A language of thought for the mental representation of geometric shapes

ElsevierVolume 139, December 2022, 101527Cognitive PsychologyAuthor links open overlay panelHighlights•

Some geometrical shapes are universally attested in humans, but not other animals.

We formalize the hypothesis of a compositional language of thought for shapes.

We argue for modeling human shape perception as program induction.

We provide empirical evidence of our proposal and outline the space of alternatives.

Abstract

In various cultures and at all spatial scales, humans produce a rich complexity of geometric shapes such as lines, circles or spirals. Here, we propose that humans possess a language of thought for geometric shapes that can produce line drawings as recursive combinations of a minimal set of geometric primitives. We present a programming language, similar to Logo, that combines discrete numbers and continuous integration to form higher-level structures based on repetition, concatenation and embedding, and we show that the simplest programs in this language generate the fundamental geometric shapes observed in human cultures. On the perceptual side, we propose that shape perception in humans involves searching for the shortest program that correctly draws the image (program induction). A consequence of this framework is that the mental difficulty of remembering a shape should depend on its minimum description length (MDL) in the proposed language. In two experiments, we show that encoding and processing of geometric shapes is well predicted by MDL. Furthermore, our hypotheses predict additive laws for the psychological complexity of repeated, concatenated or embedded shapes, which we confirm experimentally.

Keywords

Geometry

Program induction

Shape perception

Language of thought

Complexity in cognition

Compositionality

Data availability

The data from the experiment, the scripts to generate the figures and statistical analyses performed, an interpreter for our language, and a modified version of DreamCoder to handle it are provided in an Open Science Framework repository: https://osf.io/zcb64/?view_only=7abbac57edf34b5ab98e976da1a79b6b.

The latest version of DreamCoder is available online on GitHub https://github.com/ellisk42/ec.

The reader can test our language for geometric shapes by using the following online interpreter: https://private.unicog.org/msm/LoT_Geometric_Shapes.html.

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