When time travelling, be sure to dress iconically


Don’t you see what’s going on? The Doctor is facing his biggest challenge yet. Time has collapsed. Churchill is prime minister, Roman chariots are chilling at the stoplights, and Charles Dickens is telecasting an interview. If he doesn’t find a way to reverse time and repair the broken fixed point, then all of time will dissolve into the void.

Of all the guilty pleasure television out there, Doctor Who is one of the best. Space aliens and monsters, witty companions, clever technological fast-talk, a time-traveling police box, and a manically upbeat protagonist with more brains than brawn and a dislike for violence and weapons: what more quality can you possibly cram into a 45-minute show?

My answer to that question is: deep analytical inquiry. Though I don’t actually believe that what happens on the show is real, unlike some crackpots out there, there are some fun theories that are suggested. After all, when writing about time-travel, especially for a show as wacky and no-holds-barred as Doctor Who, the writers are forced to answer some questions. What happens when you go back and meet yourself? Doesn’t changing the littlest moment in the past alter your own future irrevocably?

How do the writers explain away their erratic games of time? None of us can pretend that we understand it all of the time, or even that it always makes sense. But unlike shows like Lost, which utterly abandon any intention of making sense in the quest to wrap up the script, Doctor Who tends to really play with the elasticity of time in a thought-provoking way, to create universal rules, and attempt to explain it if those rules are bent. How far, after all, can you bend time before it snaps?

I’m going to poke at a couple of particularly bizarre time-bending moments in the Doctor Who reboot and attempt to explain why they don’t, after all, snap.If you’re coming to this without much Doctor Who under your belt, or you’ve watched the first couple of seasons of the reboot and haven’t finished it yet, I find myself compelled to say just this before I go on.

Spoilers, sweetie.

The butterfly effect.


One of the big stressors that comes up when discussing time travel is the so-called “butterfly effect.” If a butterfly in Arizona decides not to flap its wings, isn’t there rain in Bangladesh, instead of sunny weather in China? And, if you go back in time and eat an apple, won’t Benjamin Franklin invent edible panties instead of electricity?

The answer, according to Doctor Who’s writers, is “no.” In the show (and maybe in real life), time is a highly durable substance that manages to stabilize itself when variables enter the mix. When hit with the wonky hammer of time travel, the fabric of time resolves itself in one of two ways. To illustrate this, I like to think of “happy numbers” and “sad numbers”.

Before people had television and the The Dark Knight Rises free downloadable Android game, people used to play with things like number theory. One of the games they came up with was happy numbers and sad numbers. To find a happy number, you take a stable, positive full number, like, say,


Then you hit it with a big stick to destabilize it. Take each of the digits of that integer, in this case 1 and 3, rip ‘em apart from one another, then square them.

12 = 1, 32 = 9

Then you add those squares together.

1 + 9 = 10

Then you repeat the process until one of two things happens. If you end up with 1, which will always be 1, then it’s a happy number. If not, you get this sequence:

4, 16, 37, 58, 89, 145, 42, 20, 4, . . .

In this case, the original number was a sad number.

What’s interesting here is that all numbers end with one of these sequences: either 1 infinitely, or 4, 16, 37 . . . and back to 4 again. In either case, you can predict the outcome. With happy numbers, the outcome is 1. With sad numbers, the outcome, 1/8 of the time, is 4; 1/8 of the time it’s 16; 1/8 of the time it’s 37; and so on.

What’s the purpose of this game? No idea. According to wikipedia it “may have come from Russia,” but it doesn’t illustrate much beside the behavior of numbers when hit with a sticky equation: it’s truly “recreational math.”

This is useful for our purposes though, because like numbers, time, when rocked like a hurricane by destabilizing time travel, stabilizes itself in one of these two ways: either with a constant time stream, or with multiple time streams which overlap and, eventually, create a predictable sequence of events.

Happy numbers v sad numbers


Consider The Master. If you’ve watched much of the Doctor Who reboot, then you know that The Master is the only Time Lord who survived the Time War beside The Doctor. Which is a real shame, because he’s dangerously insane. Ever since he was a kid and looked into the void (a special box the Time Lords had which allowed them to see all of space and time at once), drums have been playing in his mind—a sequence of four beats repeated—and they’ve driven him to all kinds of crazy, world-dominion acts, everything from throwing rocks at the other kids on the playground to changing every human being on earth into himself. He believes that the tormenting drums lead him to war, and set his destiny apart as superior.

