Lévy Flights of the Collective Imagination

We present a structured random-walk model that captures key aspects of how people communicate in groups. Our model takes the form of a correlated L\'{e}vy flight that quantifies the balance between focused discussion of an idea and long-distance leaps in semantic space. We apply our model to three cases of increasing structural complexity: philosophical texts by Aristotle, Hume, and Kant; four days of parliamentary debate during the French Revolution; and branching comment trees on the discussion website Reddit. In the philosophical and parliamentary cases, the model parameters that describe this balance converge under coarse-graining to limit regions that demonstrate the emergence of large-scale structure, a result which is robust to translation between languages. Meanwhile, we find that the political forum we consider on Reddit exhibits a debate-like pattern, while communities dedicated to the discussion of science and news show much less temporal order, and may make use of the emergent, tree-like topology of comment replies to structure their epistemic explorations. Our model allows us to quantify the ways in which social technologies such as parliamentary procedures and online commenting systems shape the joint exploration of ideas.