"Work by Strominger and Witten showed that the masses of the particles in each family depend upon... the way in which the boundaries of the various multidimensional holes in the Calabi-Yau shape intersect and overlap with one another. ...as strings vibrate through the extra curled-up dimensions, the precise arrangement of the various holes and the way in which the Calabi-Yau shape folds around them has a direct impact on the possible resonant patterns of vibration. ...as with the number of families, string theory can provide us with a framework for answering questions—such as why the electron and other particles have the masses they do—on which previous theories are completely silent. ...carrying through with such calculations requires that we know which Calabi-Yau space to take for the extra dimensions."