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Aging in language dynamics.

Mukherjee A, Tria F, Baronchelli A, Puglisi A, Loreto V - PLoS ONE (2011)

Bottom Line: The observed emerging asymptotic categorization, which has been previously tested--with success--against experimental data from human languages, corresponds to a metastable state where global shifts are always possible but progressively more unlikely and the response properties depend on the age of the system.This aging mechanism exhibits striking quantitative analogies to what is observed in the statistical mechanics of glassy systems.We argue that this can be a general scenario in language dynamics where shared linguistic conventions would not emerge as attractors, but rather as metastable states.

View Article: PubMed Central - PubMed

Affiliation: Institute for Scientific Interchange (ISI), Torino, Italy.

ABSTRACT
Human languages evolve continuously, and a puzzling problem is how to reconcile the apparent robustness of most of the deep linguistic structures we use with the evidence that they undergo possibly slow, yet ceaseless, changes. Is the state in which we observe languages today closer to what would be a dynamical attractor with statistically stationary properties or rather closer to a non-steady state slowly evolving in time? Here we address this question in the framework of the emergence of shared linguistic categories in a population of individuals interacting through language games. The observed emerging asymptotic categorization, which has been previously tested--with success--against experimental data from human languages, corresponds to a metastable state where global shifts are always possible but progressively more unlikely and the response properties depend on the age of the system. This aging mechanism exhibits striking quantitative analogies to what is observed in the statistical mechanics of glassy systems. We argue that this can be a general scenario in language dynamics where shared linguistic conventions would not emerge as attractors, but rather as metastable states.

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Persistence of the linguistic categories.(a) The rescaled average number of linguistic categories  versus the rescaled number of games for three different population sizes (,  and ). The plateau behaviour for the average number of linguistic categories is collapsed by rescaling the ordinate by  and the abscissa by . The inset shows the data collapse for the first part of the evolution where the ordinate is rescaled by  and the abscissa by . (b) The rescaled persistence time of  (i.e., the time spent by the system in a configuration corresponding to an average of  linguistic categories) versus the rescaled  for ,  and  (legends correspond to those in (a) except that the curves are plotted with both lines and symbols here). Once again the ordinate is rescaled by  and the abscissa by  for data collapse. The inset shows a zoomed and uncollapsed version of the data (indicating the need for the collapse). Here the value of  is set to the average human JND  [38].
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pone-0016677-g002: Persistence of the linguistic categories.(a) The rescaled average number of linguistic categories versus the rescaled number of games for three different population sizes (, and ). The plateau behaviour for the average number of linguistic categories is collapsed by rescaling the ordinate by and the abscissa by . The inset shows the data collapse for the first part of the evolution where the ordinate is rescaled by and the abscissa by . (b) The rescaled persistence time of (i.e., the time spent by the system in a configuration corresponding to an average of linguistic categories) versus the rescaled for , and (legends correspond to those in (a) except that the curves are plotted with both lines and symbols here). Once again the ordinate is rescaled by and the abscissa by for data collapse. The inset shows a zoomed and uncollapsed version of the data (indicating the need for the collapse). Here the value of is set to the average human JND [38].

Mentions: We start by investigating the dynamics of the number of linguistic categories emerging in the repertoire of each individual in a population. Two regimes are clearly distinguished (fig. 2a): initially, corresponding to a series of uncorrelated games, the average number of linguistic categories per individual exhibits a rapid growth due to the pressure of discrimination (for a detailed description of CG we refer to the Materials and Methods section), followed by a rapid drop due to the onset of consensus and the merging of perceptual categories. A second regime is characterized by a quasi-arrested dynamics signaled by a “plateau” region, corresponding to a value of the average number of linguistic categories of the order of ten [21], [22]. Interestingly, the dependence of the number of linguistic categories on the population size is different in the two regimes. In the first one, the average number of linguistic categories scales with (see inset of fig. 2a), while in the second regime the dependence of the height of the plateau on the population size is extremely weak (O()): the average number of linguistic categories in the population remains limited to a small value (of the order of ) even for very large population sizes (up to billions of individuals). Furthermore, in the first regime we recover a time dependence on the population size of order (fig. 2a), with a similar behaviour as in the Naming Game [34], [35], while the length of the plateau features a much stronger dependence on , reaching a practically infinite value for large populations. At very large times, when the population is finite, the average number of linguistic categories starts to drop. We shall come back to this finite-size effect later on in the article. Most importantly, at the onset of the plateau region we observe a slowing down of the dynamics signaled by the divergence of the persistence time (fig. 2b). The plateau region is thus the interesting regime describing the persistence and evolution of the category system, and we will next describe its properties by looking at a more sophisticated dynamical quantity.


Aging in language dynamics.

