"The sandpile, by virtue of being first, is the most-studied example of self-organized criticality; but there are many others. We don’t really know what it is about the rules of the sandpile that makes the system evolve inevitably towards its complex, critical state, and we don’t have a clear understanding of which cellular automata are likely to exhibit self-organized criticality.

Insight may come from the surprising connections of the sandpile with other parts of mathematics. To a geometer, like me, the sandpile has to do with the emerging field of tropical geometry, which aims to model continuous geometric phenomena by analogous discrete ones. To a probabilist, the sandpile is intimately related with something called a spanning tree, which (on a square grid) is a branching path that touches every point on the grid but never forms a closed circuit. Wherever insights come from, the sandpile reminds us that the really interesting phenomena in math, like the really interesting phenomena in physics, often happen at the phase transitions. It’s there that we are poised between two different regions of mathematics, sharing features of both, passing information across the boundary. And questions, too. Always more questions than answers." Read more at Nautil.us.

Jordan Ellenberg is the John D. MacArthur Professor of Mathematics at the University of Wisconsin-Madison. He is the author, most recently, of How Not To Be Wrong: The Power of Mathematical Thinking.

Patricia Wayne | Brand Marketing & Public Relations