Do you ever wonder if there’s something else out there – another world, a world different to our own, something bigger than this? As much as this may sound like the sort of ‘transcendental universe’ you might discuss in one of the more exciting R.E. lesson, in maths it is a real possibility.
Recently, I’ve been dipping in and out of Martin Gardner’s Colossal Book of Mathematics. If this book doesn’t live up to its title, I don’t know what does. Weighing roughly the same as a small elephant, it covers topics from recreational mathematics but also from more advanced areas , such as the concept of hyperspace. See the Resources section of this blog for a more detailed review.
When you start learning about shapes, you learn about the first three dimensions: 1D is limited to straight lines, 2D is flat, and 3D is made up of points in all three directions.
It’s perfectly reasonable to imagine, then, that shapes can extend into a fourth dimension. But how would this look? Can we even picture it?
As beings limited to a 3D world, we cannot ‘see’ the fourth dimension. We can, however, envisage it using Cartesian coordinates just like on a normal graph. To represent a 3-space (3D) shape, we add a third coordinate to the x-y graph: (x,y,z). To represent a 4-space (4D) shape, we simply add a fourth coordinate to this: (w,x,y,z).
Gardener suggests that, just as we, as humans, live on the 2D surface of a 3D sphere, the universe as we know it could well be existing on the 3D surface of a 4D sphere: a hypersphere.
Gardner introduces this concept in the form of an imaginary religion, and yet it is a very real idea. It explains an awful lot of those religion vs science questions that we are struggling to answer, and is something I am prepared, for the moment at least, to believe in.