Wow! If you ever thought that new Who had raised the stakes as far as the Doctor saving the Universe, you only need to look at "Logopolis" to see that he's been doing this far more often than I'm comfortable thinking about. Logopolis is where math is made reality and reality is defined by matb. It all starts innocently enough, with the Doctor needing to take some measurements of an actual police box and ends up with the Doctor's greatest adversary bringing about the death of the universe through entropy. And then things get interesting.
While stopping off on Earth to take said measurements, the TARDIS picks up another stowaway - a plucky young lady named Teagan. No, not that Teagan. And no, not THAT Teagan. This Teagan is a stewardess (no, still not THAT Teagan) who is just plucky as all getout. The Doctor brings the measurements (and unbeknownst to him, the ever-plucky Teagan) to Logopolis, where we find Nyssa! You know, Nyssa! From that last episode? Yeah, she's inexplicably here, looking for her missing father. Who has been possessed by the Master, now played by the slick, constantly delighted Anthony Ainley. Ainley would go on to play the Master for the remainder of the show's run before the role was recast in the 1996 Fox/BBC TV movie. And he appears to be delighted about it. Just everything, really. Oh, there's a brief moment where he accidentally causes the death of the universe, and looks a bit put out by it, but literally minutes later, he's delighted. There's also a brief moment where an obvious cardboard cutout is used to stand in for him in the background, and it is delighted.
A bit less than half of the serial takes place on Logopolis. Most of it takes place on Earth including the ending, which brings about a regeneration unlike one I've seen. The entire episode, the Doctor seems to be stalked by a full body cast that can somehow walk and talk. After the Doctor plummets from an antenna dish (just watch the episode, it kinda makes sense. Kinda.) he merges with the mysterious white figure and, through the finest in early 80s video toaster technology, sits up as the Fifth Doctor! Farewell, Tom Baker. You were MY doctor for damn near 15 years and, you know, we had a good run.
Now what's with this whippersnapper and his celery? I don't know, but I'm fairly certain Teagan is going to be plucky about it!