Given a string, to break it into 2 pieces, one can simply cut it at any point.
Given a loop, to break it into 2 pieces, there are two cuts needed, as the first cut will make it into a string and the second cut break into 2 pieces.
Then my question is does this pattern continue? Can there be some form of a 1d object such that more than 2 cuts are needed in order to break it into 2 pieces?