Internal Frame Of Reference Research Articles

Superposed transpressional tectonics of an intraterrane shear zone resulted in Shillong plateau evolution, NE India

The analysis of shear zone kinematics plays a crucial role in understanding the tectonics at micro-, meso-, and regional scales within a given terrane. This study focuses on investigating the kinematics of prominent asymmetric structural features preserved within the Barapani Shear Zone (BSZ). These features are utilized to establish vorticity numbers in relation to the reference frames of the BSZ. Typically, shear zones provide finite values for kinematics and vorticity numbers. The BSZ is identified as an intraterrane, multiply deformed shear zone within the Shillong Plateau, which exhibits varying kinematics and vorticity numbers measured across different deformation zones.The research reveals that the BSZ underwent successive D1, D2, D3, and D4 events, resulting in preserved S1, S2, and S3 planar fabrics, with D4 evidenced by brittle deformation features. However, determining shear zone kinematics purely based on the orientation of these planar fabrics and mineral lineation with respect to the external reference frame is insufficient. Consequently, this study calculates vorticity numbers and kinematics by considering both the external and internal reference frames of the BSZ. The study suggests that superposed transpressional tectonics prevailed during D2 and D3 events.

Mathematics education faculty members' perceptions of barriers to distance education: Q-method analysis

As a result of the great earthquake disaster in Turkey, mathematics education in universities was reorganized as distance education after the pandemic period. This article aims to identify the barriers to distance education practices in higher education. In line with the aim of this study; Q methodology was used to help determine the perceptions and perspectives of faculty members regarding the barriers to distance education in the process of teaching mathematics in higher education. Q methodology aims to reveal the internal frame of reference of individuals through their preferences. According to the findings of the study, participants identified barriers under 3 factors. These 3 factors, in order of weight, represent student, curriculum and technology barriers. In general, it was seen that the 4 factors revealed by the methodology in the study yielded results compatible with the literature. However, it was determined that the barriers arising from the teacher did not carry a factor load in the study. Another unique result was the identification of barriers arising from the nature of mathematics. It was understood that there are unique obstacles specific to the field of mathematics due to pedagogy and curriculum. In this respect, investigating the barriers to field-specific extended education will provide more accurate findings. In this study, which was conducted with Q methodology and supported by qualitative data, the identified barriers to distance education were consistent with the general literature. Q methodology reveals that it is a compatible tool for various research in similar situations.

Temporal and spatial reference frames in visual working memory are defined by ordinal and relational properties.

Natural environments provide a rich spatiotemporal context that allows for visual objects to be differentiated based on different types of information: their absolute or relative spatial or temporal coordinates, or their ordinal positions in a spatial or temporal sequence. Here, we investigated which spatial and temporal properties are incidentally encoded along with to-be-remembered features to provide reference frames in visual working memory (VWM). We tested the different possibilities in a spatiotemporal color change-detection task by transforming spatial and/or temporal structures of item presentation at retrieval relative to encoding. More precisely, spatial and/or temporal coordinates were (a) switched, changing the order of items in a spatial or temporal sequence (ordinal transformation); (b) multiplied by different factors, changing interitem distances (relational transformation); or (c) multiplied by a constant factor, expanding or shrinking the entire configuration (global transformation). Such transformations of the external reference frame at retrieval should only interfere with VWM if the internal reference frame relies on the spatial or temporal properties affected by the respective transformation. We found that ordinal and relational transformations of either the spatial or temporal structure impaired performance, whereas global transformations did not. Thus, reference frames appear to be primarily defined by interitem relations-including relative distances between items as well as their order-rather than absolute positions in space or time. These results corroborate and extend previous findings for the spatial domain, and highlight functional similarities of the spatial and temporal dimensions in VWM by revealing the same metrical properties for temporal reference frames. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Object representation in a gravitational reference frame.

When your head tilts laterally, as in sports, reaching, and resting, your eyes counterrotate less than 20%, and thus eye images rotate, over a total range of about 180°. Yet, the world appears stable and vision remains normal. We discovered a neural strategy for rotational stability in anterior inferotemporal cortex (IT), the final stage of object vision in primates. We measured object orientation tuning of IT neurons in macaque monkeys tilted +25 and -25° laterally, producing ~40° difference in retinal image orientation. Among IT neurons with consistent object orientation tuning, 63% remained stable with respect to gravity across tilts. Gravitational tuning depended on vestibular/somatosensory but also visual cues, consistent with previous evidence that IT processes scene cues for gravity's orientation. In addition to stability across image rotations, an internal gravitational reference frame is important for physical understanding of a world where object position, posture, structure, shape, movement, and behavior interact critically with gravity.

