Thursday, February 23, 2006

QotD: What reason do you have to believe the earth is flat?

Thought experiment: envision a one-dimensional universe. It is, quite simply, a point. We may represent it with a dot -> . However, this is only a representation, because in reality, the point is infinitely thin, viewed from any direction. It is, in fact, flat.

Now envision a two-dimensional universe. This universe includes all the points upon a plane. Think of a sheet of paper, and anything you can draw on it. Length, width, but no height. Flat. If you’ve ever visited Flatland* you know that folks there can comprehend circles (if it’s something they can walk around without turning any corners, it’s a circle (or an ovoid, etc., but let's not get into that--you get the idea), but they can't comprehend spheres, because they see only two dimensions, not three. If a sphere fell through their universe, they would see first a point, then an increasingly large circle, until the sphere reached its full circumference, whereupon the circle would grow smaller until it became a dot and disappeared. From our perspective, they and their world are flat.

Now consider our own three-dimensional universe. We see length, width and height. So we see spheres. But consider the fourth-dimensional universe equivalent of a sphere. Let’s call it a phwat. Should a phwat pass through our universe, we would see, by interpolation from our two-dimensional universe thought experiment, first a tiny sphere that would pop into sight, grow increasingly large until the phwat reached its circumference, then an increasingly smaller sphere until it popped out of existence again. So did we see the phwat? Not really. We saw only its footprint.

So what does a phwat actually look like? Who knows? We can’t see that extra dimension. But the important thing here is to consider what those four-dimensional universe denizens see when they look at us. We look…well, flat. In fact, we’d look flat to any creature from any universe with a higher number of dimensions than our own.

So how many dimensions are there? Mathematicians have proven us up into double digits thus far. This means that the majority of universes in our multi-dimensional universe see us as flat. Majority rules, folks. Our world is flat.

What's that? TIME is the fourth dimension? Say it is. Like our friends in Flatland contemplating our sphere, we can only experience the totality by interpolation. We see things happening in consecutive order. Check it out and you'll have to agree that acting as though time is something that goes forward (unless we're playing with film) is, well, a pretty flat attitude.


*Edwin A. Abbott’s classic tale of interdimensional experience: “Flatland: A Romance of Many Dimensions”

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