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Learning from conditional probabilities 从条件概率中学习
IF 2.8 1区 心理学 Q1 PSYCHOLOGY, EXPERIMENTAL Pub Date : 2024-10-18 DOI: 10.1016/j.cognition.2024.105962
Corina Strößner, Ulrike Hahn
Bayesianism, that is, the formal capturing of belief in terms of probabilities, has had a major impact in cognitive science. Decades of research have examined lay reasoners’ learning and reasoning with probabilities. The bulk of that research has concerned the response to new evidence. That response will depend on the conditional probabilities a reasoner assumes, yet little research has addressed the question of how reasoners respond when they are provided with new conditional probabilities. Furthermore, there are not just open empirical questions as to how lay reasoners actually respond, there are also open questions as to how they should respond. This is illustrated by philosophical debate about the so-called Judy Benjamin Problem. In this paper, we present experiments on belief revision problems in which the new information is a conditional probability. More specifically, we investigate two versions of these problems: one where basic probability theory (as the core of what it means ‘to be Bayesian’) provides a single correct answer, and one where that answer is under-constrained. The former provide a new type of evidence on the longstanding question of human probabilistic reasoning skill. The latter informs debate on how to expand the Bayesian toolbox to deal with the issues raised by the Judy Benjamin Problem.
贝叶斯主义,即用概率的形式捕捉信念,对认知科学产生了重大影响。数十年来,人们对非专业推理者学习和推理概率的情况进行了研究。其中大部分研究涉及对新证据的反应。这种反应取决于推理者所假设的条件概率,但很少有研究涉及推理者在获得新的条件概率时如何反应的问题。此外,关于非专业推理者究竟如何应对,不仅存在经验上的问题,而且还存在他们应该如何应对的问题。关于所谓 "朱迪-本杰明问题 "的哲学争论就说明了这一点。在本文中,我们将对新信息是条件概率的信念修正问题进行实验。更具体地说,我们研究了这些问题的两个版本。一种是基本概率论(作为 "贝叶斯 "的核心)提供了单一的正确答案,另一种是该答案受限。前者为人类概率推理技能这一长期存在的问题提供了一种新的证据。后者为关于如何扩展贝叶斯工具箱以处理朱迪-本杰明问题所提出的问题的辩论提供了信息。
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引用次数: 0
How visual experience shapes body representation 视觉体验如何塑造身体表征
IF 2.8 1区 心理学 Q1 PSYCHOLOGY, EXPERIMENTAL Pub Date : 2024-10-16 DOI: 10.1016/j.cognition.2024.105980
Iqra Shahzad , Valeria Occelli , Eléonore Giraudet , Elena Azañón , Matthew R. Longo , André Mouraux , Olivier Collignon
We do not have a veridical representation of our body in our mind. For instance, tactile distances of equal measure along the medial-lateral axis of our limbs are generally perceived as larger than those running along the proximal-distal axis. This anisotropy in tactile distances reflects distortions in body-shape representation, such that the body parts are perceived as wider than they are. While the origin of such anisotropy remains unknown, it has been suggested that visual experience could partially play a role in its manifestation. To causally test the role of visual experience on body shape representation, we investigated tactile distance perception in sighted and early blind individuals comparing medial-lateral and proximal-distal tactile distances of stimuli presented on the ventral and dorsal part of the forearm, wrist, and hand. Overestimation of distances in the medial-lateral over proximal-distal body axes were found in both sighted and blind people, but the magnitude of the anisotropy was significantly reduced in the forearms of blind people. We conclude that vision does not drive the emergence of tactile distance anisotropies, but visual experience can however modulate its expression on some specific body parts.
