*Article* **Criticality in Pareto Optimal Grammars?**

#### **Luís F Seoane 1,\*and Ricard Solé 2,3,4,\***


Received: 31 December 2019; Accepted: 27 January 2020; Published: 31 January 2020

**Abstract:** What are relevant levels of description when investigating human language? How are these levels connected to each other? Does one description yield smoothly into the next one such that different models lie naturally along a hierarchy containing each other? Or, instead, are there sharp transitions between one description and the next, such that to gain a little bit accuracy it is necessary to change our framework radically? Do different levels describe the same linguistic aspects with increasing (or decreasing) accuracy? Historically, answers to these questions were guided by intuition and resulted in subfields of study, from phonetics to syntax and semantics. Need for research at each level is acknowledged, but seldom are these different aspects brought together (with notable exceptions). Here, we propose a methodology to inspect empirical corpora systematically, and to extract from them, blindly, relevant phenomenological scales and interactions between them. Our methodology is rigorously grounded in information theory, multi-objective optimization, and statistical physics. Salient levels of linguistic description are readily interpretable in terms of energies, entropies, phase transitions, or criticality. Our results sugges<sup>t</sup> a critical point in the description of human language, indicating that several complementary models are simultaneously necessary (and unavoidable) to describe it.

**Keywords:** syntax; Pareto-optimality; bottleneck method; phase transitions; statistical mechanics
