One more thing.. the Real reason the Logopolis calculations were so important, and how it relates to the TARDIS as a whole. The hint is in the beginning of the Episode, where Adric sees the Doctor in the Cloister room, and the Doctor is discussing Thermal Dynamics, and entropic decay. The Doctor knows the TARDIS mind is capable of learning, and by getting the Logopolitans to reformat it's exterior plasmic shell, teaching the TARDIS their mathematical modeling, which is superior and is done differently, it can show the TARDIS the correct way of modeling real space-time events (matter) correctly and with an added bonus of being more stable, and less prone to Entropic decay..
The Logopolitans use Block math transfer (which is the process of modeling a 3 dimensional object in mathematical form) and Mutter in tone (vibrational frequency effecting Quantum Strings vibrations changing the building blocks of matter) those calculations are used to effect pure matter conversion. This is because on the Quantum string level, the strings Vibrate at specific frequencies which creates particles, which assembled into atomic structures can form matter. The Tardis does block math transfer computations (again the process) however it uses it's entire metal structure as the transmitter to affect particle change through broadcasting the vibrational waves within the dimension, and internal rooms, and such.
When the 4th Doctor took the TARDIS to Logopolis, it was because the TARDIS computations had developed a fault, and by correcting that by using the calculations he and Adric had written down based on the Police box in Northern England, the Logopolitans could reformat the exterior, and with those calculations in place, the Interior could also be corrected, reformatted based on the mathematical example the logopolitans did with the Police box model, in effect teaching the correct math to the TARDIS main computer, which in tern would allow it to reformat the interior to escape it's current Entropic decay. Logopolitan calculations include a superior format in mathematical form that seeks to reduce the Amount of entropy suffered by a 3 dimensional object. It's in the math!
By extrapolating this math trick (the formula arithmetic), the TARDIS then uses these calculations to create the precise Vibrations necessary to effect the Quantum Strings within it's structure and change the interior.
Basically, and I can see the Doctor some day saying this to the Ship,"Very Sloppy! lazy Math!" it was using Sloppy math to model it's interior structure before Logopolis. I can see the Doctor saying "Very Sloppy! " to the ship if it models a room that is just wrong..or prone to faults in the future..