In the 2009 special The End of Time, we learn that time is pretty bizarre and behaves in crazy ways. In this episode, the Time Lords, who died in a big explosion at the end of the Time War, are seen in those final moments. Rather than peacefully and nobly accepting their destiny, they wrack their brains for a way to escape their imminent destruction and, looking into the future, see that The Doctor and The Master escape the war. They remember that The Master has always been haunted by the four-beat drumming, and realize that this is their way out—they will send him that code, through the void, into his youth, and it would become a beacon to lead them out of annihilation and into being.

Well how the fuck is this possible? The idea is inspired by the fact that it’s already happened. Without it happening, there would be no idea, right?

Consider this. The Master is not crazy. He’s never heard the drumming. But he did survive the time war, he and The Doctor. Then, to save themselves, the Time Lords decide to send a four-beat drumming back through the void and into his brain, to lead them back.

It does lead them back, but it makes him crazy. Thus, time is changed. Despite being crazy, he still survives the time war, and then the fruition of the idea begins to inspire itself. Instead of having to come up with the idea, the time lords just have to follow it—follow the trail of their own act—without realizing how time evolved.

This is the simplest way to imagine the seeming paradox being created, but consider the other possible variations. What if The Master never survived the time war, and it was only The Doctor? The time lords sent the signal to The Doctor and it drove him crazy, and as a result, The Master survived and The Doctor did not. As a result, the Time Lords were forced to come up with the idea again, but this time, they sent it to The Master. It made him crazy, but as a result, somehow, both he and The Doctor survived.

Time could have gone through a million variations before ending on this one, stable result.

This is like a happy number—the original timestream is bent, but not broken, variations bend back and forth like a plucked string, and eventually find harmony in a single integer which fulfills itself. The original reality never actually existed. The later realities cancel it out, but find stability independent of it, like ropes strung across a chasm to keep bridge-builders safe, and then cut once the bridge is complete. Looking at the bridge you might think, how did they ever build that?

Another fun, less dramatic example of the happy number sequence is the relationship between The Doctor and River Song. We first meet River on the day she dies, in Silence in The Library, and though she’s known The Doctor for a very long time, he’s not met her yet. She (flirty) calls him “sweetie” and when he asks who she is, she (coyly) reprimands him “spoilers!” by way of a refusal. Through the next two seasons, they meet and meet again, but always in inverse order, going back through River’s timeline as we move forward through The Doctor’s; the phrases “sweetie” and “spoilers” are repeated as a flirty joke between them. Then, when we finally reach the day that River first met The Doctor in Let’s Kill Hitler, The Doctor calls her “sweetie”, and when she asks about her future, he says, “spoilers!”

Apart from the weirdness of being in a love relationship when you already know how the other person dies, and needing to check journals with one-another to make sure that you don’t tell them too much about themselves, this creates another seeming paradox. In Let’s Kill Hitler, The Doctor obviously says “spoilers” and calls her “sweetie” because she’s always called him that. But then, moving forward in her timeline, she uses these words because he always did, and by the time she gets to Silence in the Library she’s saying these words because he’s always used them. WTF?

Again, happy time, happy numbers. At some point, one of them came up with the joke, and this influenced them both to keep making it, thus creating reverberations across time, until their entire relationship was suffused with this particular flirty language. In fact, in a case like this, where the two are extremely flirtatious even on the days they meet one another, that instant chemistry can be explained by the fact that though The Doctor had never met River before, she’d known him for a long, long time, and knew how to push his buttons, and vice versa. Who knows what their relationship was like before the weird reverberations occurred. What matters is that in the end, time found its happy stream, its constant 1.

That’s some sad time.


Sometimes, when you disrupt time’s happy forward flow to go back in time to fight a space monster or free the slaves or see what that ancient Roman ice cream tasted like, the result is something like that sad number sequence: multiple time streams falling on top of one another and to create a stable and predictable sequence of events.

For example. In The Wedding of River Song, River, in that moment on the California beach, both kills and does not kill The Doctor. Though she loves him, she was programmed as a child to kill him, and in The Impossible Astronaut, when The Doctor’s companions get a little glimpse of the future, we see her kill him by a lake in Utah. Then, at the end of the season, when we arrive at this moment again, we see River come out of the water, The Doctor approach her, her take out her weapon—and not fire.

River, in doing this, is denying what is basically destiny—what is meant to happen—a “fixed point.” The Doctor talks about fixed points a lot—they’re moments in history which he is not allowed to change, because changing them will actually damage the fabric of time. Moments which have to occur—and his death, there, on that beach in Utah, is a fixed point.

