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Logopolis, written by Christopher H. Bidmead and directed by Peter Grimwade, concludes Season 18 and the Fourth Doctor's tenure. It introduces new companion Tegan Jovanka and reintroduces Nssya, who was last seen in The Keeper of Traken (the previous story).
The story is divided into three main segments - the first on Earth (episode 1, and half of episode 2), the second in the city of Logopolis (half of episode 2, all of episode 3, and some of episode 4), and the final segment at the Pharos Project site back on Earth (most of episode 4). It is along these lines that we can divide Logopolis into the good bit, the boring bit and the great bit.
Episode 1 gets Logopolis off to a good start. It establishes the tone well, introduces us to Tegan in a fun way, and has good momentum to it, despite most of it being set off the A413. I particularly like the sequence of recurring TARDIS interiors - which establishes that there's something very wrong very effectively. I particularly like the combined sound effects of the TARDIS struggling to dematerialise and the cloister bell ringing (this is the first story in which the cloister bell rings), which also adds to the foreboding atmosphere of the story. Instead of leaving for Logopolis by the start of episode 2, Bidmead decides that the Doctor needs to meet the Watcher on the Thames. These make for some very good shots (the Doctor with his head in his hands after hearing about his impending regeneration is strong imagery), but the way they end up there (the Doctor's ridiculous plan to flush the Master's TARDIS out of his own by landing inside the Thames, and somehow not drowning in the process) makes no sense whatsoever. Stranger still was Tom Baker's delivery of the line "materialise the TARDIS underwater, and open the door", but it was good acting regardless.
Once the TARDIS lands at the city of Logopolis, possibly also the planet of Logopolis (I really don't know), things take a turn for the mundane. The biggest problem with this segment of the story, I think, is the realisation of the city. The sets look cheap and overlit, the Logopolitans are boring (and there are no women for some reason), there is too much emphasis of maths and side-quests, and not enough emphasis on keeping the story going - this segment feels more like an untelevised interlude between adventures than an actual Doctor Who adventure, never mind a regeneration story (in short: it's minisode material). If it were up to me, I'd have turned down the lighting, redesigned the sets to look more "computerised castle" and less "planet polystyrene", and have the block-transfer computations carried out on computers. The imagery of crackling, smoking computers shorting out due to the Master's machinations was a real missed opportunity. Moreover, instead of the Logopolitans preserving the universe, their calculations should threaten to destabilise it (if they go wrong). It's also during these middle episodes that Nyssa appears, and remains a blank-slate for the rest of the story. Whilst Tegan does react with some emotion upon the news that Auntie Vanessa is dead (Nyssa's reaction to her father's dead is essentially non-existent), both Nyssa and Tegan seem to be completely unphased for rest of the story - which is a shame, because it means that they don't seem like real people. Characters don't seem to be Bidmead's strong point in this serial. I still have no idea why the Logopolitans copied the Pharos Project radio telescope and control room in universe, but I'm pretty sure we all know it was so that they didn't have to build as many sets. It is here that we learn that the Logopolitans have created the CVEs (through which the TARDIS fell in Full Cirlce), which is a rare and satisfying example of series arc elements in the Classic Series. The Doctor's short speech about how he didn't choose his company is a nice addition.
After everything starts falling apart on Logopolis (and elsewhere) due to entropy, everybody (except the Monitor because he got Thanos'd) return to Earth and decide to use the real Pharos Project's radio telescope to beam a code to hold open a CVE thorugh which to drain excess entropy (I can't imagine this story was particularly easy on the casual viewer). This is easily the best segment of the story. The Doctor's confrontation with the Master atop the telescope is tense, and the ensuing sequence where the Doctor falls off the telescope is still one of the most exciting and intense in the show's history, and one of the best ways to set up a regeneration in my opinion - even with the unconvincing model shots. If you want an even better experience, watch the blu-ray edition of this episode. The Watcher being a decayed version of the future Fifth Doctor was a nice touch, but I wish it was explained more to the audience than Nyssa expositioning "he was the Doctor all along!".
It's here that I should talk about the music, which most people agree is one of the best soundtracks of the Classic Series. Paddy Kingsland crafts a very funereal, foreboding score, fitting for the Fourth Doctor's final story - although I still prefer his State of Decay work. As for performances, Tom Baker is at the top of his game, and Anthony Ainley makes a suitably unhinged debut. Despite a lack of good characterisation, there are subtleties in Sarah Sutton's performance in Nyssa's reaction to her father's death and the destruction of Traken which I appreciate, even if her reactions weren't believable. Tegan seems to be sidelined for most of the story (which is a good reason not to introduce a new companion on the final story of the longest-running Doctor), but Janet Fielding's performance is mostly good, except for the over-acting inside the TARDIS's "vine room" (or whatever it is).
Breifly, Logopolis is a story that's good in the beginning, dull in the middle and brilliant at the end. It serves as a solid finale to Season 18. It's good, but it should have been even better.
For those who haven't read my above rating: 8/10