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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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Relaxation of the correlation functions.(a) The autocorrelation  for ,  and , . The inset shows the collapse of the  relaxation regime. In this regime, there is a very weak violation of the dependence of  on  (time-translation invariance). (b) The collapse of the autocorrelation functions shown in (a) in the  relaxation regime indicating sub-aging (). This result shows that the relaxation is strongly dependent on the size of the population ( with ). Here again the value of  is set to the average human JND  [38].
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pone-0016677-g003: Relaxation of the correlation functions.(a) The autocorrelation for , and , . The inset shows the collapse of the relaxation regime. In this regime, there is a very weak violation of the dependence of on (time-translation invariance). (b) The collapse of the autocorrelation functions shown in (a) in the relaxation regime indicating sub-aging (). This result shows that the relaxation is strongly dependent on the size of the population ( with ). Here again the value of is set to the average human JND [38].

Mentions: A system is said to be in dynamical equilibrium when it shows invariance under time translations; if this holds, any observable comparing the system at time with the system at time does not depend on . In contrast, a system undergoing aging is not invariant under time translation, i.e., time is not homogeneous. This property can be revealed by measuring correlations of the system at different times. Here we consider a suitably defined autocorrelation function, which we term : at time we save a copy of the configuration of all the agents in the population and subsequently, at time instances greater than , we compute the linguistic overlap of each agent with its copy saved at ; finally, we average this quantity over all agents (see Materials and Methods for detailed definitions). Results are presented in fig. 3 for two different population sizes. We recognize two different time scales, which we can associate to local or individual (fast) and collective or population-related (slow) dynamics. In particular, for , depends (almost) only on (see inset of fig. 3a). This phenomenon corresponds to what is known in the physics of glassy systems as the -relaxation regime. This fast dynamics corresponds to the microscopic dynamics of the boundaries between linguistic categories at the individual level.


Aging in language dynamics.

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

Relaxation of the correlation functions.(a) The autocorrelation  for ,  and , . The inset shows the collapse of the  relaxation regime. In this regime, there is a very weak violation of the dependence of  on  (time-translation invariance). (b) The collapse of the autocorrelation functions shown in (a) in the  relaxation regime indicating sub-aging (). This result shows that the relaxation is strongly dependent on the size of the population ( with ). Here again the value of  is set to the average human JND  [38].
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3040735&req=5

pone-0016677-g003: Relaxation of the correlation functions.(a) The autocorrelation for , and , . The inset shows the collapse of the relaxation regime. In this regime, there is a very weak violation of the dependence of on (time-translation invariance). (b) The collapse of the autocorrelation functions shown in (a) in the relaxation regime indicating sub-aging (). This result shows that the relaxation is strongly dependent on the size of the population ( with ). Here again the value of is set to the average human JND [38].
Mentions: A system is said to be in dynamical equilibrium when it shows invariance under time translations; if this holds, any observable comparing the system at time with the system at time does not depend on . In contrast, a system undergoing aging is not invariant under time translation, i.e., time is not homogeneous. This property can be revealed by measuring correlations of the system at different times. Here we consider a suitably defined autocorrelation function, which we term : at time we save a copy of the configuration of all the agents in the population and subsequently, at time instances greater than , we compute the linguistic overlap of each agent with its copy saved at ; finally, we average this quantity over all agents (see Materials and Methods for detailed definitions). Results are presented in fig. 3 for two different population sizes. We recognize two different time scales, which we can associate to local or individual (fast) and collective or population-related (slow) dynamics. In particular, for , depends (almost) only on (see inset of fig. 3a). This phenomenon corresponds to what is known in the physics of glassy systems as the -relaxation regime. This fast dynamics corresponds to the microscopic dynamics of the boundaries between linguistic categories at the individual level.

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