Changes in complex systems

Imagine a small table. Onto the center of this table, sand is being poured from above, at a slow, steady pace. After a while, a pile of sand covers the entire table top, and sand starts pouring over the edges of the table, in small avalanches – some bigger than others. The sizes of these avalanches follow a power law – that is, that most of them are really small, and few of them are large, but for any given size, the frequency is the inverse of some power of the size.

This is Per Bak’s analogy for how changes occur in complex systems, quoted in Complexity. Earthquake magnitudes also follow power laws, and at the time the book was written, the people at the Santa Fe Institute suspected that this was true of economies, stock markets, and many other such systems, although it hadn’t been proved. I wonder if they have proven it by now.