In 1919, Theodor Kaluza suggested that perhaps the universe has more than three spacial dimensions, and that the extras are curled up so tightly that they are undetectable. Starting with the assumption that there is one extra spacial dimension, he formulated several equations, most very much like Einstein's originals. There were others, however, that were totally different. To his surprise, they matched the equations written down in the 1800s by Maxwell for the electromagnetic force! Problems were eventually found with his idea. For example, any time electrons were included in the theory, their mass and charge were predicted to be very different than what they have been measured experimentally. Interest in the theory faded. In 1926, Oskar Klein added ideas to Kaluza's theory from the field of quantum mechanics and calculated that the curled up dimensions might be as small as the Planck length. Ever since, the idea of extra curled-up dimension has been called Kaluza-Klein theory.

String theory predicts six extra spacial dimensions. The ways in which these dimensions can be curled up are known as Calabi-Yau spaces or Calabi-Yau shapes. As of yet, we don't know which of these possible shapes is the real way which the dimensions are curled up. If string theory is correct, at every point in space the extra six dimensions are curled up in one of these Calabi-Yau shapes. The Calabi-Yau shape determines the properties of the universe. For example, the number of holes in a Calabi-Yau shape is equal to the number of particle families in the universe. Thus, because there are three particle families in our universe, our Calabi-Yau shape must have three holes.