While in graduate school in mathematics at the University of Wisconsin-Madison, I took a logic course from David Griffeath. The class was fun. Griffeath brought a playfulness and openness to problems. Much to my delight, about a decade later, I ran into him at a conference on traffic models. During a presentation on computational models of traffic jams, his hand went up. I wondered what Griffeath—a mathematical logician—would have to say about traffic jams. He did not disappoint. Without even a hint of excitement in his voice, he said: ‘If you are modeling a traffic jam, you should just keep track of the non-cars.’
The collective response followed the familiar pattern when someone drops an unexpected, but once stated, obvious idea: A puzzled silence, giving way to a roomful of nodding heads and smiles. Nothing else needed to be said.
Griffeath had made a brilliant observation. During a traffic jam, most of the spaces on the road are filled with cars. Modelling each car takes up an enormous amount of memory. Keeping track of the empty spaces instead would use less memory—in fact almost none. Furthermore, the dynamics of the non-cars might be more amenable to analysis.