Just as extra dimensions are curled up, it is possible that one or more of our familiar three dimensions actually curls back around on itself. In this case, if you began traveling in one direction, you would eventually end up right back where you started.

Imagine a universe with two spacial dimensions, one curled up and the other extended like a straw. There are two kinds of strings in this universe. The first is the "unwrapped" version that we are familiar with and the other is the "wrapped" version which is wound around the curled dimension one or more times, as in the picture. These strings can move in two ways, by vibrating or sliding along the dimension. These two kinds of movement are called ordinary and uniform vibrations. The energy of the string depends on two things: how the string is wound (giving its length) and its vibration. The larger the radius of the dimension and the more times it is wound, the longer the string must be. This gives the string its mass, or its energy. The energy contribution from the winding is directly proportional to the radius. Oppositely, as the string becomes smaller, quantum claustrophobia from the uncertainty principle causes it to vibrate frantically, increasing its energy. The vibrational energy contribution is inversely proportional to the radius. Therefore, for a string wrapped around a dimension with a large radius, its energy from winding is equal to that of the energy from vibration of a dimension with a certain smaller radius, and the larger's energy from vibrations is equal to that of the smaller's energy from winding. In this way it was shown that for a curled dimension with radius R, a dimension with radius 1/R would lead to a universe with particles of the same charges and masses (with R being a multiple of the Planck length). This simplified universe can be extended to reach the same conclusion about our universe. If our familiar dimensions are circular, then a universe with radii of 10 times the Planck length would have exactly the same properties as ours! In principle, if we could measure the length of the universe using a wound, heavy, high-energy probe currently unreachable with our technology, this is about the length we would measure. Instead we take the "easy" route and use unwound photons (light) to measure distances with our telescopes, measuring the extremely large distance of ten trillion trillion trillion trillion trillion (10) times the Planck length. Using light to measure, our universe is large and expanding. Using a high energy probe, it is small and shrinking.

You may remember that measuring lengths smaller than Planck length is meaningless, so why are we even discussing it? As the length being measured reaches R=1 (Planck length), the wound strings actually becomes lighter - easier to use - than the unwound strings. As long as you measure using the easy way, you would never encounter a length smaller than Planck length. If you were to employ the "hard" method to continue to probe smaller than Planck length, the concept of distance would change, because as we said earlier, R is the same as 1/R. While you would be measuring 1/R, the physics would still be the same as if you were measuring R, which is what matters.