Ramon Ferrer i Cancho

Least effort and the origins of scaling in human language

The emergence of a complex language is one of the fundamental events of human evolution, and several remarkable features suggest the presence of fundamental principles of organization. These principles seem to be common to all languages. The best known is the so-called Zipfs law, which states that the frequency of a word decays as a (universal) power law of its rank. The possible origins of this law have been controversial, and its meaningfulness is still an open question. In this article, the early hypothesis of Zipf of a principle of least effort for explaining the law is shown to be sound. Simultaneous minimization in the effort of both hearer and speaker is formalized with a simple optimization process operating on a binary matrix of signal–object associations. Zipfs law is found in the transition between referentially useless systems and indexical reference systems. Our finding strongly suggests that Zipfs law is a hallmark of symbolic reference and not a meaningless feature. The implications for the evolution of language are discussed. We explain how language evolution can take advantage of a communicative phase transition.

Two Regimes in the Frequency of Words and the Origins of Complex Lexicons: Zipf’s Law Revisited∗

Zipf’s law states that the frequency of a word is a power function of its rank. The exponent of the power is usually accepted to be close to (-)1. Great deviations between the predicted and real number of different words of a text, disagreements between the predicted and real exponent of the probability density function and statistics on a big corpus, make evident that word frequency as a function of the rank follows two different exponents, ˜(-)1 for the first regime and ˜(-)2 for the second. The implications of the change in exponents for the metrics of texts and for the origins of complex lexicons are analyzed.

Optimization in complex networks

Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous distributions of links, providing an extraordinary source of robustness against perturbations. Although most theories concerning the origin of these topologies use growing graphs, here we show that a simple optimization process can also account for the observed regularities displayed by most complex nets. Using an evolutionary algorithm involving minimization of link density and average distance, four major types of networks are encountered: (a) sparse exponential-like networks, (b) sparse scale-free networks, (c) star networks and (d) highly dense networks, apparently defining three major phases. These constraints provide a new explanation for scaling of exponent about -3. The evolutionary consequences of these results are outlined.

The consequences of Zipf's law for syntax and symbolic reference

Although many species possess rudimentary communication systems, humans seem to be unique with regard to making use of syntax and symbolic reference. Recent approaches to the evolution of language formalize why syntax is selectively advantageous compared with isolated signal communication systems, but do not explain how signals naturally combine. Even more recent work has shown that if a communication system maximizes communicative efficiency while minimizing the cost of communication, or if a communication system constrains ambiguity in a non-trivial way while a certain entropy is maximized, signal frequencies will be distributed according to Zipfs law. Here we show that such communication principles give rise not only to signals that have many traits in common with the linking words in real human languages, but also to a rudimentary sort of syntax and symbolic reference.

ZIPF'S LAW AND RANDOM TEXTS

Random-text models have been proposed as an explanation for the power law relationship between word frequency and rank, the so-called Zipfs law. They are generally regarded as null hypotheses rather than models in the strict sense. In this context, recent theories of language emergence and evolution assume this law as a priori information with no need of explanation. Here, random texts and real texts are compared through (a) the so-called lexical spectrum and (b) the distribution of words having the same length. It is shown that real texts fill the lexical spectrum much more efficiently and regardless of the word length, suggesting that the meaningfulness of Zipfs law is high.

Quantifying the Semantic Contribution of Particles

Certain word types of natural languages - conjunctions, articles, prepositions and some verbs - have a very low or very grammatically marked semantic contribution. They are usually named functional categories or relational items. Recently, the possibility of considering prepositions as simple parametrical variations of semantic features instead of categorial features or as the irrelevance of such categorial features has been pointed out. The discussion about such particles has been and still is widespread and controversial. Nonetheless, there is no quantitative evidence of such semantic weakness and no satisfactory evidence against the coexistence of categorial requirements and the fragility of the semantic aspects. This study aims to quantify the semantic contribution of particles and presents some corpora-based results for English that suggest that such weakness and its relational uncertainty come from the categorial irrelevance mentioned before.