**THE FABRIC of the COSMOS,****Brian Greene,**2004

```(annotated and with added

**bold highlights by Epsilon=One**)

**Chapter 12 - The World on a String**

The Shape of Hidden Dimensions

The equations of string theory actually determine more than just the number of spatial dimensions. They also determine the kinds of shapes the extra dimensions can assume.

If these ideas are right, the ultramicroscopic fabric of the cosmos is embroidered with the richest of textures.

**In the figures above, we focused on the simplest of shapes — circles, hollow spheres, solid balls — but the equations of string theory pick out a significantly more complicated class of six-dimensional shapes known as Calabi-Yau shapes or Calabi-Yau spaces. These shapes are named after two mathematicians, Eugenio Calabi and Shing-Tung Yau, who discovered them mathematically long before their relevance to string theory was realized; a rough illustration of one example is given in Figure 12.9a. Bear in mind that in this figure a two-dimensional graphic illustrates a six-dimensional object, and this results in a variety of significant distortions. Even so, the picture gives a rough sense of what these shapes look like. If the particular Calabi-Yau shape in Figure 12.9a constituted the extra six dimensions in string theory, on ultramicroscopic scales space would have the form illustrated in Figure 12.9b. As the Calabi-Yau shape would be tacked on to every point in the usual three dimensions, you and I and everyone else would right now be surrounded by and filled with these little shapes. Literally, as you walk from one place to another, your body would move through all nine dimensions, rapidly and repeatedly circumnavigating the entire shape, on average making it seem as if you weren't moving through the extra six dimensions at all.***18*If these ideas are right, the ultramicroscopic fabric of the cosmos is embroidered with the richest of textures.

**Figure 12.9: (a)**One example of a Calabi-Yau shape.

**(b)**A highly magnified portion of space with additional dimensions in the form of a tiny Calabi-Yau shape.