In this study, we directly contrast two approaches that have been proposed to explain the SNARC effect. The traditional direct mapping account suggests that a direct association exists between the position of a number on the mental number line and the location of the response. On the other hand, accounts are considered that propose an intermediate step in which numbers are categorized as either small or large between the number magnitude and the response representations. In a magnitude comparison task, (...) we departed from the usual bimanual left/right response dimension and instead introduced the unimanual close/far dimension. A spatial-numerical association was observed: small numbers were associated with a close response, while large numbers were associated with a far response, regardless of the movement direction (left/right). We discuss why these results cannot be explained by assuming a direct mapping from the representation of numbers on a mental number line to response locations and discuss how the results can be explained by the alternative accounts. (shrink)

We argue that the logical outcome of the cladistics revolution in biological systematics, and the move towards rankless phylogenetic classification of nested monophyletic groups as formalized in the PhyloCode, is to eliminate the species rank along with all the others and simply name clades. We propose that the lowest level of formally named clade be the SNaRC, the Smallest Named and Registered Clade. The SNaRC is an epistemic level in the classification, not an ontic one. Naming stops at (...) that level because there is no currently acceptable evidence for clades within it, not because no smaller clades exist. Later, included clades may be named. They would then become the SNaRCs, while the original SNaRC would keep its original name. We argue that all theoretical tasks of biology, in evolution and ecology, as well as practical tasks such as conservation assessment, are better approached using this rankless phylogenetic approach. (shrink)

Spatial, physical, and semantic magnitude dimensions can influence action decisions in human cognitive processing and interact with each other. For example, in the SNARC effect, semantic numerical magnitude facilitates left-hand or right-hand responding dependent on the small or large magnitude of number symbols. SNARC-like interactions of numerical magnitudes with the radial spatial dimension (depth) were postulated from early on. Usually, the SNARC effect in any direction is investigated using fronto-parallel computer monitors for presentation of stimuli. In such (...) 2D setups, however, the metaphorical and literal interpretation of the radial depth axis with seemingly close / far stimuli or responses are not distinct. Hence, it is difficult to draw clear conclusions with respect to the contribution of different spatial mappings to the SNARC effect. In order to disentangle the different mappings in a natural way, we studied parametrical interactions between semantic numerical magnitude, horizontal directional responses, and perceptual distance by means of stereoscopic depth in an immersive virtual reality (VR). Two VR experiments show horizontal SNARC effects across all spatial displacements in traditional latency measures and kinematic response parameters. No indications of a SNARC effect along the depth axis, as it would be predicted by a direct mapping account, were observed, but the results show a non-linear relationship between horizontal SNARC slopes and physical distance. Steepest SNARC slopes were observed for digits presented close to the hands. We conclude that spatial-numerical processing is susceptible to effector-based processes but relatively resilient to task-irrelevant variations of radial-spatial magnitudes. (shrink)

Do people represent space, time, number, and other conceptual domains using a generalized magnitude system (GMS)? To answer this question, numerous studies have used the spatial‐numerical association of response codes (SNARC) task and its variants. Yet, for a combination of reasons, SNARC‐like effects cannot provide evidence for a GMS, even in principle. Rather, these effects support a broader theory of how people use space metaphorically to scaffold their understanding of myriad non‐spatial domains, whether or not these domains exhibit (...) variation in magnitude. (shrink)

Small numbers are spontaneously associated with left space and larger numbers with right space (the SNARC effect), for example when classifying numbers by parity. This effect is often attributed to reading habits but a causal link has so far never been documented. We report that bilingual Russian-Hebrew readers show a SNARC effect after reading Cyrillic script (from left-to-right) that is significantly reduced after reading Hebrew script (from right-to-left). In contrast, they have similar SNARC effects after listening to (...) texts in either language. These results support the view that spatially directional scanning habits contribute to the spatial association of numbers but also emphasize its flexibility. (shrink)

In a recent paper by Casasanto and Pitt (2019), the authors addressed a debate regarding the role of order and magnitude in SNARC and SNARC‐like effects. Their position is that all these effects can be explained by order, while magnitude could only account for a subset of evidence. Although we agree that order can probably explain the majority of these effects, in this commentary we argue that magnitude is still relevant, since there is evidence that cannot be explained (...) based on ordinality alone. We argue that SNARC‐like effects can occur for magnitudes not clearly characterized by overlearned ordinality and that magnitude can prevail on order, when the two are pitted against each other. Finally, we propose that different interpretations of the role of order and magnitude depend on the interaction of stimulus properties and task demands. (shrink)

