Formation of Languages; Equality, Hierarchy and Teachers
  A quantitative method is suggested, where meanings of words, and grammatic rules about these, of a vocabulary are represented by real numbers. People meet randomly, and average their vocabularies if they are equal; otherwise they either copy from higher hierarchy or stay idle. Presence of teachers broadcasting the same (but arbitrarily chosen) vocabulary leads the language formations to converge more quickly. 
Caglar Tuncay