Arithmetic Notation…now in 3D!

When people reason formally, they often make use of special notations—algebra and arithmetic are familiar examples. These notations are often treated as mere shorthand—a concise way of referring to meaningful mathematical concepts. Other authors have argued that people treat notations as pictures—literal diagrams of an imagined set of objects (Dörfler, 2003; Landy Goldstone, 2009). If notations depict objects that exist in space, then it makes sense to wonder how they are arranged not just in the two visible dimensions, but in depth. In four experiments, we find a consistent pattern: properties that increase mathematical precedence also tend to make objects appear closer in space. This alignment of formal pressures and informal pressures suggests that perceived depth may play a role in supporting computational reasoning processes. Although our primary focus is documenting the existence of depth illusions in notations, we also evaluate several sources of information that might guide depth judgments: availability of an object for computational actions, formal syntactic structure, relative symbol salience and voluntary attention shifts. We consider relationships between these nonexclusive possible sources of information in guiding how people judge depth in mathematics

Intention and motor representation in purposive action

Are there distinct roles for intention and motor representation in explaining the purposiveness of action? Standard accounts of action assign a role to intention but are silent on motor representation. The temptation is to suppose that nothing need be said here because motor representation is either only an enabling condition for purposive action or else merely a variety of intention. This paper provides reasons for resisting that temptation. Some motor representations, like intentions, coordinate actions in virtue of representing outcomes; but, unlike intentions, motor representations cannot feature as premises or conclusions in practical reasoning. This implies that motor representation has a distinctive role in explaining the purposiveness of action. It also gives rise to a problem: were the roles of intention and motor representation entirely independent, this would impair effective action. It is therefore necessary to explain how intentions interlock with motor representations. The solution, we argue, is to recognise that the contents of intentions can be partially determined by the contents of motor representations. Understanding this content-determining relation enables better understanding how intentions relate to actions

Sharing Space: The Presence of Other Bodies Extends the Space Judged as Near

Background: As social animals we share the space with other people. It is known that perceived extension of the peripersonal space (the reaching space) is affected by the implicit representation of our own and other's action potentialities. Our issue concerns whether the co-presence of a body in the scene influences our extrapersonal space (beyond reaching distance) categorization. Methodology/Principal Findings: We investigated, through 3D virtual scenes of a realistic environment, whether egocentric spatial categorization can be influenced by the presence of another human body (Exp. 1) and whether the effect is due to her action potentialities or simply to her human-like morphology (Exp. 2). Subjects were asked to judge the location ("Near" or "Far") of a target object located at different distances from their egocentric perspective. In Exp. 1, the judgment was given either in presence of a virtual avatar (Self-with-Other), or a non-corporeal object (Self-with-Object) or nothing (Self). In Exp. 2, the Self condition was replaced by a Self-with-Dummy condition, in which an inanimate body (a wooden dummy) was present. Mean Judgment Transition Thresholds (JTTs) were calculated for each subject in each experimental condition. Self-with-Other condition induced a significant extension of the space judged as "Near" as compared to both the Selfwith- Object condition and the Self condition. Such extension was observed also in Exp. 2 in the Self-with-Dummy condition. Results suggest that the presence of others impacts on our perception of extrapersonal space. This effect holds also when the other is a human-like wooden dummy, suggesting that structural and morphological shapes resembling human bodies are sufficient conditions for the effect to occur. Conclusions: The observed extension of the portion of space judged as near could represent a wider portion of "accessible" space, thus an advantage in the struggle to survive in presence of other potential competing individuals

Using a Stick Does Not Necessarily Alter Judged Distances or Reachability

Background It has been reported that participants judge an object to be closer after a stick has been used to touch it than after touching it with the hand. In this study we try to find out why this is so. Methodology We showed six participants a cylindrical object on a table. On separate trials (randomly intermixed) participants either estimated verbally how far the object is from their body or they touched a remembered location. Touching was done either with the hand or with a stick (in separate blocks). In three different sessions, participants touched either the object location or the location halfway to the object location. Verbal judgments were given either in centimeters or in terms of whether the object would be reachable with the hand. No differences in verbal distance judgments or touching responses were found between the blocks in which the stick or the hand was used. Conclusion Instead of finding out why the judged distance changes when using a tool, we found that using a stick does not necessarily alter judged distances or judgments about the reachability of objects

