- "What's a police public call box?"
The Chameleon Circuit is the greatest lie that Satan ever told the world.
The Karma-Karma-Karma-Karma-Karma-Chameleon Circuit broke sometime in 1963 while the Doctor was trying to get a girl with no birth certificate or vaccination record signed up for an urban comprehensive school, and in the days before the Psychic Paper, too. If it was working, the TARDIS would be a sneaky box, pretending to be something appropriate to the locale when the Doctor landed. But it's broken, so instead he bums around the universe in a cardboard box painted blue.
Other TARDISes have allegedly working Chameleon Circuits, though they tend to be immediately obvious anyways.
Behind the Scenes Edit
Originally, the writers wanted the TARDIS to be invisible, until Verity Lambert reminded them that CSO wouldn't be invented for a few years, so that was impossible. So they came up with having it camouflage itself with its surroundings in each episode, which would be even cooler. So it was a police box for the first episode, because that fits in with 1963 London.
But then someone pointed out that this would mean creating a new prop every couple weeks. The whole point of the BBC is that if you want to set a story in Regency England, they've got all the props, sets, and costumes already lying around that you can use for free. But none of those props is a piano with a door in it that the characters can walk in and out. And building new props is hard, you guys, especially when the show is on a budget of 13 shillings a year. So, they decided, screw it, we'll just keep the police box prop and explain it by having the Doctor shrug at Susan and nobody ever mention it again.
Years later, JNT wasn't happy with that. How can you do continuity porn about a thing that hasn't even been named, much less had a bunch of technobabble attached to it? Also, a police box no longer even worked as a disguise in London by the 80s, and he wanted to make sure everyone noticed that and realized how clever it was that the police box had become more iconic of Doctor Who than of the police. By the end of Tom Baker's only season with JNT, we knew what it was called, how it worked, why it was broken, and why the Doctor couldn't fix it without Romana or someone similarly skilled to help him. And the high point of JNT-era chameleon circuit autism was the scene where Sixie fixes the chameleon circuit and it turns into an organ and he doesn't know where the door is, because the three people in the world who remembered the ancient Barry Letts interview where he gave the door-in-the-piano explanation would have really appreciated that reference, if he (or maybe Levine?) hadn't misremembered it and used a pipe organ instead of a piano.
Eventually, they got to do the invisible TARDIS in one of the Virgin Missing Adventures, because it's a lot cheaper when you can just write "And it was invisible." And eventually, like everything from any novel, Moffat plagiarised the scene for TV.
The novels also had jokey references to other TARDIS chameleon circuits getting stuck, most famously in Alien Bodies, where Homonculette's humanoid TARDIS gets stuck in the shape of a blue-uniformed 1963 London policewoman. Since that was not only in a novel, but also by Larry Miles, Moffat especially had to plagiarize it, but the best he came up with was the diner; if you want to see Clara entering a 1963 policewoman, you'll have to wait for his spinoff.