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MatheMUSEments
Tesseracts: Cubes Get Hyper
By Ivars Peterson
Muse, September 2000, p. 18.
Madeleine L'Engle, who wrote these words in A
Wrinkle in Time, used tesseract to mean a shortcut
through space and time. In her story, space-time wrinkles,
or folds onto itself, creating new paths that allow characters to
tesser, or travel from one end of the galaxy to the
other in an instant.
Mathematicians also use the word tesseract,
but they mean something different. A tesseract is another name
for a four-dimensional cube, or a hypercube.
Here's one way to picture what this strange
object might look like. You can start by imagining a point
floating in space. A mathematical point has no length or width.
Mathematicians say the point has no dimension. Moving the point
along a straught path to a new position traces out a line. That
line is a one-dimensional object. Shifting the line at right
angles to its length traces out a square, and a square is a two-dimensional
object. Moving the square at right angles to its flat surface
traces out a cube—a three-dimensional object.
Here's the mind-boggling part. You have to try to
imagine what would happen if you could move the cube in a new,
fourth dimension at right angles to the three you've already used.
Any drawing or model you might make of the resulting object would
look horribly distorted. But you can still get an idea of what a
tesseract would look like and even sometimes "see" it
in flashes.
How might you recognize a tesseract if you ever
encountered one in your multidimensional travels? Well, in our
three-dimensional world, it might look something like a large
cube that seemed to be spitting out a smaller one.
Even though L'Engle's concept of a tesseract is
different, her book has inspired many readers to think more
deeply about time and space and mathematics.
You can learn more about dimensions,
tesseracts, and even Madeleine L'Engle at mathforum.com/mam/00/612/index.html.
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