Enabling a New Methodology of Neural Coding: Multiplexing Temporal Encoding in Neuromorphic Computing

From rate to temporal encoding, spiking information processing has demonstrated advantages across diverse neuromorphic applications. In the aspects of data capacity and robustness, multiplexing encoding outperforms alternative encoding schemes. In this work, we aim to implement a new class of multiplexing temporal encoders, patterning stimuli in multiple timescales to improve the information processing capability, and robustness of systems deployed in noisy environments. Benefitted by the internal reference frame using subthreshold membrane oscillation (SMO), the encoded spike patterns are less sensitive to the input noise, increasing the encoder’s robustness. Our design results in a tremendous saving on power consumption and silicon area compared with the power-hungry analog-to-digital converters. Furthermore, a working prototype of the multiplexing temporal encoder built based on an interspike interval (ISI) encoding scheme is implemented on a silicon chip using the standard 180-nm CMOS process. To the best of our knowledge, our introduced encoder demonstrates the first integrated circuit (IC) implementation of neural encoding with multiplexing topology. Finally, the accuracy and efficiency of our design are evaluated through standard machine learning benchmarks, including Modified National Institute of Standards and Technology (MNIST), Canadian Institute For Advanced Research (CIFAR)-10, Street View House Number (SVHN), and spectrum sensing in high-speed communication networks. While our multiplexing temporal encoder demonstrates a higher classification accuracy across all the benchmarks, the power consumption and dissipated energy per spike reach merely <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2.6~\mu \text {W}$ </tex-math></inline-formula> and 95 fJ/spike, respectively, with an effective frame rate of 300 MHz. Compared with alternative encoding schemes, our multiplexing temporal encoder achieves at most 100% higher data capacity, 11.4% more accurate in classification, and 25% more robust against noise. Compared with the state-of-the-art designs, our work achieves up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$105 \times $ </tex-math></inline-formula> power efficiency without significantly increasing the silicon area.

A dinâmica do autoconceito da fala de um aluno de EFL: percepções a partir de experiências auto-relatadas e dados de observação em sala de aula

Abstract: This case study explores the dynamics of the English as a Foreign Language (EFL) speaking self-concept of a female university student. The study focuses on the participant’s internal and external frames of reference ( MERCER, 2011b) to analyze how her EFL speaking self-concept has been constructed throughout her years of English language instruction, and how it is re-constructed and developed in the current course. Findings show that such self-concept originates from beliefs systems, emotions, learner characteristics, previous English language learning context/method, critical experiences and experiences of success/failure using the oral language. Results indicate that critical positive experiences and perceived experiences of success appear to influence positively the learner’s self-efficacy beliefs and emotional experiences about the oral task.

Entanglement-Asymmetry Correspondence for Internal Quantum Reference Frames.

In the quantization of gauge theories and quantum gravity, it is crucial to treat reference frames such as rods or clocks not as idealized external classical relata, but as internal quantum subsystems. In the Page-Wootters formalism, for example, evolution of a quantum system S is described by a stationary joint state of S and a quantum clock, where time dependence of S arises from conditioning on the value of the clock. Here, we consider (possibly imperfect) internal quantum reference frames R for arbitrary compact symmetry groups, and show that there is an exact quantitative correspondence between the amount of entanglement in the invariant state on RS and the amount of asymmetry in the corresponding conditional state on S. Surprisingly, this duality holds exactly regardless of the choice of coherent state system used to condition on the reference frame. Averaging asymmetry over all conditional states, we obtain a simple representation-theoretic expression that admits the study of the quality of imperfect quantum reference frames, quantum speed limits for imperfect clocks, and typicality of asymmetry in a unified way. Our results shed light on the role of entanglement for establishing asymmetry in a fully symmetric quantum world.

