Left to right: representational biases for numbers and the effect of visuomotor adaptation

Adaptation to right-shifting prisms improves left neglect for mental number line bisection. This study examined whether adaptation affects the mental number line in normal participants. Thirty-six participants completed a mental number line task before and after adaptation to either: left-shifting prisms, right-shifting prisms or control spectacles that did not shift the visual scene. Participants viewed number triplets (e.g. 16, 36, 55) and determined whether the numerical distance was greater on the left or right side of the inner number. Participants demonstrated a leftward bias (i.e. overestimated the length occupied by numbers located on the left side of the number line) that was consistent with the effect of pseudoneglect. The leftward bias was corrected by a short period of visuomotor adaptation to left-shifting prisms, but remained unaffected by adaptation to right-shifting prisms and control spectacles. The findings demonstrate that a simple visuomotor task alters the representation of space on the mental number line in normal participants.     

A colorful walk on the mental number line: Striving for the right direction

Verguts and Van Opstal [Verguts, T., & Van Opstal, F. (2008). A colorful walk, but is it on the mental number line? Reply to Cohen Kadosh, Tzelgov, and Henik, Cognition, 106, 558-563] cleverly explained the results of Cohen Kadosh, Tzelgov, and Henik [Cohen Kadosh, R., Tzelgov, J., & Henik, A. (2008). A synesthetic walk on the mental number line: The size effect, Cognition, 106, 548-557] as a result of different association strength between the size of a number and its color in synesthesia. Here we present three challenges to their alternative explanation, and support our original suggestion.     

The SNARC effect does not imply a mental number line

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.     

一个新的中医研究范式:从非线性动力学的角度解读中医

西方对中医的研究多是利用随机控制试验来检验其疗效。通过讨论,认为这类研究有其局限性。同时探讨一种新的研究范式,即非线性动力学理论。认为这一理论能够提供理论依据来设计适合中医特征的临床试验,并可望得出为西方医学界所接受的研究结果。     

3~6岁儿童数感发展的研究

从上海两所中等水平幼儿园以年龄班分层随机抽取180名3~6岁儿童为被试,采用个别测查法考察其数感发展状况。结果表明:(1)3~6岁儿童的数感发展存在显著年龄差异,无性别差异;(2)顺数、实物比较和数符号辨认是其表现较好的三项技能,而倒数和序数却表现较差;(3)数感各组成部分发展不同步,倒数,序数和数符号在中班到大班期间发展迅速,而顺数,基数概念,加减理解却在小班到中班期间发展较快。     

Exploring the impact of phonological awareness, visual–spatial working memory, and preschool quantity–number competencies on mathematics achievement in elementary school: Findings from a 3-year longitudinal study

This longitudinal study explored the importance of kindergarten measures of phonological awareness, working memory, and quantity–number competencies (QNC) for predicting mathematical school achievement in third graders (mean age 8 years 8 months). It was found that the impact of phonological awareness and visual–spatial working memory, assessed at 5 years of age, was mediated by early QNC, which predicted math achievement in third grade. Importantly, and confirming our isolated number words hypothesis, phonological awareness had no impact on higher numerical competencies (i.e., when number words needed to be linked with quantities [QNC Level II and above]) but predicted basic numerical competencies (i.e., when number words were isolated from quantities [QNC Level I]), explaining the moderate relationship between early literacy development and the development of mathematical competencies.     

Hilbert,logicism, and mathematical existence

David Hilbert’s early foundational views, especially those corresponding to the 1890s, are analysed here. I consider strong evidence for the fact that Hilbert was a logicist at that time, following upon Dedekind’s footsteps in his understanding of pure mathematics. This insight makes it possible to throw new light on the evolution of Hilbert’s foundational ideas, including his early contributions to the foundations of geometry and the real number system. The context of Dedekind-style logicism makes it possible to offer a new analysis of the emergence of Hilbert’s famous ideas on mathematical existence, now seen as a revision of basic principles of the “naive logic” of sets. At the same time, careful scrutiny of his published and unpublished work around the turn of the century uncovers deep differences between his ideas about consistency proofs before and after 1904. Along the way, we cover topics such as the role of sets and of the dichotomic conception of set theory in Hilbert’s early axiomatics, and offer detailed analyses of Hilbert’s paradox and of his completeness axiom (Vollständigkeitsaxiom).     

The mental time line: An analogue of the mental number line in the mapping of life events

A crucial aspect of the human mind is the ability to project the self along the time line to past and future. It has been argued that such self-projection is essential to re-experience past experiences and predict future events. In-depth analysis of a novel paradigm investigating mental time shows that the speed of this “self-projection” in time depends logarithmically on the temporal-distance between an imagined “location” on the time line that participants were asked to imagine and the location of another imagined event from the time line. This logarithmic pattern suggests that events in human cognition are spatially mapped along an imagery mental time line. We argue that the present time-line data are comparable to the spatial mapping of numbers along the mental number line and that such spatial maps are a fundamental basis for cognition.     

Common Representations of Abstract Quantities

ABSTRACT— Representations of abstract quantities such as time and number are essential for survival. A number of studies have revealed that both humans and nonhuman animals are able to nonverbally estimate time and number; striking similarities in the behavioral data suggest a common magnitude-representation system shared across species. It is unclear, however, whether these representations provide animals with a true concept of time and number, as posited by Gallistel and Gelman (2000) . In this article, we review the prominent cognitive and neurobiological models of timing and counting and explore the current evidence suggesting that nonhuman animals represent these quantities in a modality-independent (i.e., abstract) and ordered manner. Avenues for future research in the area of temporal and mathematical cognition are also discussed.     

为什么无效的药物治疗会被认为有效？

把无效的治疗误认为有效,不仅在大众中非常普遍,而且很多医生也常如此。造成这种疗效假象有许多原因,主要由于疾病的自愈或自发缓解、药物和治疗的安慰效应、缺乏严格的评价疗效标准以及诊断不确实,以及把良性疾病误诊为严重或恶性疾病所造成的。对传统医疗的信仰也是原因之一。因此,对任何药物或医疗的效果必须进行严格的随机对照临床试验,并且得到同行的检验和公认。