P326 Modeling language evolution with spin glass dynamics
Hediye Yarahmadi*1, Alessandro Treves1
1Cognitive Neuroscience, SISSA, Trieste, Italy
*Email: hediye.yarahmadi@sissa.it
Introduction
Recent advances in phylogenetic linguistics by Longobardi and colleagues [1], based on syntactic parameters, seem to reconstruct language evolution farther in the past than traditional etymological approaches. Combined with quantitative statistics, this Parametric Comparison Method also raises general questions: why does syntax keep changing? Why do languages diversify instead of converging into efficient forms? And why is this change so slow, over centuries? We hypothesize that the fundamental reasons are disorder and frustration: syntactic parameters interact through disordered interactions, subject to weak external drives and, unable to settle into a state fully compatible with all interactions, they evolve slowly with “glassy” dynamics.
Methods
To explore such hypothesis, we model a “language” as a binary vector of the 94 syntactic parameters considered in the Longobardi database, and assume that they interact both through the explicit and asymmetric dependencies that linguists call “implications” (which may lead to rotating changes [2]) and through weak, partly asymmetric interactions, which we assign at random with a relative strengthσand a degree of asymmetryφranging from 0° (symmetric) to 90° (fully antisymmetric). Using Glauber dynamics, we simulate the evolution of these parameters, assuming external fields to only set the initial conditions. We then introduce a Hopfield-like symmetry component to the interaction term, expected to glassify syntax dynamics further.
Results
(Fig. 1a) sketches the (φ,σ,γ=0) phase diagram based on simulations of the average number of parameters flip at the 100thtime step. Syntactic parameters get trapped in a steady state (one of a disordered multiplicity) for low asymmetry, while they continue to evolve for higher asymmetry. The strength of random interactions is almost irrelevant, but when they dominate (σ→∞),the transition is sharp atφ=30°. For lowσ,dynamics slow, but atσ≡0 they continue indefinitely: implications alone allow no steady state. (Fig. 1b) presents the phase diagram in (φ=90°,σ,γ) space, showing a transition from a glassy to a chaotic state. The balance between symmetry and asymmetry is crucial, and a large γ stabilizes the system via the Hopfield term.
Discussion
The sharp transition atφ=30° forσ→∞ and γ→0aligns with previous studies of asymmetric spin glasses [3] (η=1/2 in their notation), indicating that varying the interaction symmetry induces a phase transition from glassy to chaotic dynamics. This suggests that to understand language evolution in the syntax domain it is essential to include, along the implicational structure constraining parameter changes, disordered interactions which have so far eluded linguistic analysis, in part because of their quantitative rather than logical nature. We are now working on integrating this Hopfield-like structure, which brings languages closer to metastable states.
Figure 1. Phase diagrams: (a) At γ=0 in the σ-φ plane, the system freezes with symmetric interactions (up to φ≈30°) and becomes fluid as asymmetry increases for large σ. Similar behavior occurs to σ→0, but with slower fluid dynamics, and with σ ≡ 0, it is chaotic. (b) At φ=90° in the σ-γ plane, freezing occurs for γ/σ > 0.01, becoming fluid as the Hopfield term decreases. Symmetry balance is key.
Acknowledgements
We would like to express our sincere gratitude to G. Longobardi for providing access to the database used in this study.
References
[1]Ceolin A, Guardiano C, Longobardi G et al (2021).At the boundaries of syntactic prehistory.Phil Trans Roy Soc B,376(1824), 20200197. http://doi.org/10.1098/rstb.2020.0197
[2] Crisma P, Fabbris G, Longobardi G & Guardiano C (2025).What are your values? Default and asymmetry in parameter states.J Historical Syntax,9, 1-26.https://doi.org/10.18148/hs/2025.v9i2-10.182
[3]Nutzel K & Krey U (1993). Subtle dynamic behaviour of finite-size Sherrington-Kirkpatrick spin glasses with nonsymmetric couplings.J Physics A: Math Gen,26, L591.https://10.1088/0305-4470/26/14/011.
