A Block Transfer Computation was a mathematical process used to create objects and affect spacetime in other ways through the power of pure mathematics. The process usually involved chanting.
Block Transfer Computations could create or re-create any object or spacetime event, provided enough mathematical information was supplied. (TV: Logopolis) The Computations could also re-create or even duplicate people. Adric, imprisoned by the Master in a hadron web, created an entire city and its people. (TV: Castrovalva) Living creatures, like the Ceccec, could be made using Block Transfer Computation. (PROSE: The Tomorrow Windows) Artificial intelligences could be made as well. (AUDIO: Unregenerate!) Block Transfer Computation could even allow time travel, though it would require a quorum of twelve people. (AUDIO: The Boy That Time Forgot)
Computers could not do Block Transfer Computations as the calculations themselves would alter the nature of the computer. Though they were working on technological means to do so, the Logopolitans were destroyed before they completed it. As such, organic life forms had to do the work as morphologically unstable living organic matter could handle the stress of reality-changes caused by block transfer mathematics. The Monitor's people spoke their computations aloud for this reason, (TV: Logopolis) but there were few others. The correct organic material could be found with Gallifrey, Axos, and possibly even Nestene matter. (PROSE: Cat's Cradle: Witch Mark)
The Logopolitans were the first to develop Block Transfer Computations. (PROSE: Cat's Cradle: Witch Mark) They used Block Transfer Computations to create a duplicate of the Pharos Project to maintain the CVEs which prevented entropy from destroying the universe. (TV: Logopolis)
The Time Lords used block transfer matrixes as a function of maintaining the outer plasmic shell and interior configurations of TARDISes. (TV: Logopolis, PROSE: Cat's Cradle: Witch Mark) The Eighth Doctor used it to design the TARDIS' gardens. (AUDIO: Scaredy Cat) They also used Block Transfer Computations to create duplicates of the Eye of Harmony to power Gallifreyan timecraft. (PROSE: The Quantum Archangel)
Using Block Transfer Computations and wormhole technology, the Eleventh Doctor was able to connect the inside of the TARDIS and a safe in which Harry Houdini was locked inside. (PROSE: Houdini and The Space Cuckoos)
The Fifth Doctor attempted to use Block Transfer Computation to locate the TARDIS when it was stolen by Thomas Brewster. However, because of the Doctor's subconscious guilt over the recent death of his companion Adric, he inadvertently sleep walked through time to the moment of his death and helped Adric use the computations to land the Freighter he was about to crash into Earth, creating an alternative timeline. (AUDIO:The Boy That Time Forgot)
The Remote were known to use Block Transfer Computations. (PROSE: Interference - Book One) The Remote receiver of the Eighth Doctor's companion Compassion also unintentionally processed the signals she received from the Doctor's TARDIS into Block Transfer Computations, resulting in Compassion mutating into a Type 102 TARDIS. (PROSE: The Shadows of Avalon)