A new mathematical equation explains why broken objects – from vases to sugar cubes to bursting bubbles – always seem to fall apart in the most frustratingly consistent manner. Research published in Physical Review Letters reveals that fragmentation follows a principle of “maximal randomness,” meaning objects break into pieces in the most disordered way physically possible.
The Science of Messiness
For years, scientists have observed that regardless of the material, shattered objects yield a predictable ratio of large to small fragments. This consistency suggested a hidden universal rule governing how things break. Physicist Emmanuel Villermaux, from Aix-Marseille University in France, took a fresh approach: instead of studying how things break, he focused on the fragments themselves.
Villermaux’s key insight is that shattering isn’t about complex fracture patterns, but about maximizing disorder (entropy). The equation he developed combines this principle with a previously discovered conservation law governing fragment density, effectively predicting the size distribution of shards from almost any breaking event.
From Stone Tools to Sugar Cubes
The equation has been tested against decades of fragmentation data, including glass, spaghetti, liquid droplets, plastic in the ocean, and even ancient stone tools. Remarkably, all matched the predicted size distribution. Villermaux even validated the equation with a hands-on experiment: dropping heavy objects onto sugar cubes with his daughters.
“That was a summer project with my daughters… they were illustrating my point well.” – Emmanuel Villermaux
Limitations and Future Applications
The law of maximal randomness isn’t absolute. It doesn’t apply when breaking is perfectly ordered (like uniform liquid droplets) or when fragments interact after breaking (certain plastics). However, the findings could have practical implications. Understanding fragmentation could improve efficiency in industrial mining (shattering ore) and better prepare for natural disasters (rockfalls).
Future research will explore the theoretical minimum size a fragment can reach before it no longer exists. This law of breaking may seem trivial, but it demonstrates that even chaos has underlying mathematical order.
