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Sciencey Wiencey: The TARDIS – Bigger on the inside?

Guest contributor Caleb Howells explores the possibilities.

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Non-Euclidian geometry is a mad, wonderful thing. For those of you who don’t know, non-Euclidian geometry is geometry that doesn’t work according to how it works in real life. For instance, lets say you’re in a room, and you walk through a door and into a perfectly straight hallway. On the other side of the hallway is the same room you were just in. That’s not possible, is it? Of course not. That’s not how geometry works. Therefore, that is geometry of the non-Euclidian kind.

Doctor Who has a very iconic example of this kind of thing, so let’s investigate.

Bigger on the inside?

Every time someone new steps into the TARDIS, we always get that same, inevitable reaction: “It’s bigger on the inside!” Quite understandable. But really, how possible is it for something to be bigger on the inside? Well, it’s probably not possible at all for humans to build, since we live in three dimensional space (geometrically, I mean). But if we’re dealing with theoretical physics, which we are, then it’s perfectly possible. Allow me to explain:

In terms of geometry, we live in a three dimensional world. There’s left and right, up and down, and backwards and forwards. The X, Y, and Z axes, respectively. And from there we have every direction we can think of. But what if we lived in four dimensions? What other direction could we go in? That’s impossible to comprehend, but what it is possible to do is work out what fourth dimensional movement would look like in three dimensional space.

So, what would it look like? Well, pretty much the same as three dimensional movement (probably). Why is that? Well, let’s take a look at what we do definitely know and understand. Let’s scale the dimensions back by one, and examine what three dimensional movement looks like in two dimensional space:

Imagine you are playing a game of Mario (because that’s really showing off the validity of my scientific knowledge…). There’s a wall in front of you, but you can only move along two axes (hence why it’s a two dimensional game). You can go left and right, and up and down. You can’t carry on walking forward, along the X axis, because the wall is blocking your path. You can try jumping over it (moving along the Y axis), but it’s too tall. So how do you get past? Easy, if you can move in three dimensions. You simply move backwards or forwards (from your perspective, not the character’s) and go around it. You are now travelling along the Z axis. So to anyone watching from a 2D view, such as yourself, you look like you’re going straight through the wall (you would also get a bit bigger or smaller, depending on which way you went, but regardless). Makes sense?

Well, that wasn’t actually answering the question about how the TARDIS can be bigger on the inside, but now you’re thinking fourth dimensionally.

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So anyway, here’s a different scenario. Imagine that you, again controlling Mario, walk into a box. And bearing in mind you’re back on the regular 2D plane, you, as the player, are unaware that it actually has a length of a mile, but along the Z axis. So you walk into it, but for Mario, he’s now in 3D space! But to you, looking at it from side-on, it looks like a normal 2D box. But Mario can wander around for a mile inside, staying in the same X and Y space.

Now let’s just move that up by one dimension. You’re wandering around in 3D space, when you walk into the TARDIS. Suddenly, you’re in 4D space! You can wander around as much as you like, while still staying in the same 3D space.

However, I’m not totally sure whether it would work quite like that, or whether it would just make the TARDIS very long, like in the Mario example. If that is the case, then just remember that the TARDIS isn’t necessarily limited to being four dimensions. It could be 42 for all we know.

So, is it possible?

Theoretically, yes, it’s possible for something to be bigger on the inside. But as far as I’m aware, it’s completely and utter impossible for us to actually make anything that’s not three dimensional. However, it could be the case that it’s possible if you have sufficiently advanced technology, as the Time Lords evidently do. But of course, that’s where we depart from the scientific reality and just use Arthur C. Clarke’s third law to hand-wave.

Step back in time...

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