Much research supports the existence of an Approximate Number System (ANS) that is recruited by infants, children, adults, and non-human animals to generate coarse, non-symbolic representations of number. This system supports simple arithmetic operations such as addition, subtraction, and ordering of amounts. The current study tests whether an intuition of a more complex calculation, division, exists in an indigene group in the Amazon, the Mundurucu, whose language includes no words for large numbers. Mundurucu children were presented with a video event (...) depicting a division transformation of halving, in which pairs of objects turned into single objects, reducing the array's numerical magnitude. Then they were tested on their ability to calculate the outcome of this division transformation with other large-number arrays. The Mundurucu children effected this transformation even when non-numerical variables were controlled, performed above chance levels on the very first set of test trials, and exhibited performance similar to urban children who had access to precise number words and a surrounding symbolic culture. We conclude that a halving calculation is part of the suite of intuitive operations supported by the ANS. (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)

A classical definition of automaticity establishes that automatic processing occurs without attention or consciousness, and cannot be controlled. Previous studies have demonstrated that semantic priming can be reduced if attention is directed to a low-level of analysis. This finding suggests that semantic processing is not automatic since it can be controlled. In this paper, we present two experiments that demonstrate that semantic processing may occur in the absence of attention and consciousness. A negative semantic priming effect was found when a (...) low-level prime-task was required and when a masked lexical decision prime-task was performed . This paper also discusses the limitations of the inhibitory mechanism involved in negative semantic priming effect. (shrink)

Cohen Kadosh & Walsh (CK&W) present convincing evidence indicating the existence of notation-specific numerical representations in parietal cortex. We suggest that the same conclusions can be drawn for a particular type of numerical representation: the representation of time. Notation-dependent representations need not be limited to number but may also be extended to other magnitude-related contents processed in parietal cortex (Walsh 2003).

The repercussions of unconscious priming on the neural correlates subsequent cognition have been explored previously. However, the neural dynamics during the unconscious processing remains largely uncharted. To assess both the complexity and temporal dynamics of unconscious cognition the present study contrasts the evoked response from classes of masked stimuli with three different levels of complexity; words, consonant strings, and blanks. The evoked response to masked word stimuli differed from both consonant strings and blanks, which did not differ from each other. (...) This response was qualitatively different to any evoked potential observed when stimuli were consciously visible and peaked at 140 ms, earlier than is usually associated with differences between words and strings and 100 ms earlier than word-consonant string differences in the visible condition. The evoked response demonstrates a qualitatively distinct signature of unconscious cognition and directly demonstrates the extraction of abstract information under subliminal conditions. (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)

Comparisons of indirect measures with direct measures can help elucidate the relationship between nonconscious and conscious perception. We report three experiments on masked word priming in which we observed a negative correlation between prime discriminability and priming , i.e. where priming decreased with increasing prime visibility. While such observations are rare , they may indicate a conflict between conscious and nonconscious processing when primes are shown close to the subjective visibility threshold for the priming-relevant information. For instance, such a conflict (...) could occur between nonconscious processing of a prime’s meaning and conscious perception of prime letters. Theoretical accounts that discuss similar conflicts assume that the conflict is resolved either by automatically prioritising conscious processes or by discounting the estimated confusion caused by a prime-target pair . In both cases, priming is predicted to decrease when prime visibility increases from below threshold to perithreshold levels. Therefore, we suggest that negative priming-d’ relationships are most likely observed when the d’ measure assesses prime visibility at a level of representation that is below the level of representation at which priming arises, in terms of a putative hierarchy of word processing. (shrink)

Despite its strengths, Leech et al.'s model fails to address the important benefits that derive from self-explanation and task feedback in analogical reasoning development. These components encourage explicit, self-reflective processes that do not necessarily link to knowledge accretion. We wonder, therefore, what mechanisms can be included within a connectionist framework to model self-reflective involvement and its beneficial consequences.

Leech et al.'s model proposes representing relations as primed transformations rather than as structured representations (explicit representations of relations and their roles dynamically bound to fillers). However, this renders the model unable to explain several developmental trends (including relational integration and all changes not attributable to growth in relational knowledge). We suggest looking to an alternative computational model that learns structured representations from examples.

Multicultural environments require learning multiple number notations wherein some are encountered more frequently than others. This leads to differences in exposure and consequently differences in usage between notations. We find that differential notational usage imposes a significant neurocognitive load on number processing. Despite simultaneous acquisition, forty-two adult binumerate populations, familiar with two positional writing systems namely Hindu Nagari digits and Hindu Arabic digits, reported significantly lower preference and usage for Nagari as compared to Arabic. Twenty-four participants showed significantly increased reaction (...) times and reduced accuracy while performing magnitude comparison tasks in Nagari with respect to Arabic. Functional magnetic resonance imaging revealed that processing Nagari elicited significantly greater activity in number processing and attention networks. A direct subtraction of networks for Nagari and Arabic notations revealed a neural circuit comprising of bilateral intra-parietal sulcus, inferior and mid frontal gyri, fusiform gyrus and the anterior cingulate cortex (FDR p<0.005). Additionally, whole brain correlation analysis showed that activity in the left inferior parietal region was modulated by task performance in Nagari. We attribute the increased activation in Ng to increased task difficulty due to infrequent exposure and usage. Our results reiterate the role of the left intra-parietal sulcus in modulating performance in numeric tasks and highlight that of the attention network for monitoring symbolic notation mode in binumerates. (shrink)