Perception of Elementary Mathematical Objects: Geometric Shapes, Patterns, and Graphs
There is no human culture without material symbols, often abstract and organized according to obvious geometric regularities. Maps, diagrams, decorative and architectural motifs, paintings and body ornaments all reflect the beginnings of abstract, proto-mathematical thought. How can we understand and model mental objects such as straight lines, circles and squares ? Are they unique to our species, or are these concepts accessible to other animals ? What are their cerebral mechanisms ? Can they be modeled by artificial neural networks ? From children's drawings to the geometric symbols that decorate the walls of decorated caves, from perception to graphic production, from static forms to musical sequences, and from prehistory to the present day, the lecture will attempt to provide an overview of recent research into the origins of the most elementary mathematical objects in geometry.