FRAMES OF REFERENCE FOR PLACE DESIGNATION IN THE LITERARY REPORTAGE “DER WALD DER GESCHICHTE – IN DER GOTTSCHEEˮ BY KARL-MARKUS GAUSS

Spatial phenomena, including the location of the event, the distance between the characters, the characterization of characters through spatial conditions, the symbolization of action by spatial phenomena, spatial descriptions and topoi are extremely important for a narrative text. The key unit of space is the place, the functionality and reference systems of which are the subject of this study. The purpose of the study is to identify the frames of reference of the place in Karl-Markus Gauss’s literary reportage “Der Wald der Geschichte – In der Gottsche,” to conduct their lexical-stylistic analysis and to determine their functional potential. Taking into account the dynamism of the literary reportage and its diachronic component, the problem of the frame of reference was chosen as the central one, since in this way it is possible not only to ascertain the presence of a description of individual places, but also to determine how they relate to each other in the plane of the text. It has been revealed that the author uses absolute (internal, topological, georeferenced, metric) and deictic systems to depict places. The analysis showed that the text is dominated by referential and metrical systems, as well as their combination. Topological and internal frames of reference occur less often and usually in combination with the previous two, and the used deixis is still specifi ed by clarifi cations from the absolute frame of reference. This indicates the author’s desire to strengthen the documentary level of literary reportage. One of the defi ning motifs is the dichotomy “then-now”, which is also conveyed mostly through descriptions of individual places which the author compares with the past. The system of places in space successfully built by the author in the text not only helps the reader better navigate the described world, but also makes it possible to create an imaginary map of the area. It serves as a kind of medium for conveying the historical and cultural aspects of the life of Gottscheers. Through the imagination of individual places, the author managed to textualize, enliven and convey to a wide range of readers what remained in the memories of several people. The geographical journey acquires a historical character, because with each place Gauss opens a new vertical axis for the reader, presenting it in a diachronic section, based on his own observations, historical facts, memories of residents, and statistical data. Key words: frame of reference, place, space, literary reportage, Karl-Markus Gauss.

Perpendicular probing and screwing technique: A simple method for accurate pedicle screw placement based on the human internal reference frame for angle estimation.

The pedicle screw (PS) is widely used for spinal fixation surgery. However, PS malpositioning can cause critical complications; thus, the accuracy of ascertaining PS trajectory is paramount. This study aimed to demonstrate the accuracy and safety of a simple and cost-effective PS placement technique using a human internal reference frame for angle estimation. Ex vivo lumbar porcine spine samples were fixed to a wooden board with rostrocaudal and mediolateral rotational angles adjusted by two angle vises. PS entry points (EPs) were identified using clear anatomical vertebral landmarks. PS placement was performed on one side using the perpendicular probing and screwing technique (PPST), wherein the attitude angle of the sample was adjusted such that the longitudinal axis of the target pedicle was perpendicular to the ground. The pedicle probe and PS driver were manually maintained perpendicular to the ground during probing and PS placement. PS placement on the contralateral side was performed freehand as a control. Offsets between the preoperatively planned and implanted PS rotational angles measured using computed tomography for PPST and freehand method were analyzed. Pedicle wall penetration was also evaluated. The mean ± standard error of the medial rotational offsets was 5.83° ± 0.57° in the freehand group versus 2.89° ± 0.31° in the PPST group (p <0.001), and the rostrocaudal rotational offsets were 4.81° ± 0.65° in the freehand group versus 2.92° ± 0.45° in the PPST group (p = 0.01). The mean pedicle wall penetration distance was significantly reduced by PPST (0.28 ± 0.12 mm vs 0.80 ± 0.17 mm in the freehand group, p = 0.0071). Thus, PPST improved PS positioning accuracy, resulting in reduced pedicle wall penetration and increased PS placement safety. This simple technique is also potentially cost-effective for institutions without computer-assisted surgical systems.

