What processes can explain how very large populations are able to converge on
the use of a particular word or grammatical construction without global
coordination? Answering this question helps to understand why new language
constructs usually propagate along an S-shaped curve with a rather sudden
transition towards global agreement. It also helps to analyze and design new
technologies that support or orchestrate self-organizing communication systems,
such as recent social tagging systems for the web. The article introduces and
studies a microscopic model of communicating autonomous agents performing
language games without any central control. We show that the system undergoes a
disorder/order transition, going trough a sharp symmetry breaking process to
reach a shared set of conventions. Before the transition, the system builds up
non-trivial scale-invariant correlations, for instance in the distribution of
competing synonyms, which display a Zipf-like law. These correlations make the
system ready for the transition towards shared conventions, which, observed on
the time-scale of collective behaviors, becomes sharper and sharper with system
size. This surprising result not only explains why human language can scale up
to very large populations but also suggests ways to optimize artificial
semiotic dynamics.Comment: 12 pages, 4 figure