Memory for numbers improves with age. One source of this improvement may be learning linear spatial-numeric associations, but previous evidence for this hypothesis likely confounded memory span with quality of numerical magnitude representations and failed to distinguish spatial-numeric mappings from other numeric abilities, such as counting or number word-cardinality mapping. To obviate the influence of memory span on numerical memory, we examined 39 3- to 5-year-olds’ ability to recall one spontaneously produced number (1-20) after a delay, (...) and the relation between numeric recall (controlling for non-numeric recall) and quality of mapping between symbolic and non-symbolic quantities using number-line estimation, give-a-number estimation, and counting tasks. Consistent with previous reports, mapping of numerals to space, to discrete quantities, and to numbers in memory displayed a logarithmic-to-linear shift. Also, linearity of spatial-numeric mapping correlated strongly with multiple measures of numeric recall (percent correct and percent absolute error), even when controlling for age and non-numeric memory. Results suggest that linear spatial-numeric mappings may aid memory for number over and above children’s other numeric skills. (shrink)

Three-to-five-year-old French children were asked to add or remove objects to or from linear displays. The hypothesis of a universal tendency to represent increasing number magnitudes from left to right led to predict a majority of manipulations at the right end of the rows, whatever children's hand laterality. Conversely, if numbers are not inherently associated with space, children were expected to favour laterality-consistent manipulations. The results showed a strong tendency to operate on the right end of the rows in right-handers, (...) but no preference in left-handers. These findings suggest that the task elicited a left-to-right oriented representation of magnitudes that counteracted laterality-related responses in left-handed children. The young age of children and the lack of a developmental trend towards right preference weaken the hypothesis of a cultural origin of this oriented representation. The possibility that our results are due to weaker brain lateralisation in left-handers compared to right-handers is addressed in Discussion section. (shrink)

Núñez and Fias raised concerns on whether our results demonstrate a linear number-space mapping. Patro and Nuerk urge caution on the use of animal models to understand the origin of the orientation of spatial–numerical association. Here, we discuss why both objections are unfounded.

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)

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)

Numerical magnitude information is assumed to be spatially represented in the form of a mental number line defined with respect to a body-centred, egocentric frame of reference. In this context, spatial language skills such as mastery of verbal descriptions of spatial position have been proposed to be relevant for grasping spatial relations between numerical magnitudes on the mental number line. We examined 4- to 5-year-old’s spatial language skills in tasks that allow responses in egocentric (...) and allocentric frames of reference, as well as their relative understanding of numerical magnitude. In addition, we evaluated influences of children’s absolute understanding of numerical magnitude assessed by their number word comprehension and of their knowledge on numerical sequences. Results indicated that when considering responses that corresponded to the egocentric perspective, children’s spatial language was associated significantly with their relative numerical magnitude understanding, even after controlling for covariates, such as children’s SES, mental rotation skills, and also absolute magnitude understanding or knowledge on numerical sequences. This suggests that the use of egocentric reference frames in spatial language may facilitate spatial representation of numbers along a mental number line and thus seem important for preschoolers’ relative understanding of numerical magnitude. (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)

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)

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)

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)

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)

According to the Temporal Focus Hypothesis, space–time mappings in people’s minds are shaped by their attentional focus. Previous research has shown that numerous cultural and individual factors underpinning temporal focus may contribute to the direction of space–time mappings in people’s mental models. However, the role of time of day in shaping spatial conceptions of time has not been investigated. In a series of three experiments, Chinese participants, who were more likely to be future-focused in the morning than afternoon, were (...) also more likely to produce a future-in-front mapping. However, this morning future-minded effect can only be found in morning people, suggesting a mediating role of chronotype processes. Taken together, the findings across studies suggest that people’s representations of time may arise from an interaction between a person’s chronotype and time-of-day, a phenomenon that we refer to as the chronotype future-minded effect. (shrink)

Block building is a popular play activity among young children and is also used by psychologists to assess their intelligence. However, little research has attempted to systematically explore the cognitive bases of block-building ability. The current study (N= 66 Chinese preschoolers, 32 boys and 34 girls; mean age = 4.7 years, SD = 0.29, range = 3.4 to 5.2 years) investigated the relationships between six measures of spatial skills (shape naming, shape recognition, shape composition, solid figure naming, cube transformation, (...) and mental rotation, with the former four representing form perception and the latter two representing visualization) and block-building complexity. Correlation results showed that three of the four measures of form perception (shape naming, shape recognition, and shape composition) were significantly and positively correlated with block-building complexity, whereas the two measures of visualization were not. Results from regression models indicated that shape recognition and shape composition, as well as shape-recognition-by-gender interaction, were unique predictors of children’s block-building complexity. These findings provide preliminary evidence for the basic spatial skills underlying children’s block-building complexity and have implications for classroom instructions aimed at improving preschoolers’ block-building complexity. (shrink)

