How to conceptualise the 11 dimensions of space

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

19 April 2009

George Kimathi asks two questions; one easy, the other a little involving. First, he wants to know if it possible to walk around the continent of Africa. The quick answer is no. The reason is that there are too many obstacles along the way. For example, many mouths of rivers do not have bridges.

In addition, it is difficult to decide where the coast line ends as one walks “around the continent”. Suppose you start the journey in Mombasa and you walk northwards. When you reach the mouth of River Sabaki, how far inland (along the river bank) will you go, before crossing to the other side?

The second question is about the so-called 11 dimensions of the universe. He writes: “Astrophysics says that universe has 11 dimensions i.e. one of time and the other ten of space. I only know about 3D. So which are these 11D?”

First of all, three dimensions are a recognition of the fact that you can get to any point from any where by moving in a combination of three basic directions, namely, left/right, up/down and forward/backward. Indeed, every place on Earth is defined by three coordinates: latitude (north-south position), longitude (east-west position) and altitude (height or elevation).

The idea of extra dimensions is developed progressively as follows. We start with a point; it has no size at all therefore it has no dimensions. Then we move to two points; they can be joined by one line segment thereby presenting a length that can be measured. This is a one-dimensional space enclosed by the two points.

Now consider two lines joined together and pointing in different directions. They present two measurable lengths, but the do not enclose any space. To attain an enclosure, we need a third line to form a triangle.

A triangle is the simplest enclosed two-dimensional space possible. However, we can make an infinite number of other two-dimensional spaces – squares (four lines), pentagons (five sides), hexagons etc.

If we put two triangles in different directions, we will have three distinct measurable lengths. But again, to enclose some three-dimensional space, we need at least four triangles to make the shape of a milk tetra-pack. We may also use six squares to make a cubic enclosure, and so on.

However, unlike the infinite number of two-dimensional spaces, we can only make only five regular three-dimensional enclosures. “Regular” here means that the faces are made of equilateral and equiangular shapes; e.g., the square sides of a cube.

To get four-dimensional space, we mould a shape that can be enclosed by regular three-dimensional solids. In the case of five dimensions, we need make spaces that are enclosed by four-dimensional shapes…and so on…therefore; ten-dimensional space is enclosed by nine-dimensional shapes.

Theoretically, any number of dimensions can be created in this manner but physicists have stopped at ten; time being the eleventh. Why stop at ten? Because this is the number required to explain the existence of all the known elementary particles – electrons and the like.

Luckily, the seven extra dimensions can only exist in the atomic scale of space. In “our” universe, there can only be three spatial dimensions and they are enough to explain all the laws of nature that we observe “out here”.