The Force of Numbers: Investigating Manual Signatures of Embodied Number Processing

Open hands, large numbers: manual gestures influence random number generation

Several studies suggest that numerical cognition interacts with spatial cognition. Here, we explored spatial-numerical associations through the lens of manual gestures. We asked English and Italian participants to generate 'random' sequences of numbers while simultaneously moving the hands outwards, away from the torso, or inwards, towards the mid center of the body. These manual gestures were modeled after gestures that are common in naturally occurring numerical discourse, such as when people talk about "huge numbers" or "tiny numbers." Results showed that in both participant groups, outwards movements coincided with relatively larger numbers compared to inwards movements, for which generated numbers were smaller. This effect was small in magnitude. We also explored individual differences and found that self-reported numeracy as well as levels of gesture production and perception modulated the effect of our gesture manipulation very little, if at all.

Invariant representations in abstract concept grounding - the physical world in grounded cognition

Grounded cognition states that mental representations of concepts consist of experiential aspects. For example, the concept "cup" consists of the sensorimotor experiences from interactions with cups. Typical modalities in which concepts are grounded are: The sensorimotor system (including interoception), emotion, action, language, and social aspects. Here, we argue that this list should be expanded to include physical invariants (unchanging features of physical motion; e.g., gravity, momentum, friction). Research on physical reasoning consistently demonstrates that physical invariants are represented as fundamentally as other grounding substrates, and therefore should qualify. We assess several theories of concept representation (simulation, conceptual metaphor, conceptual spaces, predictive processing) and their positions on physical invariants. We find that the classic grounded cognition theories, simulation and conceptual metaphor theory, have not considered physical invariants, while conceptual spaces and predictive processing have. We conclude that physical invariants should be included into grounded cognition theories, and that the core mechanisms of simulation and conceptual metaphor theory are well suited to do this. Furthermore, conceptual spaces and predictive processing are very promising and should also be integrated with grounded cognition in the future.

Spontaneous grip force fluctuations mirror semantic numerical magnitude processing: Larger numbers elicit larger forces

This study investigated the relationship between semantic numerical magnitudes and motor magnitudes. We asked whether the processing of numbers can affect motor behavior such as the size of numbers affecting the size of motor actions. For this, we recorded continuous grip force fluctuations from 43 healthy adults during a symbolic magnitude comparison task. We found that numbers induced spontaneous grip force fluctuations during number processing. Smaller numbers induced lower grip forces, whereas larger numbers induced larger forces. This result constitutes strong behavioral support for a generalized magnitude processing by continuously quantifying the response that challenges binary accounts of cross-domain interactions.

Do numbers make us handy? Behavioral and electrophysiological evidence for number-hand congruency effect

Finger counting facilitates numerical representations and mathematical processing. The current study investigated the association between finger counting habits and number processing by employing behavioral and electrophysiological measures. We explored whether small and large numerical primes influence the recognition of embodied target hand stimuli. Twenty-four right-handed participants that were grouped into right-starters (n = 13) and left-starters (n = 11) for finger counting performed a hand recognition task that consisted of numerical magnitudes as prime and hand recognition as targets. Based on the finger counting habits, congruent (i.e., left-starters: small number/left hand or large number/right hand; right-starters: small number/right hand or large number/left hand) and incongruent (i.e., left-starters: large number/left hand or small number/right hand; right-starters: large number/right hand or small number/left hand) conditions were presented to the participants. The participants were required to indicate whether the targets were left or right hand by simply pressing the left or the right key, respectively. Results indicated faster reaction times (RTs) for congruent as opposed to incongruent trials for all participants. The mean amplitude of the centro-parietal P300 component was significantly increased for the incongruent compared to congruent condition, indicating increased mental effort. Also, analysis of the latency of the P300 in terms of congruency effect in all participants revealed significant results. These combined results provide behavioral and electrophysiological evidence indicating the embodied nature of numbers. The results are interpreted in light of the general findings related to the P300 component. This research supports the association of number-hand representations and corroborates the idea of embodied numerosity.

