Dimensional transcendentalism

A dimensionally transcendental, sometimes called transcendentally dimensional, object was one which appeared larger inside than outside, an effect made possible by transcendental engineering.

The Fourth Doctor once explained the principle to Leela by using the analogy of how a larger cube might appear to be able to fit inside a smaller one were the larger cube further away, yet immediately accessible at the same time. He described this as "a key Time Lord discovery". (TV: The Robots of Death) Rory Williams later surprised the Doctor with his understanding of the principle, that the inside was "basically another dimension." (TV: The Vampires of Venice)

The relationship between the interior and exterior sizes of a TARDIS could be controlled via the dimensional stabiliser. (TV: The Time Meddler) Known dimensionally transcendental objects other than TARDISes included Dalek time machines, the SIDRATs constructed by the War Chief, the Genesis Ark, the Doctor's pockets, and The Towers of Canonicity and Likelihood on Gallifrey. (TV: The Chase, The War Games, Doomsday, The Runaway Bride, The Vampires of Venice; PROSE: The Gallifrey Chronicles)

Sometimes when a TARDIS was dying, the dimension dams started to break down in what was called a "size leak". The Eleventh Doctor described it as "All the bigger on the inside starts leaking to the outside. It grows." This happened to the Doctor's TARDIS in the future as it was dying on Trenzalore, where it served as the Doctor's tomb after he fought his final battle there. The Eleventh Doctor and Clara Oswald discovered the ruined future TARDIS when they went to Trenzalore, it still appeared as a police box but was much larger. Clara described it as "one hell of a monument." (TV: The Name of the Doctor)

Some of the Doctor's incarnations had a habit of pulling a wide array of items from their pockets, presumably an effect of dimensional transcendentalism. These incarnations included the Second, Third, Fourth, Seventh, Tenth and Eleventh Doctors. It was also known that the Daleks were capable of creating dimensionally transcendent factory ships. (PROSE: War of the Daleks)

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

Upon discovering the large subterranean (and thus hidden) portion of the PhiCorp warehouse, Jack Harkness remarked that it was "bigger on the inside", although he was presumed to be referring simply to the fact that much of warehouse was concealed from the exterior, rather than to true dimensional transcendentalism. (TV: Dead of Night)

Upon meeting the Teselecta, "a robot worked by tiny people", the Eleventh Doctor, wondering how they could all fit inside, briefly suggested that it was bigger on the inside until he discovered it was via basic miniaturisation sustained by a compression field. (TV: Let's Kill Hitler)