Information spreading on a small-world network: how instant long-range access turns slow gossip into near-instant shared knowledge.
Model and sources
Each mind is a node. Every mind links to its k nearest neighbours; a fraction ω of those links is rewired to a random distant mind (Watts-Strogatz small-world model, Nature 393, 1998). ω = 100% means every mind can reach every other directly: the idealised omniscient space.
Information spreads as a stochastic SI/SIS process: an informed mind passes the fact along each link with probability 1 − exp(−β·dt) per step, and may forget at rate γ. The dashed curve is the well-mixed mean-field equation df/dt = β⟨k⟩f(1 − f) − γf (Pastor-Satorras and Vespignani, PRL 86, 2001), which only matches when long-range links dominate. Uncertainty is the Shannon entropy of a random mind being informed or not, H(f) = −f·log2 f − (1 − f)·log2(1 − f).