Dove and Machery both argue that recent findings about the nature of numerical representation present problems for Concept Empiricism. I shall argue that, whilst this evidence does challenge certain versions of CE, such as Prinz, it needn’t be seen as problematic to the general CE approach. Recent research can arguably be seen to support a CE account of number concepts. Neurological and behavioral evidence suggests that systems involved in the perception of numerical properties are also implicated in (...) class='Hi'>numerical cognition. Furthermore, the discovery of associations between spatial and numerical representations also lends independent support to a CE approach. Although these findings support CE in general, certain versions of the theory may need revising in order to accommodate them. In particular, it may be necessary to either jettison Prinz's Modal Specificity Hypothesis or to revise one’s method for individuating modal representational formats. (shrink)

Consistent with numerous electrophysiological studies, we recently reported that conscious perception is associated with a widely distributed modulation of the P3 component . We also showed that correct objective performance in the absence of subjective awareness is associated with a spatially more restricted modulation of the P3. The relatively late occurrence of the P3 along with lack of control for post-perceptual processes suggests that this component might reflect processes related to stimulus evaluation or confidence rather than to visual awareness or (...) objective performance. The main aim of the current study was to test this hypothesis. While EEG was recorded, participants performed a forced-choice localization task and reported their subjective perception of the target on a 3-level scale that also indexed their confidence. The results showed that our previous findings are replicated when confidence is controlled for. (shrink)

Often implicit in visual display design and development is a gold standard of photorealism. By approximating direct perception, photorealism appeals to users and designers by being both attractive and apparently effortless. The vexing result from numerous performance evaluations, though, is that increasing realism often impairs performance. Smallman and St. John (2005) labeled misplaced faith in realistic information display Naïve Realism and theorized it resulted from a triplet of folk fallacies about perception. Here, we illustrate issues associated with the wider trend (...) towards realism by focusing on a specific current trend for high-fidelity perspective view (3D) geospatial displays. In two experiments, we validated Naïve Realism for different terrain understanding tasks, explored whether certain individuals are particularly prone to Naïve Realism, and determined the ability of task feedback to mitigate Naïve Realism. Performance was measured for laying and judging a concealed route across realistic terrain shown in different display formats. Task feedback was either implicit, in Experiment 1, or explicit in Experiment 2. Prospective and retrospective intuitions about the best display formats for the tasks were recorded and then related to task performance and participant spatial ability. Participants generally intuited they would perform tasks better with more realism than they actually required. For example, counter to intuitions, lowering fidelity of the terrain display revealed the gross scene layout needed to lay a well-concealed route. Individuals of high spatial ability calibrated their intuitions with only implicit task feedback, whereas those of low spatial ability required salient, explicit feedback to calibrate their intuitions about display realism. Results are discussed in the wider context of applying perceptual science to display design, and combating folk fallacies. (shrink)

Being able to estimate quantity is important in everyday life and for success in the STEM disciplines. However, people have difficulty reasoning about magnitudes outside of human perception. This study examines patterns of estimation errors across temporal and spatial magnitudes at large scales. We evaluated the effectiveness of hierarchical alignment in improving estimations, and transfer across dimensions. The activity was successful in increasing accuracy for temporal and spatial magnitudes, and learning transferred to the estimation of numeric magnitudes associated (...) with events and objects. However, there were also a number of informative differences in performance on temporal, spatial, and numeric magnitude measures, suggesting that participants possess different categorical information for these scales. Educational implications are discussed. (shrink)

Number-form synesthetes consciously experience numbers in spatially-defined locations. For non-synesthete individuals, a similar association of numbers and space appears in the form of an implicit mental number line as signified by the distance effect–reaction time decreases as the numerical distance between compared numbers increases. In the current experiment, three number-form synesthetes and two different non-synesthete control groups performed a number comparison task. Synesthete participants exhibited a sizeable distance effect only when presented numbers were congruent with their number-form. In (...) contrast, the controls exhibited a distance effect regardless of congruency or presentation type. The findings suggest that: number-form synesthesia impairs the ability to represent numbers in a flexible manner according to task demands; number-form synesthesia is a genuine tangible experience, triggered involuntarily; and the classic mental number line can be more pliable than previously thought and appears to be independent of cultural-lingo direction. (shrink)