Abstract concepts: external influences, internal constraints, and methodological issues

There is a longstanding and widely held misconception about the relative remoteness of abstract concepts from concrete experiences. This review examines the current evidence for external influences and internal constraints on the processing, representation, and use of abstract concepts, like truth, friendship, and number. We highlight the theoretical benefit of distinguishing between grounded and embodied cognition and then ask which roles do perception, action, language, and social interaction play in acquiring, representing and using abstract concepts. By reviewing several studies, we show that they are, against the accepted definition, not detached from perception and action. Focussing on magnitude-related concepts, we also discuss evidence for cultural influences on abstract knowledge and explore how internal processes such as inner speech, metacognition, and inner bodily signals (interoception) influence the acquisition and retrieval of abstract knowledge. Finally, we discuss some methodological developments. Specifically, we focus on the importance of studies that investigate the time course of conceptual processing and we argue that, because of the paramount role of sociality for abstract concepts, new methods are necessary to study concepts in interactive situations. We conclude that bodily, linguistic, and social constraints provide important theoretical limitations for our theories of conceptual knowledge.

Spatial-numerical associations without a motor response? Grip force says 'Yes'

In numerical processing, the functional role of Spatial-Numerical Associations (SNAs, such as the association of smaller numbers with left space and larger numbers with right space, the Mental Number Line hypothesis) is debated. Most studies demonstrate SNAs with lateralized responses, and there is little evidence that SNAs appear when no response is required. We recorded passive holding grip forces in no-go trials during number processing. In Experiment 1, participants performed a surface numerical decision task ("Is it a number or a letter?"). In Experiment 2, we used a deeper semantic task ("Is this number larger or smaller than five?"). Despite instruction to keep their grip force constant, participants' spontaneous grip force changed in both experiments: Smaller numbers led to larger force increase in the left than in the right hand in the numerical decision task (500-700 ms after stimulus onset). In the semantic task, smaller numbers again led to larger force increase in the left hand, and larger numbers increased the right-hand holding force. This effect appeared earlier (180 ms) and lasted longer (until 580 ms after stimulus onset). This is the first demonstration of SNAs with passive holding force. Our result suggests that (1) explicit motor response is not a prerequisite for SNAs to appear, and (2) the timing and strength of SNAs are task-dependent. (216 words).

Reduced choice-confidence in negative numerals

Negative numbers are central in math. However, they are abstract, hard to learn, and manipulated slower than positive numbers regardless of math ability. It suggests that confidence, namely the post-decision estimate of being correct, should be lower than positives. We asked participants to pick the larger single-digit numeral in a pair and collected their implicit confidence with button pressure (button pressure was validated with three empirical signatures of confidence). We also modeled their choices with a drift-diffusion decision model to compute the post-decision estimate of being correct. We found that participants had relatively low confidence with negative numerals. Given that participants compared with high accuracy the basic base-10 symbols (0–9), reduced confidence may be a general feature of manipulating abstract negative numerals as they produce more uncertainty than positive numerals per unit of time.

Catch the star! Spatial information activates the manual motor system

Previous research demonstrated a close bidirectional relationship between spatial attention and the manual motor system. However, it is unclear whether an explicit hand movement is necessary for this relationship to appear. A novel method with high temporal resolution–bimanual grip force registration–sheds light on this issue. Participants held two grip force sensors while being presented with lateralized stimuli (exogenous attentional shifts, Experiment 1), left- or right-pointing central arrows (endogenous attentional shifts, Experiment 2), or the words "left" or "right" (endogenous attentional shifts, Experiment 3). There was an early interaction between the presentation side or arrow direction and grip force: lateralized objects and central arrows led to a larger increase of the ipsilateral force and a smaller increase of the contralateral force. Surprisingly, words led to the opposite pattern: larger force increase in the contralateral hand and smaller force increase in the ipsilateral hand. The effect was stronger and appeared earlier for lateralized objects (60 ms after stimulus presentation) than for arrows (100 ms) or words (250 ms). Thus, processing visuospatial information automatically activates the manual motor system, but the timing and direction of this effect vary depending on the type of stimulus.

"BreaThink": breathing affects production and perception of quantities

Cognition is shaped by signals from outside and within the body. Following recent evidence of interoceptive signals modulating higher-level cognition, we examined whether breathing changes the production and perception of quantities. In Experiment 1, 22 adults verbally produced on average larger random numbers after inhaling than after exhaling. In Experiment 2, 24 further adults estimated the numerosity of dot patterns that were briefly shown after either inhaling or exhaling. Again, we obtained on average larger responses following inhalation than exhalation. These converging results extend models of situated cognition according to which higher-level cognition is sensitive to transient interoceptive states.