Threefold death

The threefold death was a form of sacrifice from old Celtic mythology in which an individual simultaneously died in three ways: often drowning, being nailed to a tree, and being stabbed. (PROSE: The Shadows of Avalon) The ritual had a role in Time Lord mythology, connected to the sacrifices Time Lords would make to higher powers and to the resurrective nature of regeneration. (PROSE:  Revelation, Human Nature)

Traditionally, the threefold death had an association with the prophetic power of Myrddin. (PROSE:  Revelation, Human Nature) The tree involved also invoked Yggdrasil, (PROSE:  Revelation) and therefore Odin's sacrifice of his eye down the Well of Mimir for wisdom. (PROSE: The Curse of Fenric, Just War, Seeing I)

To find his internal chaos equation which connected his dimensions with the Other, the First Doctor was guided by the One-Eyed One to conduct a ritual in which he fasted for three days and nights and made supplication to higher powers. The equation became connected with a Sarlain, and manifested at the base of the Doctor's mind as a flower under Yggdrasil. (PROSE:  Revelation)

The Menti Celesti required a sacrifice for anyone who became their Champion. (PROSE: Human Nature) To become Time's Champion, the Seventh Doctor sacrificed the Sixth Doctor's life "for wisdom". (PROSE: Love and War) Where the very heart of the Doctor's mind appeared as the base of Yggdrasil, the Fifth Doctor was tied to the tree in a state of constant death, stabbed in the side, strangled, and wheezing for air as if drowning. The Seventh Doctor's runes were marked above this, suggesting to Ace that he had done this. (PROSE:  Revelation)

The ritual was echoed when Timothy Dean was hung by his classmates while he held the eye-like biodata pod containing the Seventh Doctor's essence. After dying, Dean met Death, who resurrected him with a binary vascular system. Dean then had a psychedelic experience which echoed (PROSE: Human Nature) Myrddin's in the Cad Goddeu. (PROSE:  Revelation)

Behind the scenes

 * Paul Cornell's motif of the threefold death and sacrifice originates from Battlefield conflation of the Doctor and Merlin. To Cornell, the Seventh Doctor's wink in the title sequence evokes the sacrifice of an eye undergone by figures such as Merlin, Myrddin, and Odin. (Author's commentary for Human Nature)