Years ago, while idly wandering around the fiction section of some bookshop, I came across a mad little novel called The Planiverse. It was written by Alexander Dewdney, a Canadian computer scientist, and it speculated on the nature of the beings who might inhabit a two-dimensional universe.
In the novel, Dewdney and his students are working on a theoretical model of a 2-D world. They construct it on a computer and try to figure out what might be going on as they interact with the crude little sprites they’ve created. And crude indeed the graphics are, as you’d expect for a book written in 1984, before dinosaurs roamed the Earth.
But they get a shock when, one morning, they turn up in the lab, to find that one of the little sprites isn’t doing what it should, and they quickly realise that somehow they have made contact with creatures from a real two-dimensional world. In this reality, when two people meet, one has to lie down and let the other walk over him, but society solves this by digging a hole and tying a rope across it so that groups of people can take turns passing.
The question is, of course, how do you tie a knot in a two-dimensional world?
It’s a fascinating idea and thought-provoking as well. After all, most people, including myself, would have thought that the hardest thing to imagine might be a four- or five-dimensional universe, yet when we’re removed from our familiar 3-D comfort zone, we have great difficulty envisaging a simpler reality.
Vehicles can’t have wheels. Why? Because axles don’t exist. Obvious or what?
Yes, when it’s pointed out. Interestingly, computers are possible as long as wires don’t have to cross over each other, because this can’t happen in a two-dimensional universe.
They have wars just like us, but only the two soldiers at the front can fight each other at any one time.
Throw a rope over your head and you have a balloon.
Houses have to be underground so that people can get past.
What about food? Well, nobody can have a digestive tract for fear of splitting in two.
Life isn’t easy in a 2-D world, but they get by. If there are creatures living in a four- or five-dimensional universe, do they have equal difficulty comprehending us? Who knows?
Oddly enough, the idea is no more than an extension of early undergraduate physics where everything happens in two dimensions, but yet the entire notion has a subtly subversive tinge to it. After all, if we have difficulty comprehending a construct radically simpler than our existence, how are we supposed to grasp the truly complex? How are we to contend with the nature of the universe or of existence without inventing meaningless, undefined concepts like God to explain away with magic the things we struggle to imagine, let alone understand?