Recent research in numerical cognition has begun to systematically detail the ability of humans and nonhuman animals to perceive the magnitudes of nonsymbolic ratios. These relationally defined analogs to rational numbers offer new potential insights into the nature of human numerical processing. However, research into their similarities with and connections to symbolic numbers remains in its infancy. The current research aims to further explore these similarities by investigating whether the magnitudes of nonsymbolic ratios are associated with space just as symbolic (...) numbers are. In two experiments, we found that responses were faster on the left for smaller nonsymbolic ratio magnitudes and faster on the right for larger nonsymbolic ratio magnitudes. These results further elucidate the nature of nonsymbolic ratio processing, extending the literature of spatial–numerical associations to nonsymbolic relative magnitudes. We discuss potential implications of these findings for theories of human magnitude processing in general and how this general processing relates to numerical processing. (shrink)

According to proponents of the generalized magnitude system proposal (GMS), SNARC-like effects index spatial mappings of magnitude and provide crucial evidence for the existence of a GMS. Casasanto and Pitt (2019) have argued that these effects, instead, reflect mappings of ordinality, which people compute on the basis of differences among stimuli that vary either qualitatively (e.g., musical pitches) or quantitatively (e.g., dots of different sizes). In response to our paper, Prpic et al. (2021) argued that both magnitude and ordinality (...) play a role in SNARC-like effects. Here, we address each of their arguments and conclude that magnitude is relevant to these effects only insofar as it serves as a basis for ordinality. For this reason and others, SNARC or SNARC-like effects cannot provide evidence for the putative generalized magnitude system. (shrink)

Cognitive Science, Volume 46, Issue 2, February 2022.

Research on the Spatial Quantity Association of Response Codes (SQUARC) has documented associations between spatial position and mental representations of quantity. Large quantities are associated with right and top, small quantities are associated with left and bottom. Resulting compatibility effects have largely been documented for response speed and judgment accuracy. Recently, employing luminance as quantity, Löffler et al. (2022) generalised such SQUARC compatibility effects to affective judgments, showing that horizontally SQUARC-compatible stimulus arrangements (i.e. bright on the right, dark on the (...) left side) are liked more than SQUARC-incompatible arrangements. The present Experiment 1 (N = 296) replicated this horizontal compatibility effect, dz =.18, and generalised it to vertical luminance SQUARC compatibility (i.e. bright on the top, dark on the bottom), dz =.22. Experiments 2a-b (total N = 259; Experiment 2b preregistered) employed stimulus arrangements tilted by 45° to manipulate horizontal and vertical (in)compatibility simultaneously within the same stimulus, finding robust horizontal compatibility effects, but mixed evidence regarding vertical compatibility. (shrink)

In 2011, van Dijck and Fias described a positional SNARC effect: the SPoARC. To-be-remembered items presented centrally on a screen seemed to acquire a left-to-right spatial dimension. If confirmed, this spatialization could be crucial for immediate memory theories. However, given the intricate links between visual and spatial dimensions, this effect could be due to the visual presentation, which could have probed the left-to-right direction of reading/writing. To allow a generalization of this effect, we adapted van Dijck and Fias's task (...) using an auditory version of Sternberg's paradigm. Lists of five consonants were auditorily presented at a rate of 3 s/item. A SPoARC effect was observed. The consequences are discussed first from an immediate memory perspective, putting forward the view that order could be coded through spatialization, and then in terms of similarities between SPoARC and SNARC. (shrink)

It has been argued that numbers are spatially organized along a "mental number line" that facilitates left-hand responses to small numbers, and right-hand responses to large numbers. We hypothesized that whenever the representations of visual and numerical space are concurrently activated, interactions can occur between them, before response selection. A spatial prime is processed faster than a numerical target, and consistent with our hypothesis, we found that such a spatial prime affects non-spatial, verbal responses more when the prime follows a (...) numerical target (backward priming) then when it precedes it (forward priming). This finding emerged both in a number-comparison and a parity judgment task, and cannot be ascribed to a "Spatial-Numerical Association of Response Codes" (SNARC). Contrary to some earlier claims, we therefore conclude that visuospatial-numerical interactions do occur, even before response selection. (shrink)

