Fourth Dimension

Flatlanders cannot visualize a cube, but they can conceptualize a three-dimensional cube by unraveling it. To a Flatlander, a cube, when unfolded, resembles a cross, consisting of six squares. Similarly, we cannot visualize a four-dimensional Hypercube, but if we unfold it we have a series of cubes arranged in a cross like tesseract. Although the cubes of a tesseract appear immobile, a four-dimensional person can "wrap up" the cubes into a Hypercube.

In Christus Hypercubus, Salvador Dali depicted Christ as being crucified on a tesseract, an unraveled hypercube. (The Metropolitan Museum of Art. Gift of Chester Dale, Collection, 1955. © 1993. Ars, New York/Demart Pro Arte, Geneva)

Cubism was heavily influenced by the fourth dimension. For example, it tried to view reality through the eyes of a fourth-dimensional person. Such a being, looking at a human face, would see all angles simultaneously. Hence, both eyes would be seen at once by a fourth-dimensional being, as in Picasso's painting Portrait of Dora Maar. (Giraudon/Art Resource. ® 1993. Ars, New York/ Spadem, Paris)

The shadow of a hyper-cube is a cube within a cube. If the hypercube is rotated in four dimensions, the cubes execute motions that appear impossible to our three-dimensional brains.

Source : Michio Kaku's Parallel Worlds

Fifth Dimension

If we lived in a hyperdoughnut, we would see an infinite succession of ourselves repeated in front of us, to the back of us, and to our sides. This is because there are two ways that light can travel around the doughnut. If we hold hands with the people to our sides, we are actually holding our own hands; that is, our arms are actually encircling the doughnut.

If a rocket disappears off the right side of a video-game screen, it re-emerges on the left. If it disappears at the top, it re-emerges at the bottom. Let us now wrap the screen so that identical points match. We first match the top and bottom points by wrapping up the screen. Then we match the points on the left-and right-hand sides by rolling up the screen like a tube. In this way, we can show that a video-game screen has the topology of a doughnut.

Source : Michio Kaku's Parallel Worlds

Worm Holes

If we insert our hands into the window from two different directions, then it appears as though our hands have disappeared. We have a body, but no hands. In the alternative universe, two hands have emerged from either side of the window but they are not attached to a body.

In this purely hypothetical example, a "window" or wormhole has opened up in our universe. If we look into the window from one direction, we see one dinosaur. If we look into the other side of the window, we see another dinosaur. As seen from the other universe, a window has opened up between the two dinosaurs. Inside the window, the dinosaurs see a strange small animal (us).

Source : Michio Kaku's Parallel Worlds