Mukherjee A, Tria F, Baronchelli A, Puglisi A, Loreto V - PLoS ONE (2011)

Persistence of the linguistic categories.(a) The rescaled average number of linguistic categories  versus the rescaled number of games for three different population sizes (,  and ). The plateau behaviour for the average number of linguistic categories is collapsed by rescaling the ordinate by  and the abscissa by . The inset shows the data collapse for the first part of the evolution where the ordinate is rescaled by  and the abscissa by . (b) The rescaled persistence time of  (i.e., the time spent by the system in a configuration corresponding to an average of  linguistic categories) versus the rescaled  for ,  and  (legends correspond to those in (a) except that the curves are plotted with both lines and symbols here). Once again the ordinate is rescaled by  and the abscissa by  for data collapse. The inset shows a zoomed and uncollapsed version of the data (indicating the need for the collapse). Here the value of  is set to the average human JND  [38].
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3040735&req=5

pone-0016677-g002: Persistence of the linguistic categories.(a) The rescaled average number of linguistic categories versus the rescaled number of games for three different population sizes (, and ). The plateau behaviour for the average number of linguistic categories is collapsed by rescaling the ordinate by and the abscissa by . The inset shows the data collapse for the first part of the evolution where the ordinate is rescaled by and the abscissa by . (b) The rescaled persistence time of (i.e., the time spent by the system in a configuration corresponding to an average of linguistic categories) versus the rescaled for , and (legends correspond to those in (a) except that the curves are plotted with both lines and symbols here). Once again the ordinate is rescaled by and the abscissa by for data collapse. The inset shows a zoomed and uncollapsed version of the data (indicating the need for the collapse). Here the value of is set to the average human JND [38].
Mentions: We start by investigating the dynamics of the number of linguistic categories emerging in the repertoire of each individual in a population. Two regimes are clearly distinguished (fig. 2a): initially, corresponding to a series of uncorrelated games, the average number of linguistic categories per individual exhibits a rapid growth due to the pressure of discrimination (for a detailed description of CG we refer to the Materials and Methods section), followed by a rapid drop due to the onset of consensus and the merging of perceptual categories. A second regime is characterized by a quasi-arrested dynamics signaled by a “plateau” region, corresponding to a value of the average number of linguistic categories of the order of ten [21], [22]. Interestingly, the dependence of the number of linguistic categories on the population size is different in the two regimes. In the first one, the average number of linguistic categories scales with (see inset of fig. 2a), while in the second regime the dependence of the height of the plateau on the population size is extremely weak (O()): the average number of linguistic categories in the population remains limited to a small value (of the order of ) even for very large population sizes (up to billions of individuals). Furthermore, in the first regime we recover a time dependence on the population size of order (fig. 2a), with a similar behaviour as in the Naming Game [34], [35], while the length of the plateau features a much stronger dependence on , reaching a practically infinite value for large populations. At very large times, when the population is finite, the average number of linguistic categories starts to drop. We shall come back to this finite-size effect later on in the article. Most importantly, at the onset of the plateau region we observe a slowing down of the dynamics signaled by the divergence of the persistence time (fig. 2b). The plateau region is thus the interesting regime describing the persistence and evolution of the category system, and we will next describe its properties by looking at a more sophisticated dynamical quantity.

Bottom Line: The observed emerging asymptotic categorization, which has been previously tested--with success--against experimental data from human languages, corresponds to a metastable state where global shifts are always possible but progressively more unlikely and the response properties depend on the age of the system.This aging mechanism exhibits striking quantitative analogies to what is observed in the statistical mechanics of glassy systems.We argue that this can be a general scenario in language dynamics where shared linguistic conventions would not emerge as attractors, but rather as metastable states.

View Article: PubMed Central - PubMed

Affiliation: Institute for Scientific Interchange (ISI), Torino, Italy.

ABSTRACT
Human languages evolve continuously, and a puzzling problem is how to reconcile the apparent robustness of most of the deep linguistic structures we use with the evidence that they undergo possibly slow, yet ceaseless, changes. Is the state in which we observe languages today closer to what would be a dynamical attractor with statistically stationary properties or rather closer to a non-steady state slowly evolving in time? Here we address this question in the framework of the emergence of shared linguistic categories in a population of individuals interacting through language games. The observed emerging asymptotic categorization, which has been previously tested--with success--against experimental data from human languages, corresponds to a metastable state where global shifts are always possible but progressively more unlikely and the response properties depend on the age of the system. This aging mechanism exhibits striking quantitative analogies to what is observed in the statistical mechanics of glassy systems. We argue that this can be a general scenario in language dynamics where shared linguistic conventions would not emerge as attractors, but rather as metastable states.

Show MeSH
Related in: MedlinePlus