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.

Are you?

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