在我们的头脑中,身体并不是真实存在的。例如,沿着四肢内侧-外侧轴的等量触觉距离通常被认为比沿着近端-远端轴的触觉距离大。触觉距离的这种各向异性反映了身体形状表征的扭曲,例如,身体部位被认为比实际要宽。虽然这种各向异性的起源尚不清楚,但有人认为视觉经验可能在其表现中起了部分作用。为了检验视觉经验对身体形状表征的因果作用,我们研究了明眼人和早期盲人的触觉距离感知,比较了前臂、手腕和手的腹侧和背侧刺激物的内侧-外侧和近侧-远侧触觉距离。结果发现,明眼人和盲人都高估了身体内外侧轴和近端-远端轴的距离,但盲人前臂的各向异性程度明显降低。我们的结论是,视觉并不驱动触觉距离各向异性的出现,但视觉经验可以调节触觉距离各向异性在某些特定身体部位的表现。
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引用次数: 0
Children recognize and reject favoritism in norm enforcement 儿童认识到并拒绝规范执行中的偏袒行为
IF 2.8 1区 心理学 Q1 PSYCHOLOGY, EXPERIMENTAL Pub Date : 2024-10-16 DOI: 10.1016/j.cognition.2024.105981
Louisa Huff, Tindaya Déniz, Linda Gronem, Sebastian Grueneisen
The impartial enforcement of norms and laws is a hallmark of fair societies, yet partial, unequal norm enforcement is common, for example as a result of corruption. While children condemn norm violations and value impartiality in resource allocation contexts, children's understanding of unequal norm enforcement is currently underexplored. In three vignette studies, we investigated 4- to 8-year-old's (N = 192) developing recognition and condemnation of unequal norm enforcement, which presupposes a sensitivity to impartiality as a meta-norm. Children evaluated the actions of characters who enforced different norms equally or unequally. From age 5, children disapproved of unequal norm enforcement but approved of unequal treatment when justified (Study 1). Children of all ages accepted a lack of punishment when applied equally to all transgressors, suggesting that their negative evaluations of unequal norm enforcement were specifically guided by the element of partiality and not the desire to see transgressors sanctioned (Study 2). Further, children aged 6 years and older were sensitive to the reasons behind unequal punishment, condemning instances of favoritism while accepting selective leniency due to mitigating circumstances (Study 3). The findings show that, from around 5 to 6 years of age, children condemn unequal sanctions for equal transgressions, thereby demonstrating a deep appreciation of impartiality as a foundational principle of fair norm enforcement.
不偏不倚地执行规范和法律是公平社会的标志,但部分、不平等地执行规范的情况却很普遍,例如腐败造成的结果。虽然儿童谴责违反规范的行为,并重视资源分配中的公正性,但儿童对不平等规范执行的理解目前尚未得到充分探索。在三项小故事研究中,我们调查了 4 至 8 岁儿童(人数 = 192)对不平等规范执行的认识和谴责发展情况。儿童对平等或不平等地执行不同规范的角色的行为进行评价。从 5 岁开始,儿童就不赞成不平等地执行准则,但在有正当理由的情况下则赞成不平等待遇(研究 1)。所有年龄段的儿童都能接受对所有违规者一视同仁的惩罚,这表明他们对不平等规范执行的负面评价是受偏袒因素的具体引导,而不是希望看到违规者受到制裁(研究 2)。此外,6 岁及以上的儿童对不平等惩罚背后的原因很敏感,他们谴责偏袒行为,同时也接受因情节轻微而有选择性的宽大处理(研究 3)。研究结果表明,从 5 到 6 岁左右开始,儿童就会谴责对同等违法行为的不平等惩罚,从而显示出他们对公正性这一公平执行规范的基本原则的深刻理解。
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引用次数: 0
Recollective and non-recollective processes in working memory retrieval 工作记忆检索中的回忆和非回忆过程
IF 2.8 1区 心理学 Q1 PSYCHOLOGY, EXPERIMENTAL Pub Date : 2024-10-16 DOI: 10.1016/j.cognition.2024.105978
Fiona Laura Rosselet-Jordan , Marlène Abadie , Stéphanie Mariz Elsig , Pierre Barrouillet , Valérie Camos
The aim of this study was to investigate the nature of the processes involved in working memory (WM) retrieval by distinguishing between recollective (direct access) and non-recollective (reconstruction) recall. To this end, the trichotomous theory of recall (Brainerd et al., 2009) was applied to young adults' recall performance in a complex span task in which word lists were presented in three successive study-test trials. In three experiments, factors known to affect WM performance were manipulated, such as the cognitive load (CL) of the concurrent task and the involvement of long-term memory (LTM) knowledge through the associative relatedness of the memory items and the temporally spaced presentation of memory lists. The application of the trichotomous theory of recall proved effective and established that both recollective and non-recollective processes support WM recall, though recollective processes are predominant. The detrimental effect of increased CL on recall performance appeared to result from a reduction in direct access, while leaving reconstruction unaffected. Two manipulations aimed at increasing the involvement of LTM in recall had different effects on retrieval processes. Associative relatedness favored direct access, while spaced presentation reduced it. The implications of these findings for our understanding of the relationships between LTM and WM and for WM theories are discussed.
