After he takes complete measurements of a British Police Box, the inspiration for the exterior appearance of the TARDIS, the Doctor plans to visit Logopolis to seek the help of the mathematical geniuses there, whose near-mystic incantations of intricate mathematical formulas actually keep the universe from dying a premature death. Thanks to the interference of the Master, the Doctor becomes trapped, and an Australian stewardess named Tegan wanders into the TARDIS, assuming it to be a real Police Box. The Doctor also receives a distress call from Nyssa, whose father has gone missing on Traken. A mysterious ghostly figure appears and disappears, but the Doctor remains silent as to its identity, and the Master finally emerges from the shadows on Logopolis, poised to destroy the universe by eliminating its guardians. All the while, the TARDIS cloister bell counts down last remaining hours of the Doctor’s fourth life.
written by Christopher H. Bidmead
directed by Peter Grimwade
music by Paddy KingslandGuest Cast: Anthony Ainley (The Master), John Fraser (Monitor), Dolores Whiteman (Aunt Vanessa), Tom Georgeson (Detective Inspector), Christopher Hurst (Security Guard), Ray Knight, Peter Roy, Derek Suthern (Policemen), Robin Squire (Pharos technician)
Broadcast from February 28 through March 21, 1981
LogBook entry & review by Earl Green
Review: Someone once commented that the 1980s were an area of Doctor Who where style triumphed over storytelling substance, and I suppose that this argument could be made for Logopolis. It might just be that I’ve never been terribly fond of math, but at times Logopolis is quite simply incomprehensible. One of the worst faults is the concept that the Master would even contemplate trying to hold the entire universe hostage. This is a silly idea even when applied to taking over the world, but the thought of taking the entire cosmos hostage (and worse yet, broadcasting a “ransom 
note” from a radio telescope) is pure B-movie fodder. Janet Fielding and Sarah Sutton make their first appearances as companions, Sutton having already appeared in The Keeper Of Traken, but the most interesting dynamic, over the first two episodes, is the relationship between the Doctor and Adric, a quirky mentor-and-student routine which ended with this episode. I think that more people would have appreciated the oft-maligned Adric (and actor Matthew Waterhouse) had this combination been explored more. (On a personal note, I’ve never quite worked out what about Adric reviled so many Doctor Who fans. Adric bears a very strong resemblance in personality to Ace, who proved extremely popular when she traveled with the seventh Doctor.)
Given the abstract nature of the story, there doesn’t seem to be much atmosphere present, and what atmosphere exists can probably be credited to yet another catchy (though, in this case, a bit repetitive) Paddy Kingsland musical score, and the viewer’s knowledge that this is Tom Baker’s final appearance as the Doctor.