Dimensions

Well, there's a number of ways to think about what dimensions are. I hope we all know where three dimensions are, which you can say are left, right forward, backward, up, down. And if you think about it three we say there are three dimensions of space. And sometimes we need three coordinates to locate some objects in space. So, you can say longitude, latitude and altitude. So if there were more dimensions, you would need more coordinates. Now, of course, for whatever reason, we are not physiologically designed to observe those dimensions, but that doesn't mean they don't exist. One way of thinking about it is, maybe the best way of thinking about it is the way that someone named Edwin Abbott did it in the late 19th century in a book called Flatland. And he said suppose there were two-dimensional creatures living in a two-dimensional universe. They would have the same trouble conceptualizing three dimensions that we have when we try to conceptualize more than three, such as four. And so, he asked questions like, what would observers in this two-dimensional universe see, say, if a three-dimensional object like a sphere passed through the universe? And what this Flatland universe would see would be a series of disks that grow in size and then decreased in size. In the same way that we can certainly think about a two-dimensional world inside a three-dimensional world, it could be that we observe three dimensions but really there are more. And if a hypersphere says a four-dimensional sphere passed through our universe, we would see a series of spheres that grew in size and then decreased in size. The fact that we don't observe those extra dimensions doesn't mean they don't exist. And they are hard to conceptualize. They certainly are hard to visualize. But we can think about them mathematically and conceptually without too much trouble.