Try to imagine what it would be like to dance, or even move around, if you were forced to keep your head, back, arms, hands, legs and feet flat against a wall. You could shuffle back and forth and wave your arms up and down, but unless your head was turned to one side, you could not even see other people living in this same very restricted world. If you wanted to pass a book to a friend behind you, you would either have to pass it over your head or bend over, very carefully, and put it on the floor, after which you could step over it so she could pick it up. Courtship would be a real challenge, even if you were next to the person you cared about. If you happened to be facing the same way, you could at least see each other without undergoing severe contortions. Getting past someone would involve going over their top or having them go over you, an athletic feat in itself. A gymnast might be able to do a cartwheel, but somersaults are out of the question.
Why would anyone want to dance under such restricted conditions? Among other things, to get a better appreciation of the range of movement in three-dimensional space that we take for granted.
Some ballet moves are essentially two-dimensional, and it is possible to imagine a classical ballet "Up Against the Wall".
Most moves however require at least some freedom to extend forward and backward, and some, like spins, are impossible to think of without three dimensions.
A good site that provides images of moves from classical ballet is at the American Ballet Theatre (the images at the right are from this site).
Questions for discussion:
- How would we be able to dance if we were constrained to lie flat on the floor, either on our stomach or on our back? How could we move around? How would we get past someone else?
- What is the difference between ice dancing and individual or pairs skating? Is one more three-dimensional than the other?
- What about water ballet? What is the dimensionality there?
- What about "Egyptian hieroglyphic dancing", where dancers must keep their backs to the wall, but with head turned to the side, and feet against the wall pointed in the same direction? What kinds of movement are available under these limitations?
- What is the dimensionality of line dancing or square dancing?
- Find other examples of classical ballet steps and classify them according to whether they can be done "up against the wall" or necessarily in three-dimensional space.
Mathematics Awareness Month is sponsored each year by the Joint Policy Board for Mathematics to recognize the importance of mathematics through written materials and an accompanying poster that highlight mathematical developments and applications in a particular area.