Normal children learn tens of thousands of words, and do so quickly and efficiently, often in highly impoverished environments. In How Children Learn the Meanings of Words, I argue that word learning is the product of certain cognitive and linguistic abilities that include the ability to acquire concepts, an appreciation of syntactic cues to meaning, and a rich understanding of the mental states of other people. These capacities are powerful, early emerging, and to some extent uniquely human, but they are (...) not special to word learning. This proposal is an alternative to the view that word learning is the result of simple associative learning mechanisms, and it rejects as well the notion that children possess constraints, either innate or learned, that are specifically earmarked for word learning. This theory is extended to account for how children learn names for objects, substances, and abstract entities, pronouns and proper names, verbs, determiners, prepositions, and number words. Several related topics are also discussed, including naïve essentialism, children's understanding of representational art, the nature of numerical and spatial reasoning, and the role of words in the shaping of mental life. Key Words: cognitive development; concepts; meaning; semantics; social cognition; syntax; theory of mind; word learning. (shrink)

The last couple of years have seen a rapid growth of interest in the study of crossmodal correspondences – the tendency for our brains to preferentially associate certain features or dimensions of stimuli across the senses. By now, robust empirical evidence supports the existence of numerous crossmodal correspondences, affecting people’s performance across a wide range of psychological tasks – in everything from the redundant target effect paradigm through to studies of the Implicit Association Test, and from speeded discrimination/classification tasks (...) through to unspeeded spatial localisation and temporal order judgment tasks. However, one question that has yet to receive a satisfactory answer is whether crossmodal correspondences automatically affect people’s performance , as opposed to reflecting more of a strategic, or top-down, phenomenon. Here, we review the latest research on the topic of crossmodal correspondences to have addressed this issue. We argue that answering the question will require researchers to be more precise in terms of defining what exactly automaticity entails. Furthermore, one’s answer to the automaticity question may also hinge on the answer to a second question: Namely, whether crossmodal correspondences are all ‘of a kind’, or whether instead there may be several different kinds of crossmodal mapping . Different answers to the automaticity question may then be revealed depending on the type of correspondence under consideration. We make a number of suggestions for future research that might help to determine just how automatic crossmodal correspondences really are. (shrink)

The neural basis of progress monitoring has received relatively little attention compared to other sub-processes that are involved in goal directed behavior such as motor control and response inhibition. Studies of error-monitoring have identified the dorsal anterior cingulate cortex (dACC) as a structure that is sensitive to conflict detection, and triggers corrective action. However, monitoring goal progress involves monitoring correct as well as erroneous events over a period of time. In the present research, 20 healthy participants underwent fMRI while playing (...) a game that involved monitoring progress towards either a numerical or a visuo-spatial target. The findings confirmed the role of the dACC in detecting situations in which the current state may conflict with the desired state, but also revealed activations in the frontal and parietal regions, pointing to the involvement of processes such as attention and working memory in monitoring progress over time. In addition, activation of the cuneus was associated with monitoring progress towards a specific target presented in the visual modality. This is the first time that activation in this region has been linked to higher-order processing of goal-relevant information, rather than low-level anticipation of visual stimuli. Taken together, these findings identify the neural substrates involved in monitoring progress over time, and how these extend beyond activations observed in conflict and error monitoring. (shrink)

Tailoring climate change messages to a particular spatial scale (e.g. a specific country or region) is often seen as an effective way to frame communication about climate change. Yet the empirical evidence for the effectiveness of this strategy is scarce, and little is known about how recipients react to spatially-framed climate change messages. To learn more about the effects and usefulness of different spatial frames as a communication and engagement tool, we conducted a study in which we presented (...) members of the general public with either a national or a global framing of climate change. In contrast to previous spatial-framing studies, the present research used semi-structured interviews – rather than survey questions – to obtain rich, in-depth information about participants’ views of climate change. Irrespective of the framing, participants revealed associations that were located at various spatial scales. Moreover, when participants talked about climate change, they repeatedly switched between different spatial scales, revealing patterns that were consistent with seeking to preserve existing beliefs and preferences. These findings improve our understanding of how the public represents climate change, and provide a novel explanation as to why simple spatial framing often fails to achieve the anticipated effects. (shrink)

