The Expansion of the Universe

The Expansion of the Universe

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!

Representation of an expanding universe. A legend identifies the width of the figure (from side to side) as the x-axis, the depth of the figure (into and out of the page) as the y-axis, where x and y are both spatial dimensions, and the height of the figure (up and down) as the t-axis (where t represents time). At the base of the figure is a point surrounded by bright white, yellow, and red. Four straight lines rise up from the point, growing further and further apart as they ascend; at three heights a flat square is drawn between the four lines (and as the height increases, the size of the square increases). Four spiral galaxies are drawn on the square at each height. The galaxies are always the same size and have the same relative orientation, but at successive heights the distances between the galaxies increases more and more. While on the lowest square the galaxies appear quite close to each other, by the final square they are far apart from each other.

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.