The Logopolitans are a humanoid race of mathematicians which dwell on the planet Logopolis, in a galaxy other than the Milky Way. They have long perfected the art of Block-Transfer Computation: the ability to manipulate reality by mathematical means using only their minds.
Although they are extremely advanced, their technology is highly limited and it took them many generations before they finally started using computers to assist them with some calculations. Even then, they prefer to work without the aid of machines and using nothing more than their own brains. This is because computers aren't as suitable for Block-Transfer Computation, as the calculations themselves would compromise the physical integrity of the machine; an organic brain is much better suited to handle the stress of reality-altering calculus. Other species have been confirmedly able to master Block-Transfer Computation, including Time Lords and Alzarians.
For several ages the Logopolitans have been of pivotal importance to the integrity of the universe itself, as they were the first to realize that the accumulation of entropy was threatening to destroy the whole of creation. Using Block-Transfer Computation, they created the spatial pathways known as Charged Vacuum Emboitments, or CVEs, which allowed entropy to be dissipated between our universe (N-Space) and the smaller universe known as E-Space, thus prolonging the universe's lifespan.
Unfortunately, the Logopolitans were never able to work out a more permanent solution that would allow the universe to last forever, for while they were working on such calculus their planet received a visit from the Master, who killed several Logopolitans, without being aware of the consequences. This caused their planet to start to disintegrate and all but one of the CVEs prematurely collapsed, accidentally releasing a devastating wave of entropy which destroyed several galaxies (including the one where the Traken Union was located) before the Doctor and the Master joined forces and were able to stabilize the situation and preserve the last CVE. It was too late for Logopolis, however, and thus the universe is probably condemned to be destroyed someday, in the far future.
- Doctor Who season 18 - Logopolis (1980)