Space might not be three-dimensional. How many dimensions it might have is really up to us. For the convenience of our mathematical analogies AKA theories it is taken to have from four to 26 dimensions. The sphere is a topological entity of which a convenient mental image might be earth, but that is only two-dimensional so we would have to extend our imagination to add a third and a fourth or more dimension. Four dimensions and eight dimensions have particularly rich algebras so most theoretical work is done in those numbers. In spite of popular ideas of relativity, time is not one of the dimensions and is a very different animal.
If earth was a cube and you wanted measure the volume, wouldn't you need three variables instead of two? a x b x c = volume? Why only two variables (dimensions) to determine the volume of earth? Or were you using the word, dimensional in another sense?
Oh sure thing, that's what you think... Until you ride a river of space [WARNING: PDF file] over a waterfall that's plunging at the speed of light into a black hole and notice that time itself has been reoriented radially in the direction of your motion and become one with the other dimensions of space!
LOL, just kidding. As you may be able to tell, I did not fully understand this article. But I LOVED it and offer it up here for your enjoyment as well. :-)