And so, time collapses. Next thing everybody knows, they’re in a world where all of time is occurring at the same time—a London with Roman chariots and Charles Dickens and Churchill as Prime Minister. In this alternate world, The Doctor finds River and reveals to her that he was protected from her weapon—he knew that she had to kill him there, and so it was not him, but a shapeshifting robot (yess!) that she pointed her weapon at. Because he tells her this, she agrees to go back and shoot him, and put time right.

So, in this case, the true time stream (in which River shoots The Doctor) is dependent on the one that never actually exists (in which she does not, and time collapses), and though that second time stream never exists, in it she learns that The Doctor is safe, and that is the knowledge that she needs in order to shoot him and make the first time stream happen.

How weird is that? Well, this is just like the sad numbers. Whenever time reaches that moment, that second time stream will be created—and then destroyed. Unlike the time lords situation, where all of the bumps were ironed out by a sequence of time which seems paradoxical but can exist on its own (i.e. the world where The Master was never insane is no longer necessary to create the one where the Time Lords return), in this case, there are two parallel time streams which must occur alongside one another, even if one is perpetually erased (River will not shoot The Doctor if she believes that she is killing him).

Here’s another example. In The Girl Who Waited, Amy Pond enters a hospital ward which exists in a faster time stream. She waits for twenty years while The Doctor works for only an hour to rescue her. When he arrives and finds bitter, fiercely independent forty-year-old Amy, he has a hard time convincing her to sacrifice her own existence to save her past self from becoming . . . her.

In an attempt to bring her around and save her from twenty years of solitary confinement in a hospital ward with aggressive robot nurses, he puts her on video-chat with his (young) Amy, who’s still tooling around the hospital on her first day. Old Amy says that she remembers this conversation from her first day in the hospital—and that the older her refused, and The Doctor eventually had to leave. But at the end of this conversation, young Amy appeals to her love for her husband and says, “Do it for Rory,” and old Amy gives in.

Again, WTF? How is this possible? Aren’t these the same two Amy’s who had a conversation twenty years ago which went in the opposite direction?

Consider three time streams, three variables, and three Amys. First Amy enters the faster time stream. Because there is no old Amy around, The Doctor can’t use her to look back through time to find young Amy, and has to leave without her. Then, this first Amy becomes old without ever seeing The Doctor and Rory again. When the second Amy enters the time stream, her Doctor talks to the first Amy and puts her on videochat. Therefore, though first Amy refuses, second Amy will grow up to be slightly different than her predecessor: she saw The Doctor trying to help her, and saw herself old and cruel. She might be a bit softer than first Amy. Third Amy enters the time stream when second Amy is about forty, and when she appeals to her older self, she’s got a marginally easier job of it than the second Amy did, and succeeds.

Third Amy escapes, and second Amy is wiped out of existence in the process.

The next thing that will happen, of course, is that this process will repeat itself whenever time reaches this point.

Again, this is exactly how a sad number behaves—sad numbers become stable because they find a sequence which allows for a predictable outcome, so that the results (or, in the case of time travel, the universe) are not in flux. Outside of that time stream, all that’s important is that either Amy gets out, or Amy does not. 1/3 of the time she does, 1/3 of the time she does not, and 1/3 of the time actually never happened at all.

Sometimes fixed points break


This does bring us to one last little discussion.

The writers on Doctor Who must have found themselves in an incredible predicament. How do you raise the stakes with time travel possible? After all, you’ve got a crazy genius with a magic box that can take him anywhere. Can’t he just go back and re-do it until it goes right? Knowing how things are supposed to be, can’t he plan accordingly and fix them? And doesn’t he know if his friends are going to die?

To raise the stakes and create drama within the otherwise all-powerful Doctor’s universe, they decided that though there are “fixed points” which must stay the same (Kennedy’s death, Pompeii, the invention of taffy, River’s murder of The Doctor), time can be re-written. The Doctor is drawn to save lives and prevent disaster, but there are disasters which he must act to protect, from himself, his companions, and his enemies. And what’s more, he and any of his friends can die and he’d have no way to predict it. Another rule: he can’t travel forward or back in his own time stream—he can’t meet himself, can’t change things that happened to him. These are the laws of the Time Lords, designed to keep themselves responsible and out of trouble.

David Tennant always was the best Doctor.

This gives the writers the freedom to do stuff like making The Doctor have the final confrontation with the Dahleks time . . . and time . . . and time again, over fifty years of serials. Though every time they pop up he seems to render them extinct, they keep on returning.

It’s another answer for how time stays supple: the people with the most control over time travel are really responsible with it. But it’s also just another literary device.