The directionality of space-number association (SNA) is shaped by cultural experiences. It usually follows the culturally dominant reading direction. Smaller numbers are generally associated with the starting side for reading (left side in Western cultures), while larger numbers are associated with the right endpoint side. However, SNAs consistent with cultural reading directions are present before children can actually read and write. Therefore, these SNAs cannot only be shaped by the direction of children’s own reading/writing behavior. We propose six distinct processes (...) – one biological and five cultural/educational – underlying directional SNAs before formal reading acquisition: (i) Brain lateralization, (ii) Monitoring adult reading behavior, (iii) Pretend reading and writing, and rudimentary reading and writing skills, (iv) Dominant attentional directional preferences in a society, not directly related to reading direction, (v) Direct spatial-numerical learning, (vi) Other spatial-directional processes independent of reading direction. In this mini-review, we will differentiate between these processes, elaborate when in development they might emerge, discuss how they may create the SNAs observed in preliterate children and propose how they can be studied in the future. (shrink)

Whether negative numbers have a fixed spatial–numerical association of response codes effect, and whether the spatial representation of negative numbers is associated with negative numbers’ absolute or signed values remains controversial. In this study, through three experiments, the coding level of the magnitude and the spatial-direction is manipulated. In the first experiment, participants are required to code the magnitude and spatial-direction explicitly by using a magnitude classification task. In the second experiment, participants are forced to code the magnitude implicitly as (...) well as to code the spatial-direction explicitly by utilizing a cuing task. In the third experiment, participants are obliged to code the magnitude explicitly as well as to code the spatial-direction implicitly by adopting a magnitude and arrow-direction classification tasks with Go/No-Go responses. The results show that the absolute value of negative numbers associates with space when the magnitude of negative numbers is explicitly coded, no matter employing the explicit or implicit spatial-direction; the signed value of negative numbers associates with space under the condition of implicit magnitude as well as explicit spatial-direction. In conclusion, the current study indicates that the SNARC effect of negative numbers is variable in different conditions, and the type of SNARC effect about negative numbers is modulated by the joint coding level of the magnitude and spatial-direction. (shrink)

We assessed the automaticity of spatial-numerical and spatial-musical associations by testing their intentionality and load sensitivity in a dual-task paradigm. In separate sessions, 16 healthy adults performed magnitude and pitch comparisons on sung numbers with variable pitch. Stimuli and response alternatives were identical, but the relevant stimulus attribute (pitch or number) differed between tasks. Concomitant tasks required retention of either color or location information. Results show that spatial associations of both magnitude and pitch are load sensitive and that the spatial (...) association for pitch is more powerful than that for magnitude. These findings argue against the automaticity of spatial mappings in either stimulus dimension. (shrink)

The paper presents a formal model of the system of number representations as a multiplicity of mental number axes with a hierarchical structure. The hierarchy is determined by the mind as it acquires successive types of mental number axes generated by virtue of some algebraic mechanisms. Three types of algebraic structures, responsible for functioning these mechanisms, are distinguished: BASAN-structures, CASAN-structures and CAPPAN-structures. A foundational order holds between these structures. CAPPAN-structures are derivative from CASAN-structures which are extensions of BASAN-structures. The constructed (...) formal model unifies two competitive conceptions of cognitive arithmetic: namely, the conception of the mental number line and the conception of parallel individuation. The paper is the continuation of a paper entitled Representational structures of arithmetical thinking, in which rich empirical evidence supporting the model is presented. The main result achieved in the present paper may be philosophically interpreted as an attempt to formalize the Kantian conception of the pure idea of time, understood as the a priori form of human arithmetical thinking. In this way, our theory may be comprehended as a result of applying the hard method of logical reconstruction of fundamental epistemological categories. (shrink)

In this paper, representational structures of arithmetical thinking, encoded in human minds, are described. On the basis of empirical research, it is possible to distinguish four types of mental number lines: the shortest mental number line, summation mental number lines, point-place mental number lines and mental lines of exact numbers. These structures may be treated as generative mechanisms of forming arithmetical representations underlying our numerical acts of reference towards cardinalities, ordinals and magnitudes. In the paper, the theoretical framework for a (...) formal model of mental arithmetical representations is constructed. Many competitive conceptions of the mental system responsible for our arithmetical thinking may be unified within the presented framework. The paradigm underlying our research may be interpreted philosophically as a neo-Kantian approach to modeling the mind’s representational structures. (shrink)