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DEGREES OF FREEDOM
7
Figure 1.3 A fly that walks on a paper, even a curved piece of paper, has two
degrees of freedom and lives in a 2-D world. (Drawing by Brian Mansfield.)
You nod. "Excellent. At each location in my office you could specify
different distances in a fourth spatial direction that currently we can't see.
It's very hard to imagine such a dimension, just as it would be hard for
creatures confined to a plane, and who can only look along the plane, to
imagine a 3-D world. Tomorrow I want to do some more reasoning from
analogy, because the best way for 3-D creatures to understand the fourth
dimension is to imagine how 2-D creatures would understand our
world."
Sally taps her hand on your desk. "But how does this explain my
encounter at Cherbourg?"
"We'll get to that. By the time your lessons are finished, we're going to
see some horrifying stuff. ..." You reach for a seemingly empty jar on the
shelf and hold it in front of Sally's sparkling eyes.
She examines the jar cap, which has been sealed securely to the jar
using epoxy. "There's nothing in here."
Your grin widens. "Not yet."
She shakes her head. "You scare me sometimes."