Physicists have identified a mechanism that may help explain Zipf’s law – a unique pattern of behavior found in disparate systems, including complex biological ones. The journal Physical Review Letters is publishing their mathematical models, which demonstrate how Zipf’s law naturally arises when a sufficient number of units react to a hidden variable in a system.
“We’ve discovered a method that produces Zipf’s law without fine-tuning and with very few assumptions,” says Ilya Nemenman, a biophysicist at Emory University and one of the authors of the research.
The paper’s co-authors include biophysicists David Schwab of Princeton and Pankaj Mehta of Boston University. “I don’t think any one of us would have made this insight alone,” Nemenman says. “We were trying to solve an unrelated problem when we hit upon it. It was serendipity and the combination of all our varied experience and knowledge.”
Their findings, verified with neural data of blowflies reacting to changes in visual signals, may have universal applications. “It’s a simple mechanism,” Nemenman says. “If a system has some hidden variable, and many units, such as 40 or 50 neurons, are adapted and responding to the variable, then Zipf’s law will kick in.”
That insight could aid in the understanding of how biological systems process stimuli. For instance, in order to pinpoint a malfunction in neural activity, it would be useful to know what data recorded from a normally functioning brain would be expected to look like. “If you observed a deviation from the Zipf’s law mechanism that we’ve identified, that would likely be a good place to investigate,” Nemenman says.
The Zipf's law mechanism was verified with neural data of blowflies reacting to changes in visual signals.