Consider a 10 D spacetime which can be written as $E^1 \times X \times E^3 = Z\times E^3$ where $E^1$ is time, $X$ is the 6D (Calabi-Yau) space of extra dimensions, and $E^3$ are the 3 large spacial dimensions.

In his new book, Penrose claims that due to intrinsic perturbations of $X$ and extrinsic perturbations of how $X$ is embeded in $Z$ (that can lead away from the family of Calabi-Yau spaces!), the spacetime $Z$ would in accordance with the corresponding Einstein vacuum equations $^7G = 0$ evolve into a singular spacetime $Z^*$ due to his and Hawking's singularity theorems and if $^7G$ satisfies the strong energy condition.

Can somebody roughly outline the technical details of this argument and explain why this is not a serious issue for string theory?