Mindbending, or mind-bending, was a psychic contest the Fourth Doctor likened to "Time Lord wrestling."
A mind-bending set-up was a complicated electronic apparatus composed of a framework of girders with a circular central screen and two head-sets, enabling two opponents to match the force of their minds in direct confrontation. A player's face appearing on the screen was a sign of losing. Though usually a game played for fun, it could be dangerous if played to the ultimate, ending in mental deathlock where a winner could think his opponent to the death by driving him back to the moment of birth and then beyond.
Mehendri Solon kept a mind-bending set-up in his castle as it was one of Morbius's favourite toys; before his execution, Morbius used to boast that he'd never been beaten. (PROSE: Doctor Who and the Brain of Morbius)
The Fourth Doctor challenged Morbius to a mindbending contest on the planet Karn, eager to prove the latter's mental instability following his surgical revival. Although Morbius's face appeared first, the screen began showing the Doctor's face, followed by his first three incarnations, then eight of the Doctor's earlier lives before the device burnt out. (TV: The Brain of Morbius)
Both were badly hurt by the fight, with static electricity fusing the circuits in Morbius's brain case, reducing him to a mindless monster. (PROSE: Doctor Who and the Brain of Morbius) The Doctor was left dying, only being restored when the Sisterhood of Karn had him drink the Elixir of Life. (TV: The Brain of Morbius)
After being trapped in the Matrix by the Spy Master, the Thirteenth Doctor escaped by overloading the system with memories of her past incarnations and of all she had seen; the eight faces, as they had appeared to the Fourth Doctor during the mindbending contest, were among them. (TV: The Timeless Children)
Other instances
The Fourth Doctor later defeated the Megron in what he called "telepathic will deployment," albeit without any equipment, banishing the Megron from Earth forever. (AUDIO: Exploration Earth)
Behind the scenes
Morbius Doctors
During the mindbending sequence, several faces are shown. They were images of the production team. The appearances of these images has led to several theories concerning the Doctor's past regenerations. These pre-Hartnell incarnations of the Doctor have come to be known "Morbius" Doctors. They would appear again, through archival footage, in 2020's The Timeless Children.