Supposing that there is a dynamic process than creates new cluster, for example just like a rocket is broken into many pieces with a hammer, the problem is to use the evolution of those clusters to determine the initial position of the rock and how was the distribution of particles in the rock, that seems to me to be a beautiful problem. The hammer was just an example, another is people moving from one city to another, clustering could help to hypothesize about the process and initial state.