Monthly Archives: September 2014

Flatland and Extra Dimensions

What would life be like if you lived in two dimensions instead of three?

Back when I posted about popular science books for non-scientists, one of the suggestions I got after the fact was Flatland: A Romance of Many Dimensions, the 19th century classic by Edwin A. Abbott. Which is absolutely worth reading, and a great example of what I love in science writing (or science fiction): an idea that makes you change your whole perspective on the world and reimagine it from a different point of view.

The idea behind Flatland is this: what would it be like if the world we inhabited were flat instead of 3D? You can imagine it as living within a piece of paper, or on the surface of a table. The notion of up and down would be meaningless; we’d only have left and right, and front and back. So we’d be moving in two dimensions rather than three, and we’d also perceive everything around us to have only two dimensions. There wouldn’t be any going over a fence, or peeking under a door. If a thing blocked your way, it would block it completely, and everything behind it would be completely invisible. Of course, you wouldn’t be able to pass through things in Flatland, the same way you can’t in the real world. So if a person stopped directly in front of you, you’d have to pass to either side, or not at all.

There’s a lot of social commentary in Flatland as well, satire aimed at Victorian England that comments on gender divisions, class hierarchies, and dogmatism against new ideas. It’s worth a full read for that, though its examination of spatial dimensions is what’s kept it famous.

Life in Flatland may seem like an academic abstraction. But actually, while our world is three-dimensional, there are some things in it which effectively have only two dimensions, especially in the world of nanoscience. The touted wonder material graphene is effectively two-dimensional, because in the third dimension it’s only one atom thick. That means that electrons moving through graphene are effectively in a two-dimensional environment, a Flatland, and can’t use the third dimension to go around each other. More two-dimensional materials are being discovered every day, and taking one dimension of a material to the nanoscale while leaving the others large changes the physical laws in that material significantly!

And what if there were more dimensions to the world? What if instead of three dimensions to space, there were a fourth, or a fifth? In that case, life here in three dimensions would seem like Flatland, without the fourth dimension to move through. Some physicists studying string theory think there may in fact be additional spatial dimensions, but that they must be curled up within the three we know in order to be undetectable.

So the idea of Flatland, a world where there are only two dimensions instead of the usual three, isn’t just a science fiction classic, it’s also a valuable thought experiment that ties into both nanoscience and string theory!

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