The roles of motion, gesture, and embodied action in the processing of mathematical concepts

Motor strength as a feature of concepts and visual representations

In this article, we define motor strength as the extent to which a concept is associated with body movements and the motor system that guides body movements. We extend this notion to one of the features of visual representations of some concepts and discuss the role of the motor system in understanding concepts and visual representations that have a significant degree of motor strength. It is suggested that when a concept is understood in its literal sense, the employment of the motor system and gestures in processing that concept depends on its degree of motor strength. If a concept is understood in its metaphorical sense, the employment of the motor system and gestures is dependent on the degree of motor strength of the base of the metaphor through which that concept is understood. The degree of motor strength of a concept relies on its motor affordances and its associations with people's past experiences. Because the motor system plays an essential role in the grounding of many abstract concepts in the physical environment, the notion of motor strength can help psychologists acquire a clearer understanding of how concepts with varying degrees of motor strength are grounded in the physical environment.

Embodiment of infinity in mathematics

In this article, we discuss the embodiment of infinity as one of fundamental concepts in mathematics. In contrast to the embodiment of many other mathematical concepts, the embodiment of infinity is an endless dynamic process. In embodying +∞, an object moves rightward toward a previously-set limit and passes it. Then, a new limit is set on the right side of the moving object. The moving object continues its movement and passes it as well. The moving object can pass any limit. In other words, there is no impassable limit for it. In embodying -∞, a similar process happens but the movement is leftward. Embodiment of infinitely small quantities has a basic similarity to the embodiment of infinitely large quantities, although it is different in some respects. We call the embodiment of infinity as iterative embodiment. It is iterative because the process of setting a new limit and passing it is repeated endlessly. Finally, it is suggested that in the process of embodying infinitely large and infinitely small quantities, the visual system and the motor system play important roles, as this process involves spatial concepts and movement.

The role of perceptual and action effector strength of graphs and bases of mathematical metaphors in the metaphorical processing of mathematical concepts

Metaphors that describe an abstract concept in terms of a motion concept are widely used to enhance our understanding of abstract concepts. These metaphors are used not only in our daily language but also in learning mathematics. As an example, in the process of understanding the abstract representation of a mathematical concept, a graphical representation may play the role of a mediatory domain. This graphical representation could have a high degree of perceptual and action effector strength. This is particularly the case when a gestures (as a motion) is used to depict the graphical representation. After looking at this example, we discuss perceptual and action effector strength of the base domains of several mathematical metaphors that describe mathematical concepts in terms of spatial and motion concepts. Then, based on the data in the Lancaster Sensorimotor Norms, it is suggested that high degrees of perceptual and action effector strength of the base domains of these metaphors play an important role in the grounding of abstract mathematical concepts in the physical environment.

Gestural Embodiment of Intensifiers in Iconic, Metaphoric, and Beat Gestures

This study aimed to examine the gestural embodiment of intensifiers in iconic and metaphoric gestures when these words are used with literal and metaphoric statements. We asked a group of Persian native speakers to listen to and then retell a set of Persian stories. In these stories, a number of intensifiers were used with literal and metaphoric sentences. The results showed that when an intensifier was used with a literal sentence, there was a higher probability of using an iconic or beat gesture than when there was no intensifier in the sentence. Also, when an intensifier was used with a metaphoric sentence, there was a higher probability of using a metaphoric or beat gesture than when the sentence contained no intensifier. These results suggested that an intensifier in a literal or metaphoric sentence can strengthen the mental simulation and the embodiment of objects, ideas, or situations. When an intensifier is used with a literal or metaphoric sentence, the strength of activation in the premotor areas may be amplified and spread to motor areas. In contrast, when no such intensifier is used in a literal or metaphoric sentence, there is a higher probability of simulation in premotor areas without spreading to the primary motor areas. The production of an internal force and expressing emphasis are two other possibilities that may explain the higher use of gestures with intensifiers.

The Impact of Manner Adverb on the Gestural Embodiment of Actions Described by Literal and Metaphoric Sentences

The aim of this study was to examine the impact of manner adverbs on the gestural embodiment of actions that are described by literal and metaphoric sentences. We asked a group of participants to read and then orally retell four stories. Each story had two versions. In one version, literal and metaphoric sentences describing literal and metaphorical actions did not include manner adverbs. In the other version of each story, the same sentences included a manner adverb that provided more information about literal or metaphoric actions. Participants' reproductions of stories were recorded with a camera and were analyzed to make a comparison between gestures that accompanied sentences that included a manner adverb and sentences that did not include a manner adverb. The results showed that when literal and metaphoric sentences included a manner adverb, there was a higher probability of using a gesture than when these sentences were used without a manner adverb. In other words, using a manner adverb increases the probability of using a gesture with literal and metaphorical sentences. Therefore, it is suggested that adding a manner adverb to a literal or metaphoric sentence can strengthen the process of embodiment of the action described in that sentence. We present two explanations for this observation.

How can transforming representation of mathematical entities help us employ more cognitive resources?

This article discusses the cognitive process of transforming one representation of mathematical entities into another representation. This process, which has been called mathematical metaphor, allows us to understand and embody a difficult-to-understand mathematical entity in terms of an easy-to-understand entity. When one representation of a mathematical entity is transformed into another representation, more cognitive resources such as the visual and motor systems can come into play to understand the target entity. Because of their nature, some curves, which are one group of visual representations, may have a great motor strength. It is suggested that directedness, straightness, length, and thinness are some possible features that determine degree of motor strength of a curve. Another possible factor that can determine motor strength of a curve is the strength of association between shape of the curve and past experiences of the observer (and her/his prior knowledge). If an individual has had the repetitive experience of observing objects moving along a certain curve, the shape of the curve may have a great motor strength for her/him. In fact, it can be said that some kind of metonymic relationship may be formed between the shapes of some curves and movement experiences.

Distributed embodiment of metaphorical hope in hand, head, and eyebrow gestures

This study aimed to examine the embodied conceptualization of hope through metaphors. We asked a group of participants to discuss their hopes in a semi-structured interview. We examined the types of hand, head, and eyebrow gestures produced when they were talking about their future hopes. The obtained results showed that when participants talked about their future hopes, they mainly used forward hand gestures, rightward head gestures, and upward eyebrow gestures. Based on these results, it is suggested that various semantic components and emotional associations of hope are metaphorically embodied in different manners in various parts of the body. The future aspect of hope is conceptualized as a forward movement and is embodied as a forward hand gesture. The good or positive emotional aspect associated with future hopes is metaphorically conceptualized as a rightward head gesture or an upward eyebrow gesture. We call this process distributed embodiment of a metaphorical concept. Our proposal is supported by the findings of past studies that have found future is metaphorically embodied as something in front of us (or forward movement), and good is metaphorically embodied as upper space (or upward movement) or right side (or rightward movement).