The impact of using an upper-limb prosthesis on the perception of real and illusory weight differences

Little is known about how human perception is affected using an upper-limb prosthesis. To shed light on this topic, we investigated how using an upper-limb prosthesis affects individuals’ experience of object weight. First, we examined how a group of upper-limb amputee prosthetic users experienced real mass differences and illusory weight differences in the context of the ‘size-weight’ illusion. Surprisingly, the upper-limb prosthetic users reported a markedly smaller illusion than controls, despite equivalent perceptions of a real mass difference. Next, we replicated this dissociation between real and illusory weight perception in a group of non-amputees who lifted the stimuli with an upper-limb myoelectric prosthetic simulator, again noting that the prosthetic users experienced illusory, but not real, weight differences as being weaker than controls. These findings not only validate the use of a prosthetic simulator as an effective tool for investigating perception and action, but also highlight a surprising dissociation between the perception of real and illusory weight differences

Changing the size of a mirror-reflected hand moderates the experience of embodiment but not proprioceptive drift: a repeated measures study on healthy human participants.

Mirror visual feedback is used for reducing pain and visually distorting the size of the reflection may improve efficacy. The findings of studies investigating size distortion are inconsistent. The influence of the size of the reflected hand on embodiment of the mirror reflection is not known. The aim of this study was to compare the effect of magnifying and minifying mirror reflections of the hand on embodiment measured using an eight-item questionnaire and on proprioceptive drift. During the experiment, participants (n = 45) placed their right hand behind a mirror and their left hand in front of a mirror. Participants watched a normal-sized, a magnified and a minified reflection of the left hand while performing synchronised finger movements for 3 min (adaptive phase). Measurements of embodiment were taken before (pre) and after (post) synchronous movements of the fingers of both hands (embodiment adaptive phase). Results revealed larger proprioceptive drift post-adaptive phase (p = 0.001). Participants agreed more strongly with questionnaire items associated with location, ownership and agency of the reflection of the hand post-adaptive phase (p < 0.001) and when looking at the normal-sized reflection (p < 0.001). In conclusion, irrespective of size, watching a reflection of the hand while performing synchronised movements enhances the embodiment of the reflection of the hand. Magnifying and minifying the reflection of the hand has little effect on proprioceptive drift, but it weakens the subjective embodiment experience. Such factors need to be taken into account in future studies using this technique, particularly when assessing mirror visual feedback for pain management

Influence of Motor Planning on Distance Perception within the Peripersonal Space

We examined whether movement costs as defined by movement magnitude have an impact on distance perception in near space. In Experiment 1, participants were given a numerical cue regarding the amplitude of a hand movement to be carried out. Before the movement execution, the length of a visual distance had to be judged. These visual distances were judged to be larger, the larger the amplitude of the concurrently prepared hand movement was. In Experiment 2, in which numerical cues were merely memorized without concurrent movement planning, this general increase of distance with cue size was not observed. The results of these experiments indicate that visual perception of near space is specifically affected by the costs of planned hand movements

Distorted body representations are robust to differences in experimental instructions

Several recent reports have shown that even healthy adults maintain highly distorted representations of the size and shape of their body. These distortions have been shown to be highly consistent across different study designs and dependent measures. However, previous studies have found that visual judgments of size can be modulated by the experimental instructions used, for example, by asking for judgments of the participant’s subjective experience of stimulus size (i.e., apparent instructions) versus judgments of actual stimulus properties (i.e., objective instructions). Previous studies investigating internal body representations have relied exclusively on ‘apparent’ instructions. Here, we investigated whether apparent versus objective instructions modulate findings of distorted body representations underlying position sense (Exp. 1), tactile distance perception (Exp. 2), as well as the conscious body image (Exp. 3). Our results replicate the characteristic distortions previously reported for each of these tasks and further show that these distortions are not affected by instruction type (i.e., apparent vs. objective). These results show that the distortions measured with these paradigms are robust to differences in instructions and do not reflect a dissociation between perception and belief