Stochastic dynamical reduction for the case of spin-z measurement of a spin-1/2 particle describes a random walk on the spin-z axis. The measurement’s result depends on which of the two points: spin-z=±ħ/2 is reached first. Born’s rule is recovered as long as the expected step size in spin-z is independent of proximity to endpoints. Here, we address the questions raised by this description: (1) When is collapse triggered, and what triggers it? (2) Why is the expected step size in spin-z (...) (as opposed to polar angle) independent of proximity to endpoints? (3) Why does spin “lock” in the vertical directions? The difficulties associated with (1) are rooted, as is Bell’s theorem, in the time-asymmetric assumption that the present distribution over hidden variables is independent of future settings. We believe, a priori of any of the experiments of modern physics, that such a time-asymmetric assumption is dubious when probing the microscopic scale. As for (2) and (3), they are simultaneously resolved by abandoning the fundamental distinction drawn between spin and spatial angular momentum, and by appealing to very tiny (in both magnitude and spatial extent) but numerous patches of magnetic noise in the Stern-Gerlach’s field. (shrink)

Over the past two decades, archaeologists and physical anthropologists investigating the prehistoric Anasazi culture have identified numerous cases of suspected cannibalism. Many scholars have suggested that starvation caused by environmental degradation induced people to eat one another, but the growing number of cases as well as their temporal and spatial distribution challenge this conclusion. At the same time, some scholars have questioned the validity of the osteoarchaeological indicators that are used to identify cannibalism in collections of mutilated human remains. (...) To address these concerns, this study attempts to reconstruct the behaviors that produced the Anasazi skeletal trauma by first examining ethnographic, ethnohistoric, and archaeological material for analogues useful for interpreting mutilated human remains and then correlating these analogues with the evidence from the Southwest. The patterns suggest that different behaviors are responsible for the Anasazi skeletal mutilation seen in different time periods. To explain these differences, the study employs game theoretical models that examine how changing social and physical contexts altered the sociopolitical strategies that Anasazi groups would likely have employed. The results suggest that violent mutilation and perhaps cannibalism was an intentional sociopolitical strategy of intimidation used during Pueblo II (A.D. 900–1100), while environmental changes after this period promoted resource-based warfare and the incidental skeletal trauma associated with this behavior. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:L’esthétique de StaceA. M. KeithAnne-Marie Taisne. L’esthétique de Stace. Paris: Les Belles Lettres, 1994. 433 pp. Paper, 280 FF. (Collection d’Etudes Anciennes 122)Anne-Marie Taisne is the author of numerous articles concerning the literary history and artistic context that inform single poems in Statius’ Silvae and self-contained passages in his Thebaid and unfinished Achilleid, papers which lay the groundwork for her comprehensive new study of the literary aesthetic on (...) display in the extant poetic oeuvre of P. Papinius Statius. In this ambitious monograph, she undertakes to explore two facets of Statius’ technical artistry, his spatial and temporal imagery, within the theoretical framework provided by ancient literary criticism. She is particularly concerned to articulate the poet’s dynamic reuse of the weighty literary tradition to which he is heir, and accordingly proposes, in her introduction, to structure her discussion around such central ancient critical issues as imitatio (mimesis) along with its close relatives aemulatio and contaminatio, and doctrina with its associated critical vocabulary of ingenium, ratio, and ars (6–10). Throughout the volume, she explicates these techniques in detailed analysis of Statian imagines, which she defines generally in the sense of “imagery” following S. Viarre (“L’image et le symbole dans la poésie d’Ovide: Recherches sur l’imaginaire,” REL 62 [1974] 263–80), and particularly by reference to individual usages of the term as they are discussed in the article on imago in the Thesaurus Linguae Latinae (11).Part 1, “Correspondances dans l’espace,” examines the spatial imagery of Thebaid, Achilleid, and Silvae in three chapters which treat (1) echo and reflection (17–52), (2) metamorphosis, multiplication, and contagion (53–119), and (3) simile (120–76). Part 2, “Correspondances dans le temps,” investigates the poems’ use of time as a structural principle, again in three chapters which discuss (1) prophecies and portents (177–236), (2) digressive elements such as ecphrases and embedded narratives (237–303), and (3) leitmotifs, or repeated patterns of imagery, such as divine and human interventions and the role of nature in the poems. The material Taisne analyzes in part 1 coheres more convincingly with her overarching theme of spatial imagery than that which she discusses in part 2 under the rubric of temporal imagery. I did not understand, for example, why nature, well discussed in connection with Statius’ use of the simile in part 1 (137–62), reappears in part 2 (331–58) with no explanation of its relevance to temporal imagery.Taisne persuasively documents the wide range of literary models on which Statius draws in all his poetry, and shows that the Thebaid makes particular use of epic and tragic models (166–68, 170, 373–75), the Achilleid of tragic and lyric models (168–71, 374–78). Her discussion of the literary echoes and wider symbolic relevance of individual passages is often very interesting, and the sheer accumulation of literary parallels is extremely impressive. I was reminded of and newly alerted to significant literary resonances on almost every page, and noticed only one incomplete assemblage of literary parallels (in her discussion of Hylas [End Page 159] in Silvae 1.2.199 [27–28], there is no mention of Theocr. Id. 13, Ap. Rhod. Arg. 1.1207–72, or Nicander apud Ant. Lib. Met. 26). The service to which this material is put, however, is not as exciting as the length of the study might lead one to hope. Throughout, Taisne argues that Statius’ deployment of imagery is consistent with the overarching thematic framework of each poem, defined as furor and horror in the Thebaid (23 and passim), an ambiguous and deceptive calm in the Achilleid (353–54 and passim), and serenity and harmony in the Silvae (28 and passim), but she does not press her analysis beyond the accumulation of imagery in the service of these themes as evidence of Statian amplificatio. This is particularly disappointing in an author so well placed to discuss the material culture of the Flavian epoch and the interrelations between Statius’ poetry (especially the Silvae) and the culture of display in Domitian’s Rome. Nevertheless, scholars will be grateful to Taisne for the material she has collected... (shrink)