Internal quantum reference frames for finite Abelian groups

Employing internal quantum systems as reference frames is a crucial concept in quantum gravity, gauge theories, and quantum foundations whenever external relata are unavailable. In this work, we give a comprehensive and self-contained treatment of such quantum reference frames (QRFs) for the case when the underlying configuration space is a finite Abelian group, significantly extending our previous work [M. Krumm, P. A. Höhn, and M. P. Müller, Quantum 5, 530 (2021)]. The simplicity of this setup admits a fully rigorous quantum information–theoretic analysis, while maintaining sufficient structure for exploring many of the conceptual and structural questions also pertinent to more complicated setups. We exploit this to derive several important structures of constraint quantization with quantum information–theoretic methods and to reveal the relation between different approaches to QRF covariance. In particular, we characterize the “physical Hilbert space”—the arena of the “perspective-neutral” approach—as the maximal subspace that admits frame-independent descriptions of purifications of states. We then demonstrate the kinematical equivalence and, surprising, dynamical inequivalence of the “perspective-neutral” and the “alignability” approach to QRFs. While the former admits unitaries generating transitions between arbitrary subsystem relations, the latter, remarkably, admits no such dynamics when requiring symmetry-preservation. We illustrate these findings by example of interacting discrete particles, including how dynamics can be described “relative to one of the subystems.”

Watching the Clocks: Interpreting the Page–Wootters Formalism and the Internal Quantum Reference Frame Programme

We discuss some difficulties that arise in attempting to interpret the Page–Wootters and Internal Quantum Reference Frames formalisms, then use a ‘final measurement’ approach to demonstrate that there is a workable single-world realist interpretation for these formalisms. We note that it is necessary to adopt some interpretation before we can determine if the ‘reference frames’ invoked in these approaches are operationally meaningful, and we argue that without a clear operational interpretation, such reference frames might not be suitable to define an equivalence principle. We argue that the notion of superposition should take into account the way in which an instantaneous state is embedded in ongoing dynamical evolution, and this leads to a more nuanced way of thinking about the relativity of superposition in these approaches. We conclude that typically the operational content of these approaches appears only in the limit as the size of at least one reference system becomes large, and therefore these formalisms have an important role to play in showing how our macroscopic reference frames can emerge out of wholly relational facts.

Phase coding of spatial representations in the human entorhinal cortex.

The grid-like activity pattern of cells in the mammalian entorhinal cortex provides an internal reference frame for allocentric self-localization. The same neurons maintain robust phase couplings with local field oscillations. We found that neurons of the human entorhinal cortex display consistent spatial and temporal phase locking between spikes and slow gamma band local field potentials (LFPs) during virtual navigation. The phase locking maintained an environment-specific map over time. The phase tuning of spikes to the slow gamma band LFP revealed spatially periodic phase grids with environment-dependent scaling and consistent alignment with the environment. Using a Bayesian decoding model, we could predict the avatar’s position with near perfect accuracy and, to a lesser extent, that of heading direction as well. These results imply that the phase of spikes relative to spatially modulated gamma oscillations encode allocentric spatial positions. We posit that a joint spatiotemporal phase code can implement the combined neural representation of space and time in the human entorhinal cortex.

Self-perception in anorexia nervosa: When the body becomes an object

ObjectiveWomen with anorexia nervosa (AN) act as if they have a larger body, as evidenced in obstacle avoidance tasks, where an allocentric perspective is adopted. This alteration emerges not only when they perform, but also when they imagine movements. However, no previous study has investigated own body centered tasks. As such, in this study we aim at documenting if women with AN show an altered behaviour also when the task requires a first-person perspective. MethodWe explored the performance of eleven woman affected by AN compared to eighteen matched controls, in two motor imagery tasks based on a self-frame of reference, the Hand Laterality Task and the Mental Motor Chronometry Task. Moreover, two control tasks relative to visual imagery were administered. ResultsIn the Hand Laterality Task, affected participants did not adopt a motor strategy to judge hands laterality (i.e. no biomechanical constraints effect). Crucially, they also showed an altered behavior in the control task. Similarly, they did not show the expected isochrony in the Mental Motor Chronometry Task, when actions pertained the left (but not the right) hand, in absence of any difference in the control task. ConclusionsOur findings reveal altered imagery processes in AN. Specifically, affected participants adopt a third-person, rather than a first-person perspective, even when the task requires to imagine their own body in an internal frame of reference. In other words, participants with AN objectify body stimuli. Different mechanisms (i.e., checking behaviour; mirror self-reflection; altered multisensory integration) can explain such an altered imagery in AN.

Imagine Your Crossed Hands as Uncrossed: Visual Imagery Impacts the Crossed-Hands Deficit.

