Dimensional transcendentalism

A dimensionally transcendental (sometimes called transcendentally dimensional) object was one which appeared larger in the inside than the outside, an aspect which was made possible by transcendental engineering.

The Doctor once explained the principle to Leela by using the analogy of how a larger cube can appear to be able to fit inside a smaller one if the larger cube is further away, yet immediately accessible at the same time. He described this as "a key Time Lord discovery" (DW: The Robots of Death).

This implies that the exterior and the interior of a transcendental object, in this case the Doctor's TARDIS, existed in separate dimensions.

The Doctor himself also humorously pointed out that "dimensionally transcendental" meant no more than that an object was bigger on the inside than on the outside. (BBCR: The Paradise of Death)

A Time Lord with a TARDIS similar to the Doctor's (Mortimus in this case) could control the relationship between the interior and exterior sizes of their TARDIS via the dimensional stabiliser (DW: The Time Meddler)

Known dimensionally transcendental objects other than TARDISes included Dalek time machines, the SIDRATs constructed by the War Chief, the Genesis Ark, and (according to their owner at least) the Doctor's pockets. (DW: The Chase, The War Games, Doomsday, The Runaway Bride, The Vampires of Venice) It was also known that the Daleks were capable of creating dimensionally transcendant factory ships. (EDA: War of the Daleks)

The Doctor was also able to temporarily expand the interior dimensions of a boarding house in Cheldon Bonniface to allow all the guests at Benny's wedding to stay there. (NA: Happy Endings)