Forecasting a Language Shift Based on Cellular Automata
Journal of Artificial Societies and Social Simulation
12 (3) 5
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Received: 04-Nov-2008 Accepted: 08-May-2009 Published: 30-Jun-2009
|Figure 1. The interruption of language transmission according to the Gaelic-Arvanitika model of language shifts. Given a dominant language (DL) and a subordinate language (SL) in a community, the non-transmitted language (SL) become extinct after two generations.|
|Table 1: The transition rule of the cellular automaton that simulates the language shift. The state of the cell at t changes at t +1 if the sum value of its neighbors surpasses the value of a threshold (Sa, Sb or Sc). Note that the transition from state 0 to state 2 is difficult to observe empirically, because it involves a non-subordinate-language speaker becoming a strong subordinate-language speaker.|
|0||∑ ≤ Sb||∑ > Sb||----|
|1||∑ < Sb||Sb ≤ ∑ ≤ Sc||∑ > Sc|
|2||∑ ≤ Sa||Sa < ∑ < Sb||∑ ≥ Sb|
|Figure 2. Language map of Valencia introducing the two language areas: the Catalan area (dark green) and the Spanish area (light green). The map in the top-left corner shows the location of Valencia in Europe.|
|Figure 3a ( t = 0)||Figure 3b ( t = 1)|
|Figure 3c ( t = 4)||Figure 3d ( t = 56, the automaton stabilizes)|
|Figure 3. An example of the dynamics of the cellular automaton (a to d) that simulate a language shift. The graphics were obtained from the first sheet of the spreadsheet in which the cellular automaton was implemented. The white cells indicate state 0, the orange cells indicate state 1 and the green cells indicate state 2. At t = 0 the state-0 cells accounted for 15%, the state-1 cells represented 40%, and the state-2 cells accounted for 45%. The threshold values were set at Sa= 3, Sb= 9 and Sc= 14.|
|Figure 4. The mean percentages and standard deviations of states 0, 1 and 2 for the values of threshold Sb when the automaton stabilized (values of Sb= 5 to 14). The top graph shows the results for different percentages of the states (simulation 1) and the bottom graph shows the results for the same percentage of the states (simulation 2). The percentage of initial values ( t = 0) is also shown.|
|Table 2: Percentage of oral comprehension of Catalan in the two language areas of Valencia. The data were obtained in 2005 from a sample of 6,600 people aged 15 and over (Ninyoles 2005). The table also includes the states of the cellular automaton assigned to each oral comprehension category.|
|Catalan area||Spanish area||State of the automaton|
|Do Not Understand Catalan||4.5||18.7||0|
|Understand Some Catalan||17.3||41.8||1|
|Understand Catalan Well||21.8||21.0||2|
|Understand Catalan Very Well||56.3||18.3||2|
|Did Not Answer|
|Figure 5. The mean percentages and standard deviation of states 0, 1 and 2 for the values of threshold Sb when the automaton stabilized (values of Sb= 5 to 10). The top graph shows the data on oral comprehension of Catalan in the Catalan area of Valencia (simulation 3) and the bottom graph shows the data on oral comprehension of Catalan in the Spanish area of Valencia (simulation 4). The percentage of initial values ( t = 0) is also shown. If the standard deviations are very small, error bars are not displayed.|
|Table 3: Percentage of Catalan use in the Catalan area of Valencia in two social contexts. The data were obtained in 2005 from a sample of 6,600 people aged 15 years and over (Ninyoles 2005). The table also includes the states of the automaton assigned to each usage category.|
|Language spoken and frequency||Home||Friends||State of the automaton|
|More Catalan than Spanish||1.3||2.3||2|
|Equal Catalan and Spanish||6.2||13.8||2|
|More Spanish than Catalan||2.0||2.1||1|
|Did Not Answer||1.1||0.9||---|
|Figure 6. The mean percentages and standard deviations of states 0, 1 and 2 for the values of threshold Sb when the automaton stabilized (values of Sb= 5 to 10). The top graph shows the data on the use of Catalan at home in the Catalan area (simulation 5) and the bottom graph shows the data on the use of Catalan with friends in the same area (simulation 6). The percentage of initial values ( t = 0) is also shown.|
|Figure 7. The mean percentages and standard deviations of states 0, 1 and 2 for the values of Sa=3, Sb=9 and Sc=15 after four time units. The top graph shows the data for the use of Catalan at home in the Catalan area of Valencia (simulation 7) and the bottom graph shows the data for the use of Catalan with friends in the same area (simulation 8). The percentage of initial values ( t = 0) is also shown.|
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