-: Hyperspace :-

Hyperspace:Home Intro Time Width Walls Bridges Rounds

Near the end of Edwin A. Abbott's novel Flatland, a Romance of Many Dimensions (1884), a curious conversation occurs between two shapes, a two-dimensional Square and a three-dimensional Sphere: ¹

Sphere. But where is the land of Four Dimensions?
Square. I know not: but doubtless my Teacher knows.
Sphere. Not I. There is no such land. The very idea of it is utterly inconceivable.
Square. Not inconceivable, my Lord, to me, and therefore still less inconceivable to my Master. Nay, I despair not that, even here, in this region of Three Dimensions, your Lordship's art may make the Fourth Dimension visible to me (71).

The Square does indeed understand the fourth dimension, because it understands Hyperspace. What we shall do, is to make some models of Third dimension. What we do, is to have the Square make the third dimension, and the Sphere look at the Results.

Hyperspace is, as Rudy Rucker says, "is right next to you, but in a direction you can't point to". For the Square, this means anything out of its space (a plane). So, the Square's Hyperspace is the third dimension.


Time is often advanced as the fourth dimension. This is incorrect. Note here that the Square and the Sphere carry out a conversation in the same time: the Square's time is the same as the Sphere's.

Of course, when we visualise the fourth dimension, we set a clock ticking in that space, too. So the time of fourth dimension is hardly time: it becomes four dimensions and time.

If any further proof is needed, we note that the whole history of Square's space-time is laid out before the Sphere. There is no time for the Square, this has become space.

Kurt Vonnegut's Slaughterhouse Five explores beings who could roam over their space-time, reliving any motion of it in much the same way we can rewind a video and replay any slice. Such beings saw themselves as their time-lines stretching through time like threads.

It is best to think of space-time as a kind of graph-paper, for solving certian problems.


One gets a better idea of hyper-space by adding extra dimensions of width. Should we allow the Square and Sphere to share the same gravity and the same time, then they both share the same up and the same forward.

But for the Square, this is all he has: for anything else is not up or in front is in the unreachable hyperspace.

Te Sphere has an extra dimension of width. Directions of left and other left ².

Accordingly, we might suppose a fourth dimension has a full circle to pick from.

Walls and Bridges ³

The notion of Walls are to divide, while Bridges unite.

1. This paragraph and the following quote comes from Brad Ricca's paper Signifying Nothing: The Fourth Dimension in Modernist Art and Literature

2. Not that way, the other way! The joys of knowing left from right (are not mine!)

3. The idea of Walls dividing and Bridges uniting is borrowed from the John Lennon Parlephone/Apple album of the same name.

Hyperspace:Home Intro Time Width Walls Bridges Rounds

© 2003-2009 Wendy Krieger