Successful interaction with our environment requires accurate tactile localization. Although we seem to localize tactile stimuli effortlessly, the processes underlying this ability are complex. This is evidenced by the crossed-hands deficit, in which tactile localization performance suffers when the hands are crossed. The deficit results from the conflict between an internal reference frame, based in somatotopic coordinates, and an external reference frame, based in external spatial coordinates. Previous evidence in favour of the integration model employed manipulations to the external reference frame (e.g., blindfolding participants), which reduced the deficit by reducing conflict between the two reference frames. The present study extends this finding by asking blindfolded participants to visually imagine their crossed arms as uncrossed. This imagery manipulation further decreased the magnitude of the crossed-hands deficit by bringing information in the two reference frames into alignment. This imagery manipulation differentially affected males and females, which was consistent with the previously observed sex difference in this effect: females tend to show a larger crossed-hands deficit than males and females were more impacted by the imagery manipulation. Results are discussed in terms of the integration model of the crossed-hands deficit.

Evidence for an A-Modal Number Sense: Numerosity Adaptation Generalizes Across Visual, Auditory, and Tactile Stimuli.

Humans and other species share a perceptual mechanism dedicated to the representation of approximate quantities that allows to rapidly and reliably estimate the numerosity of a set of objects: an Approximate Number System (ANS). Numerosity perception shows a characteristic shared by all primary visual features: it is susceptible to adaptation. As a consequence of prolonged exposure to a large/small quantity (“adaptor”), the apparent numerosity of a subsequent (“test”) stimulus is distorted yielding a robust under- or over-estimation, respectively. Even if numerosity adaptation has been reported across several sensory modalities (vision, audition, and touch), suggesting the idea of a central and a-modal numerosity processing system, evidence for cross-modal effects are limited to vision and audition, two modalities that are known to preferentially encode sensory stimuli in an external coordinate system. Here we test whether numerosity adaptation for visual and auditory stimuli also distorts the perceived numerosity of tactile stimuli (and vice-versa) despite touch being a modality primarily coded in an internal (body-centered) reference frame. We measured numerosity discrimination of stimuli presented sequentially after adaptation to series of either few (around 2 Hz; low adaptation) or numerous (around 8 Hz; high adaptation) impulses for all possible combinations of visual, auditory, or tactile adapting and test stimuli. In all cases, adapting to few impulses yielded a significant overestimation of the test numerosity with the opposite occurring as a consequence of adaptation to numerous stimuli. The overall magnitude of adaptation was robust (around 30%) and rather similar for all sensory modality combinations. Overall, these findings support the idea of a truly generalized and a-modal mechanism for numerosity representation aimed to process numerical information independently from the sensory modality of the incoming signals.

Exploring Reference Frame Integration Using Response Demands in a Tactile Temporal-Order Judgement Task.

Exploring the world through touch requires the integration of internal (e.g., anatomical) and external (e.g., spatial) reference frames - you only know what you touch when you know where your hands are in space. The deficit observed in tactile temporal-order judgements when the hands are crossed over the midline provides one tool to explore this integration. We used foot pedals and required participants to focus on either the hand that was stimulated first (an anatomical bias condition) or the location of the hand that was stimulated first (a spatiotopic bias condition). Spatiotopic-based responses produce a larger crossed-hands deficit, presumably by focusing observers on the external reference frame. In contrast, anatomical-based responses focus the observer on the internal reference frame and produce a smaller deficit. This manipulation thus provides evidence that observers can change the relative weight given to each reference frame. We quantify this effect using a probabilistic model that produces a population estimate of the relative weight given to each reference frame. We show that a spatiotopic bias can result in either a larger external weight (Experiment 1) or a smaller internal weight (Experiment 2) and provide an explanation of when each one would occur.

Tracking Internal Frames of Reference for Consistent Molecular Distribution Functions.

In molecular analysis, spatial distribution functions (SDF) are fundamental instruments in answering questions related to spatial occurrences and relations of atomic structures over time. Given a molecular trajectory, SDFs can, for example, reveal the occurrence of water in relation to particular structures and hence provide clues of hydrophobic and hydrophilic regions. For the computation of meaningful distribution functions, the definition of molecular reference structures is essential. Therefore we introduce the concept of an internal frame of reference (IFR) for labeled point sets that represent selected molecular structures, and we propose an algorithm for tracking the IFR over time and space using a variant of Kabsch's algorithm. This approach lets us generate a consistent space for the aggregation of the SDF for molecular trajectories and molecular ensembles. We demonstrate the usefulness of the technique by applying it to temporal molecular trajectories as well as ensemble datasets. The examples include different docking scenarios with DNA, insulin, and aspirin.

