Magic Without Lies | Cosmos: Possible Worlds

In the quantum universe, there's an undiscovered frontier where the laws of our world give way to the ones that apply on the tiniest scale we know. They're divorced from our everyday experience. How can you think about a world that has different rules than ours? It's not easy. That's why I want to take you to this place where it's not only possible to make such a leap. It's mandatory. It's a world very much like our own except in one respect.

[ominous music]

It just happens to be missing a spatial dimension-- the third one. In order to venture into the quantum cosmos, we have to be able to imagine another dimension. That's very hard to do. It's much easier to wrap your mind around a world that's missing one of the three dimensions that we take for granted. The beings of the world we're about to enter have only two.

This world was first imagined by a man named Edwin Abbott. Everyone and everything here and everyone they know and love is flat. Their houses are flat. Some are squares. Others are triangles. Some have more complex shapes-- say, octagons. But all are completely flat. They scurry about on foot or in little vehicles, in and out of their flat buildings, busy with their flat lives. Everyone on this world has width and length but no height whatsoever. These flatworlders know about left/right and forward/back.

But have no hint, not an inkling, about up/down, except for one tiny group-- the mathematicians who imagined something more. The mathematicians dream of a world in three dimensions, but it's too hard for most of the flatworlders to think about. The mathematician says, listen, it's really very easy. We all know left/right. We all know forward/back. So let's just imagine another dimension at right angles to the other two. But the flatworlders say, what are you talking about? At right angles to the other two? Everybody knows that there can only be two dimensions. Go ahead, wise guy. Show us that third dimension. Where is it?

So the mathematician draws a picture. Poor teacher. Nobody listens to mathematicians. [electronic music] Every creature on flatworld sees its fellows as merely short lines, which are the nearest sides of their oblong bodies. But the insides of a flatworlder are forever mysterious unless exposed by some terrible accident or autopsy.

And then one day, we came along. Hello? How are you? Hi. I'm a visitor from the third dimension. Hello? I feel sorry for the little guy. To him, it appears that my greeting is emanating from his own flat body, an alien voice from within. That's because nothing can come from above. There is no above in this world. A three-dimensional creature like me can only exist on flatworld where my feet touch the surface of the plane. Sorry, little guy. I know how weird this must be for you. Don't worry. You're on a perfectly safe trip to a third dimension. Nothing's going to harm you.

But this is your chance to see a whole new perspective on where you live. At first, our flatworlder can make no sense of what is happening. It's utterly outside the realm of flatworld experience. But eventually, he realizes that he's viewing flatworld from a totally new vantage point-- above. Now, he can see into closed rooms. He can see into his flat fellows. This unprecedented three-dimensional view of his two-dimensional universe is devastating. Traveling to another dimension provides as an incidental benefit a kind of X-ray vision. Just as the flat world houses can have no roofs, their inhabitants can have no sky, because that sky could only exist in a third dimension.

Little guy has suffered enough. I'm going to put him down. From the point of view of its spouse, this flatworlder has distressingly disappeared then unaccountably materialized from out of nowhere. [ominous music]