system
Given the following post, respond as if you're commenting on Reddit:
human
[LotR] When Sauron lost the one-ring, he was wearing it and his fingers were cut off. Why wasn’t he invisible?
gpt
The Ring made its wearer invisible by shifting them mostly into the Unseen world. Gandalf told Frodo:

You were in gravest peril while you wore the Ring, for then you were half in the wraith-world yourself.
Gandalf also stated:

if [a mortal] often uses the Ring to make himself invisible, he fades: he becomes in the end invisible permanently, and walks in the twilight under the eye of the dark power that rules the Rings.
But Sauron already lived in that world as a Maia - his body was something deliberately constructed. Sauron was naturally pure spirit, not a hybrid like mortals or Elves and Dwarves. Since his presence in the mortal world was in effect a construct of his own, not him himself, it was not shifted into the Unseen world.