本研究的目的是通过区分回忆性(直接访问)和非回忆性(重建)回忆,研究工作记忆(WM)检索过程的性质。为此,研究人员将回忆的三分法理论(Brainerd 等人,2009 年)应用于年轻成人在复杂跨度任务中的回忆表现。在三项实验中,对已知会影响 WM 表现的因素进行了操作,如同时进行的任务的认知负荷(CL),以及通过记忆项目的联想相关性和记忆列表的时间间隔呈现对长时记忆(LTM)知识的参与。事实证明,三重回忆理论的应用是有效的,它确定了回忆和非回忆过程都支持 WM 回忆,但回忆过程占主导地位。CL增加对回忆成绩的不利影响似乎是由于直接访问的减少,而重构则不受影响。两种旨在增加 LTM 在回忆中的参与度的操作对检索过程产生了不同的影响。关联性有利于直接进入,而间隔呈现则会减少直接进入。本文讨论了这些发现对我们理解LTM和WM之间关系以及WM理论的影响。
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引用次数: 0
Motivational context determines the impact of aversive outcomes on mental effort allocation 动机背景决定了厌恶结果对脑力分配的影响
IF 2.8 1区 心理学 Q1 PSYCHOLOGY, EXPERIMENTAL Pub Date : 2024-10-15 DOI: 10.1016/j.cognition.2024.105973
Mahalia Prater Fahey , Debbie M. Yee , Xiamin Leng , Maisy Tarlow , Amitai Shenhav
It is well known that people will exert effort on a task if sufficiently motivated, but how they distribute these efforts across different strategies (e.g., efficiency vs. caution) remains uncertain. Past work has shown that people invest effort differently for potential positive outcomes (rewards) versus potential negative outcomes (penalties). However, this research failed to account for differences in the context in which negative outcomes motivate someone - either as punishment or reinforcement. It is therefore unclear whether effort profiles differ as a function of outcome valence, motivational context, or both. Using computational modeling and our novel Multi-Incentive Control Task, we show that the influence of aversive outcomes on one's effort profile is entirely determined by their motivational context. Participants (N:91) favored increased caution in response to larger penalties for incorrect responses, and favored increased efficiency in response to larger reinforcement for correct responses, whether positively or negatively incentivized.

Statement of relevance

People have to constantly decide how to allocate their mental effort, and in doing so can be motivated by both the positive outcomes that effort accrues and the negative outcomes that effort avoids. For example, someone might persist on a project for work in the hopes of being promoted or to avoid being reprimanded or even fired. Understanding how people weigh these different types of incentives is critical for understanding variability in human achievement as well as sources of motivational impairments (e.g., in major depression). We show that people not only consider both potential positive and negative outcomes when allocating mental effort, but that the profile of effort they engage under negative incentives differs depending on whether that outcome is contingent on sustaining good performance (negative reinforcement) or avoiding bad performance (punishment). Clarifying the motivational factors that determine effort exertion is an important step for understanding motivational impairments in psychopathology.
众所周知,如果有足够的动机,人们就会在一项任务中付出努力,但他们如何将这些努力分配到不同的策略中(例如,高效与谨慎)仍不确定。过去的研究表明,人们对潜在的积极结果(奖励)和潜在的消极结果(惩罚)所投入的精力是不同的。然而,这些研究没有考虑到负面结果激励人们的背景差异--是惩罚还是强化。因此,目前还不清楚努力程度是否因结果价值、动机背景或两者而异。通过计算建模和新颖的多重激励控制任务,我们证明了厌恶性结果对一个人努力程度的影响完全取决于其动机背景。无论是正激励还是负激励,参与者(人数:91)都倾向于在错误回答受到更大惩罚时更加谨慎,而在正确回答受到更大强化时提高效率。例如,一个人可能会坚持完成一个工作项目,希望得到晋升,或者避免被训斥甚至解雇。了解人们如何权衡这些不同类型的激励对于理解人类成就的差异性以及动机障碍(如重度抑郁症)的来源至关重要。我们的研究表明,人们在分配脑力时不仅会考虑潜在的积极和消极结果,而且在消极激励下,人们所付出的努力会因结果是取决于保持良好表现(消极强化)还是避免不良表现(惩罚)而有所不同。明确决定努力程度的动机因素是理解精神病理学中动机障碍的重要一步。
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引用次数: 0
Quantity discrimination in 9 ungulate species: Individuals take item number and size into account to discriminate quantities 9 种有蹄类动物的数量判别:个体在区分数量时会考虑物品的数量和大小
IF 2.8 1区 心理学 Q1 PSYCHOLOGY, EXPERIMENTAL Pub Date : 2024-10-14 DOI: 10.1016/j.cognition.2024.105979
Alina Schaffer , Alvaro L. Caicoya , Anja Widdig , Ruben Holland , Federica Amici
The ability to discriminate quantities is crucial for humans and other animals, by allowing individuals to maximize food intake and successfully navigate in their social environment. Here, we used a comprehensive approach to compare quantity discrimination abilities (i.e. ability to compare sets with different quantities of identical items, reliance on item size and spatial distribution, existence of irrational biases) in 9 different species of ungulates and provide novel insight into the socio-ecological conditions that might favor their emergence. We tested a total of 37 captive subjects including goats (Capra aegagrus hircus), llamas (Lama glama), guanacos (Lama guanicoe), Grevy's zebras (Equus grevyi), Chapman's zebras (Equus burchelli chapmanni), rhinos (Diceros bicornis michaeli), giraffes (Giraffa camelopardalis rothschildi), bison (Bison bonasus) and buffalos (Syncerus caffer nanus). Our results revealed that subjects were able to discriminate quantities when presented with two sets of food items that could differ in number, size and partially density. When presented with sets containing a different number of identical food items, subjects successfully selected the set with more items, with performance overall decreasing when sets had higher ratios (e.g., 1:3 vs 1:5). In addition, subjects could successfully maximize their food intake when both sets had the same number of items, but items had different sizes. However, performance decreased at chance levels when varying both the number of items and their size or distribution. Giraffes performed better than other species in most conditions, and we found no evidence for an irrational bias toward sets with more, smaller items or denser distributions. Overall, our study provides a first comparative assessment of quantity discrimination skills in several ungulate species.
