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Competition of languages in the presence of a barrier
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Competition of languages in the presence of a
barrier
Christian Schulze and Dietrich Stauffer
Institute for Theoretical Physics, Cologne University
D-50923 Ko?ln, Euroland
February 2, 2008
e-mail: stauffer@thp.uni-koeln.de
Abstract: Using the Schulze model for Monte Carlo simulations of language
competition, we include a barrier between the top half and the bottom half of
the lattice. We check under which conditions two different languages evolve as
dominating in the two halves.
Keywords: Monte Carlo simulation, geography, separation.
1 Introduction
Languages are influenced by natural barriers [1], like mountains [2], water or politics
[3]. On different sides of a mountain ridge different dialects or languages may be
spoken, and the same separation happened on the two sides of the English Channel
[4]. Our previous attempt [5] to simulate this effect with the Viviane model [6]
of language competition [7, 8, 9, 10] was unsuccessful. Thus we now try to use
the Schulze model [11, 5] to check under which conditions one barrier leads to the
domination of two different languages on the two sides of the barrier.
In the next section we define the model, section III gives some of our results,
and section IV summarises our work.
2 Model
Each site of a L × L square lattice is occupied by one adult person speaking one
language (dialect, grammar, ...). Each such language is defined by F different fea-
tures each of which can take one of Q different values. Thus we have in total QF
different possible languages. We use Q = 3 and 5 and F = 8 and 16. Changes in
the languages are ruled by two probabilities p and q. At each time step (one sweep
1
through the lattice) each language can change into another one by changing each of
its F features independently with probability p. This change means that with prob-
ability 1? q a random value between 1 and Q is selected, while with probabilit
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