  The "small-world effect" is the observation that one can find a short chain
of acquaintances, often of no more than a handful of individuals, connecting
almost any two people on the planet. It is often expressed in the language of
networks, where it is equivalent to the statement that most pairs of
individuals are connected by a short path through the acquaintance network.
Although the small-world effect is well-established empirically for
contemporary social networks, we argue here that it is a relatively recent
phenomenon, arising only in the last few hundred years: for most of mankind's
tenure on Earth the social world was large, with most pairs of individuals
connected by relatively long chains of acquaintances, if at all. Our
conclusions are based on observations about the spread of diseases, which
travel over contact networks between individuals and whose dynamics can give us
clues to the structure of those networks even when direct network measurements
are not available. As an example we consider the spread of the Black Death in
14th-century Europe, which is known to have traveled across the continent in
well-defined waves of infection over the course of several years. Using
established epidemiological models, we show that such wave-like behavior can
occur only if contacts between individuals living far apart are exponentially
rare. We further show that if long-distance contacts are exponentially rare,
then the shortest chain of contacts between distant individuals is on average a
long one. The observation of the wave-like spread of a disease like the Black
Death thus implies a network without the small-world effect.
