Long before Thomas L. Friedman argued that the world was metaphorically flat thanks to the globalization of economics, there was a brilliant piece of English satire written as if the world was literally flat.
Edwin Abbott Abbott wrote FLATLAND in 1884 to make fun of a rigid social hierarchy (in the book, the number of sides you’re born with dictates what you can and can’t be within Flatland culture), but as a young child, I didn’t care about this commentary. My mind was too busy being blown away by something else: the weirdness of living in any set of dimensions other than three.
Just as Flatlanders have a hard time conceiving of a third dimension, we have a nearly-impossible time picturing four, much less eight or nine. And please, let’s leave Time out of this, we’re having a spatial discussion.
(NOTE: I’ve mentioned before that Molly has a system for holding a dozen physical dimensions in her head. I’m not sure her paper on this topic is correct, but there are smaller contributions to geometry within it. I keep promising to get that document up on the blog, and I assure you I’ll get to it, but for now… I want to talk about the shape of the universe and how hyperspace likely works.)
The most important geometric lesson from FLATLAND is an explanation of how the universe can be finite and yet have no boundary (nothing “outside” it). Imagine only knowing two dimensions while living in a world of three (you have no concept of Up or Down). The landscape around you appears perfectly flat thanks to the enormous size of the globe you reside on.
Suppose you wanted to find out what lies “beyond” this world of yours. You take off in one direction and travel for several years until… SHOCK!! you end up right back where you started! “That’s impossible,” you’d say. I went in a perfectly straight line the entire time!
Curious and a bit upset at how sore your two-dimensional legs are, you set off in a new direction. Years later, you are right back in the same place! (and you passed the same cute girl half a world away that you saw the last time around) Your family is happy to see you and they ask that you stop sneaking up from behind like that.
You try, but you can’t figure out how the world you live on can be finite, and yet there not exist some “border” beyond which something else lies.
Dear reader, we live in a universe just like that. There are dimensions beyond the three we note around us. Travel in a “straight” line in any direction in the universe, and you’ll come back to where you started (even though the galaxy you left behind will have moved on). It’s finite and yet without border.
According to several papers in The Reader, the universe also seems to be “unfolding” rather than “stretching.” This appears to be important for understanding hyperspace travel. If the universe was “stretching,” the distance between points would be getting further apart in every dimension that matters. What appears to be the case, instead, is that the universe is acquiring ripples, or folds.
In several dimensions, this makes objects appear further away, as light travels up and down these folds in a “straight” line. In other dimensions, however, objects are not much further apart than they ever were. Traveling through the folds allows one to cut across vast distances of space.
Imagine our Flatlander doesn’t live on a perfect sphere, but rather on a flattened disk, like a ball with most of its air let out. Our intrepid explorer wants to visit the girl he met twice in his travels; unfortunately, she lives on the opposite side of his planet. Thanks to his limited awareness of dimensions, he would have to travel for several years across the surface, not noticing the sharp curve at the flattened edge, in order to reach her. He wouldn’t know that he was just a few steps away if he could cut across the center.
This is how we travel. Up and down the folds of space as they present themselves as straight lines. Meanwhile, through dimensions orthogonal to all of our familiar three, we are but a few steps from anywhere. We just don’t realize it.
What kind of adventures could a person get themselves in and out of if they ever sorted this out? What could Molly’s original and insightful method for visualizing multiple dimensions mean if she was the one? I’m afraid that the answers to these questions are not even reached in her first three books… but it’s something to be aware of nonetheless.