Visualizing Calabi-Yau spaces?

[Matt R.]

OK, so essentally Calabi-Yau spaces are multi-dimensional manifolds. There is a very precise mathematical definition, but I don't understand it so I won't bother mentioning it.

In string theory, it is hypothesized that there are extra spatial dimensions that take the form of a 6-dimensional calabi-yau manifold. I think sometimes (in M-theory?) it is 7-dimensional. But I'm not exactly sure.

What I am wondering, is how do you visualize such a structure? The 2-D and 3-D renditions are very unsatisfying, because well, they are in 3-dimensions -- not 6 or 7. They look like a giant blob with ridges on it (wikipedia has a picture).

I understand that you are simply saying spacetime at its most fundamental level is described using 11 (10, 9, whatever) coordinates instead of 4. Which means that these extra dimensions we don't see are simply extra coordinates. Is it *possible* to visualize what a 10-dimensional structure would look like in a concrete way? Any way I can think of can still adequately be described in 3-dimensions (like the 3-D rendition on wikipedia). Is the "correct" way to visualize such a structure simply to realize that it is described using extra coordinates that are unseen, and thus cannot be "seen" in traditional ways (for instance, you can't "see" the fourth dimension in space-time, but you know it's there intuitively).

The more I think about it, the more I believe that these calabi-yau spaces are simply mathematical techniques to understand string theory. They don't really physically "exist" in the sense where we are even capable of visualizing them correctly.

Anyone have a unique way of picturing what a 6-dimensional structure would look like (that can't be described in a 3-D coordinate system)? Maybe I just haven't opened my mind up yet to how higher-dimensional objects "appear".