Adults and 5-year-old children draw rectangles and triangles around a prototype but not in the golden ratio

Hearing elliptic movements reveals the imprint of action on prototypical geometries

Within certain categories of geometric shapes, prototypical exemplars that best characterize the category have been evidenced. These geometric prototypes are classically identified through the visual and haptic perception or motor production and are usually characterized by their spatial dimension. However, whether prototypes can be recalled through the auditory channel has not been formally investigated. Here we address this question by using auditory cues issued from timbre-modulated friction sounds evoking human drawing elliptic movements. Since non-spatial auditory cues were previously found useful for discriminating distinct geometric shapes such as circles or ellipses, it is hypothesized that sound dynamics alone can evoke shapes such as an exemplary ellipse. Four experiments were conducted and altogether revealed that a common elliptic prototype emerges from auditory, visual, and motor modalities. This finding supports the hypothesis of a common coding of geometric shapes according to biological rules with a prominent role of sensory-motor contingencies in the emergence of such prototypical geometry.

Visual foundations of Euclidean geometry

Geometry defines entities that can be physically realized in space, and our knowledge of abstract geometry may therefore stem from our representations of the physical world. Here, we focus on Euclidean geometry, the geometry historically regarded as "natural". We examine whether humans possess representations describing visual forms in the same way as Euclidean geometry - i.e., in terms of their shape and size. One hundred and twelve participants from the U.S. (age 3-34 years), and 25 participants from the Amazon (age 5-67 years) were asked to locate geometric deviants in panels of 6 forms of variable orientation. Participants of all ages and from both cultures detected deviant forms defined in terms of shape or size, while only U.S. adults drew distinctions between mirror images (i.e. forms differing in "sense"). Moreover, irrelevant variations of sense did not disrupt the detection of a shape or size deviant, while irrelevant variations of shape or size did. At all ages and in both cultures, participants thus retained the same properties as Euclidean geometry in their analysis of visual forms, even in the absence of formal instruction in geometry. These findings show that representations of planar visual forms provide core intuitions on which humans' knowledge in Euclidean geometry could possibly be grounded.

A Special Golden Curve in Human Upper Limbs' Length Proportion: A Functional Partition Which Is Different from Anatomy

Aim. The purpose of this study was to investigate the relationship between upper limbs' three functional partitions and the golden curve. Materials and Methods. We measured 30 subjects' right or left upper limb data and investigate the relationship between them and the golden curve by use of SPSS version 20.0 statistical software (SPSS, Inc., Chicago, Illinois), one-sample t-test. Results. There are four points on human's upper limbs which have no difference with the four points on the golden curve. And there is one point of which the difference is obvious. But we still could draw the conclusion that human upper limbs are accordant with the golden curve. Conclusion. Human upper limbs are accordant with the golden curve.

The haptic recognition of geometrical shapes in congenitally blind and blindfolded adolescents: is there a haptic prototype effect?

BACKGROUND

It has been shown that visual geometrical shape categories (rectangle and triangle) are graded structures organized around a prototype as demonstrated by perception and production tasks in adults as well as in children. The visual prototypical shapes are better recognized than other exemplars of the categories. Their existence could emerge from early exposure to these prototypical shapes that are present in our visual environment. The present study examined the role of visual experience in the existence of prototypical shapes by comparing the haptic recognition of geometrical shapes in congenitally blind and blindfolded adolescents.

METHODOLOGY/PRINCIPAL FINDINGS

To determine whether the existence of a prototype effect (higher recognition of prototypical shapes than non prototypical shapes) depended on visual experience, congenitally blind and blindfolded sighted adolescents were asked to recognize in the haptic modality three categories of correct shapes (square, rectangle, triangle) varying in orientation (prototypical/canonical orientation vs. non prototypical/canonical orientation rotated by 45°) among a set of other shapes. A haptic prototype effect was found in the blindfolded sighted whereas no difference between prototypical and non prototypical correct shapes was observed in the congenitally blind. A control experiment using a similar visual recognition task confirmed the existence of a visual prototype effect in a group of sighted adolescents.

CONCLUSION/SIGNIFICANCE

These findings show that the prototype effect is not intrinsic to the haptic modality but depends on visual experience. This suggests that the occurrence of visual and haptic prototypical shapes in the recognition of geometrical shape seems to depend on visual exposure to these prototypical shapes existing in our environment.