Tactile numerosity is coded in external space

Humans, and several non-human species, possess the ability to make approximate but reliable estimates of the number of objects around them. Alike other perceptual features, numerosity perception is susceptible to adaptation: exposure to a high number of items causes underestimation of the numerosity of a subsequent set of items, and vice versa. Several studies have investigated adaptation in the auditory and visual modality, whereby stimuli are preferentially encoded in an external coordinate system. As tactile stimuli are primarily coded in an internal (body-centered) reference frame, here we ask whether tactile numerosity adaptation operates based on internal or external spatial coordinates as it occurs in vision or audition. Twenty participants performed an adaptation task with their right hand located either in the right (uncrossed) or left (crossed) hemispace, in order for the two hands to occupy either two completely different positions, or the same position in space, respectively. Tactile adaptor and test stimuli were passively delivered either to the same (adapted) or different (non-adapted) hands. Our results show a clear signature of tactile numerosity adaptation aftereffects with a pattern of over- and under-estimation according to the adaptation rate (low and high, respectively). In the uncrossed position, we observed stronger adaptation effects when adaptor and test stimuli were delivered to the “adapted” hand. However, when both hands were aligned in the same spatial position (crossed condition), the magnitude of adaptation was similar irrespective of which hand received adaptor and test stimuli. These results demonstrate that numerosity information is automatically coded in external coordinates even in the tactile modality, suggesting that such a spatial reference frame is an intrinsic property of numerosity processing irrespective of the sensory modality.

Reliability of the Crossed-Hands Deficit in Tactile Temporal Order Judgements.

Crossing the hands over the midline impairs performance on a tactile temporal order judgement (TOJ) task, resulting in the crossed-hands deficit. This deficit results from a conflict between two reference frames - one internal (somatotopic) and the other external (spatial) - for coding stimulus location. The substantial individual differences observed in the crossed-hands deficit highlight the differential reliance on these reference frames. For example, women have been reported to place a greater emphasis on the external reference frame than men, resulting in a larger crossed-hands deficit for women. It has also been speculated that individuals with an eating disorder place a greater weight on the external reference frame. Further exploration of individual differences in reference frame weighing using a tactile TOJ task requires that the reliability of the task be established. In Experiment 1, we investigated the reliability of the tactile TOJ task across two sessions separated by one week and found high reliability in the magnitude of the crossed-hands deficit. In Experiment 2, we report the split-half reliability across multiple experiments (both published and unpublished). Overall, tactile TOJ reliability was high. Experiments with small to moderate crossed-hands deficits showed good reliability; those with larger deficits showed even higher reliability. Researchers should try to maximize the size of the effect when interested in individual differences in the use of the internal and external reference frames.

The Magnitude Effect on Tactile Spatial Representation: The Spatial–Tactile Association for Response Code (STARC) Effect

The human brain uses perceptual information to create a correct representation of the external world. Converging data indicate that the perceptual processing of, space, and quantities frequently is based on a shared mental magnitude system, where low and high quantities are represented in the left and right space, respectively. The present study explores how the magnitude affects spatial representation in the tactile modality. We investigated these processes using stimulus-response (S-R) compatibility tasks (i.e., sensorimotor tasks that present an association/dissociation between the perception of a stimulus and the required action, generally increasing/decreasing accuracy and decreasing/increasing reaction times of the subject). In our study, the participant performed a discrimination task between high- and low-frequency vibrotactile stimuli, regardless of the stimulation’s spatial position. When the response code was incompatible with the mental magnitude line (i.e., left button for high-frequency and right button for low-frequency responses), we found that the participants bypassed the spatial congruence, showing a magnitude S-R compatibility effect. We called this phenomenon the Spatial–Tactile Association of Response Codes (STARC) effect. Moreover, we observed that the internal frame of reference embodies the STARC effect. Indeed, the participants’ performance reversed between uncrossed- and crossed-hands posture, suggesting that spatial reference frames play a role in the process of expressing mental magnitude, at least in terms of the tactile modality.