Space is indeed curved — in four dimensions. Many people think the fourth dimension is simply time, and for some astronomical equations, it is. Einstein used time as a fourth dimension to describe a coordinate system called space-time. This is the stage on which planets, stars, galaxies — all matter in the universe — act their gravitational roles. In Einstein’s Theories of Relativity, time helps us understand the three-dimensional experience of gravity.
But time is not a true spatial dimension like the three we’re familiar with. Unlike width, length, and height, we only know time to move in one direction: past to present to future. In this way, time merely serves as a yardstick for our personal experiences and our laws of physics. Some theoretical equations incorporate many other “dimensions” — velocity, temperature, or density, for example.
To assist you in imagining space curved in four dimensions, pay a visit to Flatland, a two-dimensional world full of square, triangular, and circular beings. If it helps, draw Flatland and its residents on a sheet of paper and place it flat on a table in front of you.
The laws of 2D space as understood by 2D beings would restrict light (and everything else) from moving up and down; in fact, there would be no up or down. So as a three-dimensional being, your actions would violate the Flatlanders’ laws of physics. Place your fingertips on Flatland — you appear to them in many places at once. Say “Hello” to Flatland — your voice is also omnipresent. And while Flatlanders cannot see beyond the boundaries of their world, to you they are nothing more than hollow geometrical shapes.
Regardless of the number of dimensions that describe a space, the curvature of that space, by definition, implies the existence of at least one more. In other words, an additional dimension must exist into which the other dimensions can be curved. You can curve Flatland in your three-dimensional reality by rolling the piece of paper into a tube, folding it into a paper airplane, or just crumpling it into a wad. Doing so would not be immediately apparent to Flatlanders, because light still travels in straight lines within their 2D space. They might experience some interesting phenomena, though – triangular residents might find that their interior angles no longer add up to 180 degrees, and parallel lines everywhere might begin to intersect.
If a 4D being decides to “crumple” our 3D space, like the Flatlanders, you wouldn’t notice anything right away, either. You might notice some unusual phenomena, like walking to your mailbox and ending up in Mongolia. Scientists believe, however, that our space is smoothly curved — more like a ball than a wad of paper — and thus the effects are only noticeable on cosmological scales. As 3D beings, we experience just the “surface” of the 4D ball, just as Flatlanders experience only two dimensions of their space that you can curve into three dimensions.