Attraction and repelling occur among these balls. It is widely known that the biological function of a protein is very much determined by such 3-D structure. The fundamental assumption of PFP is that our Mother Nature chooses the very special 3-D structure which has the lowest system energy among all possible structures. More accurately, let xi denote the position of the i-th atom. IBM is now designing the most powerful computer in the human history called the Blue Gene.
Optimization is universal in both the physical world and human activities.
In the physical world, there are universal laws why this is always true. In quantum mechanics, therefore, the so-called ground state, i.e., the state with the lowest energy, attracts much more attention than others. Concentrated gas when released freely, always spreads out instead of further being concentrated. I suspect passenger distribution in a bus also obeys the similar law. In human activities, the fundamental role of optimization is much plainer to see, though I am much less experienced in this field.