Basic spatial dimension

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What is a dimension, and how many are there?

As you've probably noticed, we live in a world defined by three spatial dimensions and one dimension of time. In other words, it only takes three numbers to pinpoint your physical location at any given moment. On Earth, these coordinates break down to longitude, latitude and altitude representing the dimensions of length, width and height (or depth). Slap a time stamp on those coordinates, and you're pinpointed in time as well.

To strip that down even more, a one-dimensional world would be like a single bead on a measured thread. You can slide the bead forward and you can slide the bead backward, but you only need one number to figure out its exact location on the string: length. Where's the bead? It's at the 6-inch (15-centimeter) mark.

Now let's upgrade to a two-dimensional world. This is essentially a flat map, like the playing field in games such as Battleship or chess. You just need length and width to determine location. In Battleship, all you have to do is say "E5," and you know the location is a convergence of the horizontal "E" line and the vertical "5" line.

Now let's add one more dimension. Our world factors height (depth) into the equation .While locating a submarine's exact location in Battleship only requires two numbers, a real-life submarine would demand a third coordinate of depth. Sure, it might be charging along on the surface, but it might also be hiding 800 feet (244 meters) beneath the waves. Which will it be?

Could there be a fourth spatial dimension? Well, that's a tricky question because we currently can't perceive or measure anything beyond the dimensions of length, width and height. Just as three numbers are required to pinpoint a location in a three-dimensional world, a four-dimensional world would require four.

At this very moment, you're likely positioned at a particular longitude, latitude and altitude. Walk a little to your left, and you'll alter your longitude or latitude or both. Stand on a chair in the exact same spot, and you'll alter your altitude. Here's where it gets hard: Can you move from your current location without altering your longitude, latitude or altitude? You can't, because there's not a fourth spatial dimension for us to move through.

But the fact that we can't move through a fourth spatial dimension or perceive one doesn't necessarily rule out its existence. In 1919, mathematician Theodor Kaluza theorized that a fourth spatial dimension might link general relativity and electromagnetic theory [source: Groleau]. But where would it go? Theoretical physicist Oskar Klein later revised the theory, proposing that the fourth dimension was merely curled up, while the other three spatial dimensions are extended. In other words, the fourth dimension is there, only it's rolled up and unseen, a little like a fully retracted tape measure. Furthermore, it would mean that every point in our three-dimensional world would have an additional fourth spatial dimension rolled away inside it.

String theorists, however, need a slightly more complicated vision to empower their superstring theories about the cosmos. In fact, it's quite easy to assume they're showing off a bit in proposing 10 or 11 dimensions including time.

Wait, don't let that blow your mind just yet. One way of envisioning this is to imagine that each point of our 3-D world contains not a retracted tape measure, but a curled-up, six-dimensional geometric shape. One such example is a Calabi-Yau shape, which looks a bit like a cross between a mollusk, an M.C. Escher drawing and a "Star Trek" holiday ornament [source: Bryant].

Think of it this way: A concrete wall looks solid and firm from a distance. Move in closer, however, and you'll see the dimples and holes that mark its surface. Move in even closer, and you'd see that it's made up of molecules and atoms. Or consider a cable: From a distance it appears to be a single, thick strand. Get right next to it, and you'll find that it's woven from countless strands. There's always greater complexity than meets the eye, and this hidden complexity may well conceal all those tiny, rolled-up dimensions.

Yet, we can only remain certain of our three spatial dimensions and one of time. If other dimensions await us, they're beyond our limited perception -- for now.

Explore the links on the next page to learn even more about the universe.

Lots More Information

Sources

  • Bryant, Jeff. "Higher Dimensions from String Theory." Wolfram Research. (Aug. 26, 2010)http://members.wolfram.com/jeffb/visualization/stringtheory.shtml
  • Groleau, Rick. "Imagining Other Dimensions." The Elegant Universe. July 2003. (Aug. 26, 2010)http://www.pbs.org/wgbh/nova/elegant/dimensions.html
  • Kornreich, Dave. "What is a dimension?" Ask a Scientist. January 1999. (Aug. 26, 2010)http://curious.astro.cornell.edu/question.php?number=4
  • Vogt, Nicole. "Astronomy 110G: Introduction to Astronomy: The Expansion of the Universe." New Mexico State University. 2010. (Aug. 26, 2010)http://astronomy.nmsu.edu/nicole/teaching/ASTR110/lectures/lecture28/slide01.html