Imagine little flat people living on the surface of a piece of paper. Just the surface: their world is not even as thick as the paper, with no vertical dimension at all. Stick a pencil through the paper and all they would see is a circle, a two-dimensional cross section. Fold the paper or roll it up, and they wouldn't know the difference.

Now you're ready for brane-world theory, which proposes that our three-dimensional universe lies inside higher spatial dimensions, and we are no more aware of them than those flat people are of our third dimension. Since a membrane separating two spaces is a handy example of a two-dimensional object in three-dimensional space, theorists started referring to a plane as a 2-brane. By analogy, we live in a 3-brane. (Although we have four dimensions if you count time, as physicists do.)

Brane-world theory is a subset of string theory, which proposes that quarks, electrons and other elementary particles are not really tiny spheres, but actually tiny strings. They don't look like strings to us because we see only three dimensions, and strings exist in many more -- 10 or maybe 11. We're just seeing a three-dimensional cross section.

The good news about string theory is that it finally reconciles quantum mechanics with Einsteinian relativity. The bad news is that "there are an infinite number of solutions in string theory," according to S.H. Henry Tye, Cornell professor of physics, who himself offers a 10-dimensional version: three spatial dimensions, one of time, and six more that we can't see. Since the theories can make predictions about what happened at the birth of the universe, recent data from NASA's Wilkinson Microwave Anisotropy Probe (WMAP) satellite on the cosmic microwave background -- radiation left over from a short time after the big bang -- has narrowed the field a bit. So far, Tye's theory still fits.

The extra dimensions are rolled up or "compactified," and explaining this gets a little tricky. It's not, Tye explains, that our three dimensions are rolled up inside higher ones; it's the higher dimensions that are rolled up. Suppose Flatland has a third dimension, but it's compact. If a flat person somehow knew that the third dimension existed and tried to throw a ball -- rather, a circle -- "up," it would loop around through the plane and come back up to where it started so fast that it would seem not to have moved.

In brane-world theory, the ends of strings are anchored in our brane, so the particles we see can only move within the brane. But the particles that carry the gravitational force, known as gravitons, are closed strings -- little Cheerios -- and can "leak" out of the brane. This explains why gravity is much weaker than the electromagnetic force and the strong and weak nuclear forces. It also offers a possible explanation for the "dark matter" that astronomers need to explain why the mass of the universe doesn't agree with the observed objects. Dark matter could be in an adjacent brane, with its gravitons leaking into ours.

In some versions of string theory, the extra dimensions are too small to measure. But some of them, Tye says, might be as "large" as a tenth of a millimeter, "but probably much smaller." Laboratory experiments are under way to try to detect gravity and other phenomena at such tiny distances, but it will be very difficult, Tye believes. More likely tests, he says, will come from additional data on the cosmic background radiation, Laser Interferometer Gravitational-Wave Observatory (LIGO) experiments to detect gravity waves, studies of gravitational lensing of light from distant objects and proton-proton collisions in the Large Hadron Collider being built at the European Laboratory for Particle Physics (CERN) in Geneva, Switzerland.

In 1998 Tye and Gia Dvali of Harvard extended brane-world theory to offer an explanation for the expansion of the universe different from the idea that a point source spontaneously emerged out of the cosmic vacuum. Called "brane inflation," the theory proposes that two adjacent branes, each itself inflating, came together and annihilated, as an electron and positron would do, and the resulting tremendous release of energy created our universe and drove it to expand.

And where did those branes come from? "That's a whole other story," Tye says.