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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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Finite-size effects.The rescaled average number of linguistic categories  versus the rescaled number of games for five different population sizes (, , ,  and ). The bending region of the curves is collapsed by rescaling the number of linguistic categories by  and the time axis as  where , ,  and . The inset shows a zoomed version of the same plot to present a better visualization of the data collapse.
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pone-0016677-g004: Finite-size effects.The rescaled average number of linguistic categories versus the rescaled number of games for five different population sizes (, , , and ). The bending region of the curves is collapsed by rescaling the number of linguistic categories by and the time axis as where , , and . The inset shows a zoomed version of the same plot to present a better visualization of the data collapse.

Mentions: In this section, we consider finite-size effects. We focus, in particular, on the behaviour of the average number of linguistic categories as a function of time (as observed in fig. 2a). A careful observation reveals that for very long times the plateau behaviour leaves room for a bending of the curves leading to a reduction in the average number of linguistic categories. This bending occurs earlier for small populations, i.e., for small system sizes. Fig. 4 shows the collapse of the curves for the average number of linguistic categories for different system sizes from , for which the bending is stronger, to . The collapse is aimed at superimposing only the bending region. It turns out that one collapses the curves after a rescaling of the abscissa as , where the term allows to superimpose the onset of the bending region while the term is the time rescaling well inside the bending region and is a constant. The value of is consistent with what is observed in the collapse of the correlation function (see fig. 3) and confirms the idea that the length of the plateau region is scaling with a large power of the system size. On the other hand the bending region exhibits a characteristic time scaling as with and the overall behaviour is well fitted by a stretched exponential function with an exponent close to .


Aging in language dynamics.

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

Finite-size effects.The rescaled average number of linguistic categories  versus the rescaled number of games for five different population sizes (, , ,  and ). The bending region of the curves is collapsed by rescaling the number of linguistic categories by  and the time axis as  where , ,  and . The inset shows a zoomed version of the same plot to present a better visualization of the data collapse.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0016677-g004: Finite-size effects.The rescaled average number of linguistic categories versus the rescaled number of games for five different population sizes (, , , and ). The bending region of the curves is collapsed by rescaling the number of linguistic categories by and the time axis as where , , and . The inset shows a zoomed version of the same plot to present a better visualization of the data collapse.
Mentions: In this section, we consider finite-size effects. We focus, in particular, on the behaviour of the average number of linguistic categories as a function of time (as observed in fig. 2a). A careful observation reveals that for very long times the plateau behaviour leaves room for a bending of the curves leading to a reduction in the average number of linguistic categories. This bending occurs earlier for small populations, i.e., for small system sizes. Fig. 4 shows the collapse of the curves for the average number of linguistic categories for different system sizes from , for which the bending is stronger, to . The collapse is aimed at superimposing only the bending region. It turns out that one collapses the curves after a rescaling of the abscissa as , where the term allows to superimpose the onset of the bending region while the term is the time rescaling well inside the bending region and is a constant. The value of is consistent with what is observed in the collapse of the correlation function (see fig. 3) and confirms the idea that the length of the plateau region is scaling with a large power of the system size. On the other hand the bending region exhibits a characteristic time scaling as with and the overall behaviour is well fitted by a stretched exponential function with an exponent close to .

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