Following on from the 2015-2016 lecture devoted to the cerebral representation of linguistic structures, the 2016-2017 lecture focused on other related cognitive faculties that seem to be characteristic of the human species. Our species is the only one not only to express itself in words, but also to create vast mathematical, computer or musical systems. In all these fields, the human species has a singular ability to create and manipulate embedded symbolic structures: these are "languages" in the broadest sense of the word. This raises the question: does a single brain mechanism underlie these different languages? Or has evolution endowed the human brain with distinct mechanisms for representing symbolic structures, specific to each domain?
The question of "brain languages" plays a central role in contemporary reflection on the origins of our species' uniqueness. Marc Hauser, along with Tecumseh Fitch and Noam Chomsky, postulates that the appearance of the human faculty of language originates in the emergence of a unique operation: recursion, i.e. the ability to produce complex representations by embedding them one within the other, ad infinitum. But is recursion an adaptation to communication, restricted to natural language? Or does it apply to many fields? In 2016, Marc Hauser and Jeffrey Watumull hypothesized that the human species is characterized by a "universalgrammar faculty":
[this faculty] and its interfaces to the different domains of knowledge enable the generation of hierarchical (actually fractal) structures, ad infinitum, which representations are then "exapted" for language, mathematics, music, and moral sense. These different domains differ only in the values (words, numbers, notes, events) that are substituted for variables in generative procedures.
The same authors point out that, in the current state of knowledge :
[...] in most of the animal world, even where there is some evidence for the existence of generative procedures at the level of regular languages (the lowest level of Chomsky's hierarchy), there is no evidence that these procedures underlie both recognition and production [of sequences] in several domains.
Thus, the human brain may well be the only one to possess recursive generative models common to several domains of knowledge (an idea also developed by Josh Tenenbaum and detailed in a previous lecture on the "Bayesian brain").
The aim of the 2016-2017 lecture was to evaluate this hypothesis by reviewing the available data concerning the organization of mental representations in three domains: natural language, music and mathematics. Despite obvious surface differences, we tried to identify parallels between these three domains: can we, without falling into an inappropriate metaphor, speak of a mathematical language or a musical language?