A kind of thought experiment frequently used to unsettle our theories of personal identity. Two persons, A and B, enter a scrambling device, after which A (or the person looking like A, and with A's old body) emerges with B's brain installed, and vice versa. Which person is now A: the person looking like the old A, or the person controlled by the old A's brain, and therefore possessing old A's memories and personality? Variations on the case exist. Reactions include definite verdicts in favour of each candidate, but also dismissal of the case either as one that our everyday conception of identity does not cover, or as improperly transgressing the facts of neurophysiology and scientific possibility.