Permafrost Empire, Prologue
  3. 4.0 4.1
  4. Fate/Grand Order - BB (Swimsuit), Profile
  5. Fate/Extra CCC - Tamamo Ending
  6. Fate/Extra CCC
  7. Fate/Grand Order - Salomon: The Grand Time Temple
  8. Fate/Grand Order: Cosmos in the Lostbelt - Götterdämmerung: Eternal Ice-Flame Century