Indexing the archive…
Your Universe of Digital Possibilities
Tell one node. Each round, every node that knows tells one random other. Sixteen thousand know in about twenty-five rounds, and nobody had a list — no tree, no directory, no centre. Watch the wavefront cross the globe, then make the gossipers lose interest and count who never hears.
Each informed node tells one random node a round. The informed set doubles until most know (log₂ n rounds), then the last stragglers are found like coupons — each round catches a fixed fraction of the rest (another ln n).
An uninformed node asks a random node and stays ignorant only if it asked another ignorant one: the ignorant share squares every round. Push spends its last rounds looking for the few who have not heard; pull lets them come looking.
A teller who finds the listener already knew stops with chance 1/k (Demers et al.’s feedback-and-coin rule). In the continuous-time limit the fraction never told solves this equation: ≈ 0.203 at k = 1, Daley & Kendall’s number, and falling exponentially in k.
The same flow S → I → R that The Contagion runs on a network, with one change: a spreader is not cured by time but by meeting people who already know. That self-stopping is why a rumour, unlike an epidemic past threshold, always leaves some never told.
The Clock kept an order with no master clock; The Rumor spreads a fact with no directory. It is the engineered twin of The Contagion: there an infection finds its own way through a network and the threshold decides whether it takes off; here we want it to take off, and the protocol designer chooses the contact rule — push, pull, both, or a gossip that loses interest. The doubling is the same doubling that made Chord’s lookups take log₂ S hops in The Hash; next, The Generals ask what happens when some of the gossipers lie.