Probably not correct, but here's the first thing that came to mind:
A piece of music
...time is divided
A piece of music is divided into measures based on the time signature
...double or half it...
Could refer to tempo (increasing or decreasing the speed) or the length of different notes (whole notes, half notes, quarter notes, etc), or even changing time signatures
...hold it completely still...
Could refer to rests, where nothing is played so the music "stops", or a fermata, where the note is held for an indeterminately long time outside the time signature
...but never stop moving forward.
The piece of music is always moving forward to the conclusion, no matter what you do to tempo or time signature during the piece.