Topology Change Without Topology Change
If the surface being explored is flexible or elastic, the way the ball is used may affect the reported topology. If the ball is forced into a wormhole mouth that is slightly too small, and the ball and/or throat distorts to allow the ball through, then in the ball's description of the surface, a "new" wormhole connection has suddenly appeared and disappeared again, and the connectivity of the surface has fluctuated unexpectedly.
In this case, no real geometry-change occurs in the deduced shape of the underlying metric – the process identified and "caught" a wormhole candidate (getting the ball wedged in the throat), then modified the curvature of the metric over time, forcing the throat to inflate to dimensions that allowed it to be traversed.
Read more about this topic: Rolling Ball Argument
Famous quotes containing the word change:
“How vigilant we are! determined not to live by faith if we can avoid it; all the day long on the alert, at night we unwillingly say our prayers and commit ourselves to uncertainties. So thoroughly and sincerely are we compelled to live, reverencing our life, and denying the possibility of change. This is the only way, we say; but there are as many ways as there can be drawn radii from one centre. All change is a miracle to contemplate; but it is a miracle which is taking place every instant.”
—Henry David Thoreau (1817–1862)