Continuity does not rule out fresh approaches to fresh situations.
We were eyeball-to-eyeball and the other fellow just blinked.
While we are sleeping, two-thirds of the world is plotting to do us in.
The best way to persuade people is with your ears - by listening to them.
Physicists and astronomers see their own implications in the world being round, but to me it means that only one-third of the world is asleep at any given time and the other two-thirds is up to something.