Language simulation after a conquest
aa r X i v : . [ phy s i c s . s o c - ph ] J un Language simulation after a conquest
Christian Schulze and Dietrich StaufferInstitute for Theoretical Physics, Cologne UniversityD-50923 K¨oln, EurolandAbstract: When a region is conquered by people speaking another lan-guage, we assume within the Schulze model that at each iteration each personwith probability s shifts to the conquering language. The time needed forthe conquering language to become dominating is about 2 /s for directedBarab´asi-Albert networks, but diverges on the square lattice for decreasing s at some critical value s c .The language competition model of Abrams and Strogatz assumes thepossibility that of two competing languages one has a higher status [1]. Wenow look for an analogous question in the multi-language Schulze model [2]:Will the language of the conquerors finally always win?We used the Schulze model with F features, each of which takes an integervalue between 1 and Q . All speakers are positioned on a directed Barab´asi-Albert network of N people surrounding a fully connected core of m = 3nodes. Each node added to the network selects m already existing nodesas teachers, via preferential attachment. At each iteration, with probability p = 0 . q = 0 .
85 the feature value of a randomly selected neighbour(teacher) is taken, while with probability 1 − q a randomly selected newvalue between 1 and Q is taken. Also, at each iteration each speaker withprobability (1 − x ) r ( r = 0 .
9) gives up the old language and takes overthe language of a randomly selected neighbour; here x is the fraction of thewhole population speaking the old language.Initially the N people surrounding the core select their own languagerandomly, while the m core members select the “central” language whereeach feature is 2 for Q = 3 and 3 for Q = 5. Later, the core members are notsubject to the above modifications and represent a “royal family” speakingthe unmodified official language. As a result, after a few iterations nearlyeverybody speaks the central language of the core.The influence of war is simulated as follows: A foreign power, speakinga language where all features are 1, conquers the country during ten itera-tions. From then on everybody, including the core, at each iteration with1robability s adopts the language of the conquerer. The effect of this lan-guage shift is particularly drastic on the whole population if a core membershifts to the conquering language. The winning time is defined as the totalnumber of iterations (including the initial ten iterations of war) needed forthe conquering language to become the numerically strongest language in thepopulation and for all core members to adopted it.
10 100 1000 10000 100000 .00001 .0001 0.001 0.01 0.1 1 w i nn i ng t i m e probability sMedian, 5 samples, (F,Q)=(8,5,+),(8,3,x),(16,3,*) Figure 1: Winning time versus adoption probability s , for N = 10 . Thedeviations for small times come from the initial time of war, 10 iterations,after which the process of adopting the conquering language begins. Thestraight line gives 2 /s .Fig.1 shows for three choices of F and Q that the winning time is aboutinversely proportional to the probability s . It seems to be independent of N ,Fig.2. The fluctuations in the winning time are very large and do not seemto diminish if N increases, Fig.3. Varying p at fixed q = 0 .
85, or q at fixed p = 0 . s in the winning times.Even for very small s the conquering language will win, after a time of the2 w i nn i ng t i m e population NMedian of 10 samples, s = 0.001, F = 8, Q = 5 Figure 2: Independence of the winning time of the population size N , at s = 10 − , F = 8 , Q = 5.order of 2 /s . Reality is, of course, more complicated that this model. TheBasque language is still used in Northeastern Spain thousands of years afterthe neighbours started to speak an Indo-European language, while CelticFrance mostly started to speak Latin and French only very few centuries afterthe Roman conquest. Within this model these differences would require thatdifferent populations have different probabilities s to adopt the conqueringlanguage.A rather different picture is obtained if we put the speakers on a squarelattice instead of the Barab´asi-Albert network. Then Fig.4 shows rathersmall time with little sample-to-sample fluctuations, diverging at some crit-ical value for the probability s . (Numerically, divergence means a mediantime above one million.) Thus perhaps the Basque country in this versionhad an s below this critical value ever since the Indo-European settlement ofthe Iberian peninsula, while the s for France was higher.We thank L. Litov for suggesting this work and S. Wichmann for com-ments. References [1] D.M. Abrams and S.H. Strogatz, Nature 424 (2003) 900.[2] C. Schulze, D. Stauffer, S. Wichmann, Comm. Comp. Phys., submitted.3 w i nn i ng t i m e population N10 samples, F=8, Q=5, p=0.5, q=0.85, s=0.00001 Figure 3: Distribution of winning times at s = 10 − , F = 8 , Q = 5 versuspopulation size N .
10 100 1000 10000 0.01 0.1 1 w i nn i ng t i m e probability s301*301 (+,*), 101*101(x): p=0.2(+,x) and .001(*) Figure 4: Winning time versus adoption probability ss