If the Universe is expanding, what is it expanding into? Our explorations have already answered this question too. Every universe expands into a higher dimension that those that it occupies.

• The one dimensional universe is expanding into two dimensions. A line (one dimensional) becomes a circle (two dimensional). As we pull on the rubber band, it expands in size at all points along its length.

• The two dimensional universe is expanding into three dimensions. A plane (two dimensional) becomes the surface of a sphere (three dimensional). As we inflate the balloon, all points on the surface move away from each other.

• The three dimensional universe is expanding into four dimensions. A sphere (three dimensional) becomes ... ah, if only we could properly visualize four dimensions, we could finish this sentence!

In this figure, x and y represent distances and t represents time. Like points inked on the surface of an inflating balloon, galaxies move away from each other over time as the universe expands in size.