“If you want to know why there are riots at some football games, and not at Caltech football games,” said then-Caltech professor John Hopfield to an audience at the 1983 Corporate Associates meeting of the American Institute of Physics, “it has to do simply with the scale: 10 people don’t riot!”1
It was a flippant comment in support of a broader point. In a large enough gathering of anything—whether atoms, cells, insects, or people—collective phenomena emerge that are completely different from anything one might see in smaller groups of the same constituents. Moreover, the collective behaviors can often be meaningfully understood without appealing to the interactions of the individuals at all.
Hopfield was interested in collective behaviors of neurons, and for his work he was awarded a share of last year’s Nobel Prize in Physics (see Physics Today, December 2024, page 12). But similar principles have come...
