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DEGREES OF FREEDOM
5
Figure 1.1 A fly in a box is essentially confined to a point. It has zero degrees of freedom
and lives its (depressing) life in a 0-D world. (Drawing by Brian Mansfield.)
"Yes, I understand." Sally's hand darts out at the fly and captures it. You
never knew she could move so fast. "This fly has three different directions
it can travel in the room. Now that it is in my hand, it has zero
degrees of freedom. I'm holding my hand very still. The fly can't move.
It's just stuck at a point in space. It would be the same if I placed it in a
tiny box. Now, if I stick the fly in a tube where it can only move back and
forth in one direction, then the fly has one degree of freedom" (Fig. 1.1
and 1.2).
"Correct! And if you were to pull off its wings—"
"Sadist."
"—and let it crawl around on a plane, it would have two degrees of
freedom. Even if the surface is curved, it still lives in a 2-D world with
two degrees of freedom because its movement can be described as combinations
of two directions of motion: forward/backward and left/right.
Since it can't fly, it can't leave the surface of the paper" (Fig. 1.3).
"The surface is a curved 3-D object, but the fly's motion, confined to
the surface, is essentially a 2-D motion."