The language of geometry: Fast comprehension of geometrical primitives and rules in human adults and preschoolers

Abstract

During language processing, humans form complex embedded representations from sequential inputs. Here, we ask whether a “geometrical language” with recursive embedding also underlies the human ability to encode sequences of spatial locations. We introduce a novel paradigm in which subjects are exposed to a sequence of spatial locations on an octagon, and are asked to predict future locations. The sequences vary in complexity according to a well-defined language comprising elementary primitives and recursive rules. A detailed analysis of error patterns indicates that primitives of symmetry and rotation are spontaneously detected and used by adults, preschoolers, and adult members of an indigene group in the Amazon, the Munduruku, who have a restricted numerical and geometrical lexicon and limited access to schooling. Furthermore, subjects readily combine these geometrical primitives into hierarchically organized expressions. By evaluating a large set of such combinations, we obtained a first view of the language needed to account for the representation of visuospatial sequences in humans, and conclude that they encode visuospatial sequences by minimizing the complexity of the structured expressions that capture them.

Bayesian selection of grammar productions for the language of thought

“…In the same way, adults use more repetitions than children. This could mean that the ideal learner is capable of reproducing the sequences by recursively embedding other smaller programs, whereas adults and children more so have problems understanding or learning the smaller concept that can explain all the sequences from the experiments, which is consistent with the results from the MDL model in (Amalric et al, 2017).…”

“…The LoT is not necessarily unique. In fact, the form that it takes has been modeled in many different ways depending on the problem domain: nu-merical concept learning (Piantadosi, Tenenbaum, & Goodman, 2012), sequence learning (Amalric et al, 2017;Romano, Sigman, & Figueira, 2013;Yildirim & Jacobs, 2015), visual concept learning (Ellis, Solar-Lezama, & Tenenbaum, 2015), theory learning (Ullman, Goodman, & Tenenbaum, 2012), etc.…”

“…Most studies of LoTs have focused on the compositional aspect of the language, which has either been modeled within a Bayesian (Tenenbaum et al, 2011) or a Minimum Description Length (MDL) framework (Amalric et al, 2017;Goldsmith, 2001Goldsmith, , 2002Romano et al, 2013).…”

“…In the next section we formalize this procedure and then apply it on the language of geometry presented by Amalric et al (2017) in a recent study about geometrical sequence learning. This LoT de-fines a language with some basic geometric instructions as the grammar productions and then models their composition within the MDL framework.…”

Neurophysiological dynamics of phrase-structure building during sentence processing

“…A similar compression effect, called "chunking," has been described when lists of numbers are committed to working memory (48). Similarly, memory for spatial sequences has recently been shown to involve an internal compression based on nested geometrical regularities, with the rate of errors being proportional to "minimal description length"-that is, the size of the internal representation after compression (49). Tree structures and tree-based compression may therefore characterize many domains of human information processing (50,51).…”