The number-line estimation task has become one of the most important methods in numerical cognition research. Originally applied as a direct measure of spatial number representation, it became also informative regarding various other aspects of number processing and associated strategies. However, most of this work and associated conclusions concerns processing numbers in a symbolic format, by school children and older subjects. Symbolic number system is formally taught and trained at school, and its basic mathematical properties can easily be (...) transferred into a spatial format of an oriented number line. This triggers the question on basic characteristics of number line estimation before children get fully familiar with the symbolic number system, i.e., when they mostly rely on approximate system for non-symbolic quantities. In our three studies, we examine therefore how preschool children estimate position of non-symbolic quantities on a line, and how this estimation is related to the developing symbolic number knowledge and cultural directionality. The children were tested with the Give-a-number task, then they performed a computerized number-line task. In Experiment 1, lines bounded with sets of 1 and 20 elements going left-to-right or right-to-left were used. Even in the least numerically competent group, the linear model better fit the estimates than the logarithmic or cyclic power models. The line direction was irrelevant. In Experiment 2, a 1–9 left-to-right oriented line was used. Advantage of linear model was found at group level, and variance of estimates correlated with tested numerosities. In Experiment 3, a position-to-number procedure again revealed the advantage of the linear model, although the strategy of selecting an option more similar to the closer end of the line was prevalent. The precision of estimation increased with the mastery of counting principles in all three experiments. These results contradict the hypothesis of the log-to-linear shift in development of basic numerical representation, rather supporting the linear model with scalar variance. However, the important question remains whether the number-line task captures the nature of the basic numerical representation, or rather the strategies of mapping that representation to an external space. (shrink)

As an essential direction for developing inclusive finance, digital financial inclusion breaks through the time and space constraints of inclusive finance development and has extensive connections between different regions. However, no research has modelled the network connections and the role and position of different digital financial inclusion development regions. This study constructed the spatial association network of China’s digital financial inclusion development and used the network analysis method and the quadratic assignment procedure method to study the structural and (...) locational properties and the influencing factors of the network. We found that although the network had a relatively low density, its connectivity and stability were excellent, and the network structure is not hierarchical; the centrality of some rapidly developing central and western provinces was greater than that of some developed eastern provinces; developed eastern provinces played a net spillover role, driving the development of digital financial inclusion in central and western provinces; and the spatial association was affected by the development level of the PC Internet and economy, the industrial structure, and the spatial adjacency. This study enriches the research on digital financial inclusion and provides a scientific basis for the formulation and implementation of policies to promote the further development of digital financial inclusion. (shrink)

The reliable covariation between numerosity and spatial extent is considered as a strong constraint for inferring the successor principle in numerical cognition. We suggest that children can derive a general number concept from the (experientially) infinite succession of spatial positions during object manipulation.

