An engineer, a mathematician and a physicist walk into a universe. How many dimensions do they find?
The engineer whips out a protractor and straightedge. That’s easy, she says. With her instruments she demonstrates the trio of directions at right angles to each other: length, width and height. “Three,” she reports.
The mathematician gets out his notepad and creates a list of regular, symmetric geometric shapes with perpendicular sides. Squares have four linear edges, he notes. Cubes have six square sides. By extrapolation, hypercubes have eight cubic sides. Continuing the pattern, he realizes that he could keep going forever. “Infinity,” he says.
Credit: Sven Geier/Flickr, under a Creative Commons license.
Finally it is the physicist’s turn. She gazes at the stars and carefully records their behavior. She determines that they attract each other through gravity, which drops off as the square of their mutual distances—an indication, she thinks, of three dimensions. However, once she derives the equation for how their light moves through space, she finds that it is best expressed in four dimensions. Then, after much thought, she tries to think of ways to describe gravity and light in a common theory, which seems to require at least ten ...