Imagine what it would be like being a square, living on a flat plane surface with no knowledge of the third space dimension which we call height; and no ability to move in that direction. If a sphere were to descend from the third dimension down into your world (which is a plane), to you, it would look as if a small circle had appeared from nowhere. If the sphere were to continue its journey straight down through the plane, you would observe the circle gradually becoming larger until the sphere had moved into the position where the plane exactly bisected the sphere. Then, if the sphere were to continue this motion, the square would see the circle gradually becoming smaller again, until it would finally vanish from sight.

We can understand the reasons why such events can occur because we can understand the concept of the higher, third space dimension; but to the inhabitants of Flatland, these phenomena are truly amazing and absolutely inexplicable. Our enlightened square, though thoroughly familiar with the concept of two-dimensional space, has a delightfully tough time explaining it to the King of Lineland42; a one dimensional creature who has no concept of the second dimension.

The King: Exhibit to me, if you please, this motion from left to right.

Square: Nay, that I cannot do, unless you could step out of your line altogether.

The King: Out of my line? Do you mean out of the world? Out of Space?

Square: Well, yes. Out of your world. Out of your space, For your space is not the true space. True space is a plane; but your space is only a line.

There are significant parallels when we come to consider the possible existence of dimensions higher than out own. For example, we might consider what amazing feats a being from four-dimensional space would be capable of accomplishing within our three-dimensional space. This idea is not simply science-fiction, because the existence of a higher dimension appears to be inferred by the Big Bang theory itself. If our four dimensions - three of space and one of time - came into existence at the instant of the Big Bang, as the scientists suggest, then ‘we need [at least] five dimensions to explain where the Big Bang took place43’(my italics).

In Hawkings theory, his imaginary-time dimension attempts to avoid the problem of infinity; the infinite density, or singularity, which should occur at a black hole. In classic theory, there would be infinite density and infinite curvature of space-time; ‘all the known laws of science would break down at such a point44’ - infinity is a particularly irksome quantity for physicists. In Hawking’s universe, time, with its imaginary component, has no beginning and space has no boundaries45. But this idea, as elegant a proposal as it may be, does not provide us with a complete or satisfactory explanation of the origin of the universe. We must always be forced to consider how the set-up, no matter how complex it may be, came into being.