The origin and evolutionary dynamics of the spatial heterogeneity in genomic base composition have been debated since its discovery in the 1970s. With the recent availability of numerous genome sequences from a wide range of species it has been possible to address this question from a comparative perspective, and similarities and differences in base composition between groups of organisms are becoming evident. Ample evidence suggests that the contrasting dynamics of base composition are driven by GC‐biased gene conversion (gBGC), a (...) process that is associated with meiotic recombination. In line with this hypothesis, base composition is associated with the rate of recombination and the evolutionary dynamics of the recombination landscape, therefore, governs base composition. In addition, and at first sight perhaps surprisingly, the relationship between demography and genomic base composition is in agreement with the gBGC hypothesis: organisms with larger populations have higher GC content than those with smaller populations. (shrink)

The target article undermines the existence of a shared unitary numerical format, illustrating a variety of representations. The / dichotomy does not capture their specific features. These representations are with respect to the sensory modality of the stimulus, and independent of its specific notation, with a main role of spatial codes, both related and unrelated to the mental number line.

A MAJOR PHILOSOPHICAL INTERPRETER of Kant and critic of Herbart and Hegel, Hermann Lotze ( 1817-1881) is known to historians of psychology primarily for his theory of spatial perception.' As Professor of Philosophy at Gottingen University from 1845 to 1880, he published his theory of the physiological mechanism for spatial consciousness no less than six times.2 Standard accounts present his local sign theory as an associationistic, empiricistic, or empiristic view.3 Yet they also mention its influence among nativists such (...) as Lotze's own student Carl Stumpf. Certainly there is an historical irony here which deserves explanation. This paper will describe Lotze's theory, indicate its origins in the work of scientists such as E. H. Weber and Johannes Muiller and philosophers such as Jakob Friedrich Fries and Johann Friedrich Herbart, and trace its transformation at the hands of psycholo- gists of various theoretical persuasions.4 The intent is not to argue for Lotze's personal influence so much as to illustrate how one fertile idea in the history of science can serve as the catalyst for a much broader conceptual development. (shrink)

The dynamics of single populations up to ecosystems, are often described by one or a set of non-linear ordinary differential equations. In this paper we review the use of bifurcation theory to analyse these non-linear dynamical systems. Bifurcation analysis gives regimes in the parameter space with quantitatively different asymptotic dynamic behaviour of the system. In small-scale systems the underlying models for the populations and their interaction are simple Lotka-Volterra models or more elaborated models with more biological detail. The latter ones (...) are more difficult to analyse, especially when the number of populations is large. Therefore for large-scale systems the Lotka-Volterra equations are still popular despite the limited realism. Various approaches are discussed in which the different time-scale of ecological and evolutionary biological processes are considered together. (shrink)

Selecting a large and diverse sample of 5–6-year-old preschool children, we aimed to extend previous findings on variability in children’s home math environment and its association with children’s mathematical skills. We operationalized mathematics in a broader way than in previous studies, by considering not only children’s numerical skills but also their patterning skills as integral components of early mathematical development. We investigated the effects of children’s gender and socioeconomic status on their home math environment, examined the associations between (...) children’s home math environment and their mathematical skills, and verified whether these associations were moderated by children’s gender and/or SES. Parents of 353 children completed a home math environment questionnaire and all children completed measures of their numerical and patterning skills. Results indicated no effect of children’s gender on their home math environment. There was no effect of SES on the performed home math activities, but small SES differences existed in parents’ math-related expectations and their attitudes. We found no evidence for associations between children’s home math environment and their mathematical skills. Furthermore, there were no moderating effects of gender or SES on these associations. One explanation for these findings might relate to the characteristics of the general preschool system in the country of the present study. Future studies should consider the effect of the preschool learning environment because it might explain differences between studies and countries with regard to the home math environment and its association with mathematical skills. (shrink)

In this study, we test whether children whose culture lacks CWs and counting practices use a spatial strategy to support enumeration tasks. Children from two indigenous communities in Australia whose native and only language (Warlpiri or Anindilyakwa) lacked CWs and were tested on classical number development tasks, and the results were compared with those of children reared in an English-speaking environment. We found that Warlpiri- and Anindilyakwa-speaking children performed equivalently to their English-speaking counterparts. However, in tasks in which they (...) were required to match the number of objects in a display, they were more likely to reconstruct part or all of the spatial arrangement of the target than were their English-speaking counterparts. Following John Locke's interpretation of users of similar American languages and in contrast with later Whorfian interpretations, we suggest that CWs may be strategically useful, but that in their absence, other task-specific strategies will be deployed. (shrink)