数量辨别能力对人类和其他动物至关重要,它能使个体最大限度地摄取食物,并成功地在社会环境中游刃有余。在这里,我们采用了一种综合方法来比较 9 种不同蹄类动物的数量辨别能力(即比较具有不同数量相同物品的集合的能力、对物品大小和空间分布的依赖性、是否存在非理性偏差),并对可能有利于其出现的社会生态条件提供了新的见解。我们一共测试了 37 个圈养对象,包括山羊(Capra aegagrus hircus)、骆马(Lama glama)、羚牛(Lama guanicoe)、格瑞斑马(Equus grevyi)和查普曼斑马(Chapman's zebras)、查普曼斑马(Equus burchelli chapmanni)、犀牛(Diceros bicornis michaeli)、长颈鹿(Giraffa camelopardalis rothschildi)、野牛(Bison bonasus)和水牛(Syncerus caffer nanus)。我们的研究结果表明,当两组食物的数量、大小和部分密度不同时,受试者能够区分数量。当一组食物中含有不同数量的相同食物时,受试者会成功地选择含有较多食物的一组,而当两组食物的比例较高时(如 1:3 与 1:5),受试者的整体表现会下降。此外,当两组食物的数量相同,但大小不同时,受试者也能成功地将食物摄入量最大化。然而,当物品数量、大小或分布都不同时,受试者的表现就会下降到偶然水平。在大多数情况下,长颈鹿的表现都优于其他物种,而且我们没有发现任何证据表明长颈鹿会不合理地偏向于选择物品数量更多、更小或分布更密集的食物组。总之,我们的研究首次对几种蹄类动物的数量辨别能力进行了比较评估。
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引用次数: 0
Revisiting the concreteness effect: Non-arbitrary mappings between form and concreteness of English words influence lexical processing 重新审视具体性效应:英语单词的形式和具体程度之间的非任意映射影响词汇加工。
IF 2.8 1区 心理学 Q1 PSYCHOLOGY, EXPERIMENTAL Pub Date : 2024-10-09 DOI: 10.1016/j.cognition.2024.105972
Elaine Kearney , Katie L. McMahon , Frank Guenther , Joanne Arciuli , Greig I. de Zubicaray
How do we represent and process abstract and concrete concepts? The “concreteness effect”, in which words with more concrete meanings are processed more quickly and accurately across a range of language tasks compared to abstract ones, suggests a differential conceptual organization of these words in the brain. However, concrete words tend to be marked by specific phonotactic features, such as having fewer syllables and more phonological neighbours. It is unclear whether these non-arbitrary form-meaning relationships that systematically denote the concreteness of a word impact language processing. In the current study, we first establish the extent of systematic mappings between phonological/phonetic features and concreteness ratings in a large set of monosyllabic and polysyllabic English words (i.e., concreteness form typicality), then demonstrate that they significantly influence lexical processing using behavioural megastudy datasets. Surface form features predicted a significant proportion of variance in concreteness ratings of monomorphemic words (25 %) which increased with the addition of polymorphemic forms (43 %). In addition, concreteness form typicality was a significant predictor of performance on visual and auditory lexical decision, naming, and semantic (concrete/abstract) decision tasks, after controlling for a range of psycholinguistic variables and concreteness ratings. Overall, our results provide the first evidence that concreteness form typicality influences lexical processing. We discuss theoretical implications for interpretations of the concreteness effect and models of language processing that have yet to incorporate non-arbitrary relationships between form and meaning into their feature sets.
我们如何表示和处理抽象和具体概念?具体词义效应 "表明,在一系列语言任务中,具体词义的词语比抽象词义的词语处理得更快、更准确。然而,具体词语往往具有特定的语音战术特征,如音节较少、音素邻接较多。目前还不清楚这些非任意性的形义关系是否会对语言加工产生影响。在本研究中,我们首先在一大批单音节和多音节英语单词中建立了语音/音素特征与具体程度评级之间的系统映射关系(即具体程度形式典型性),然后利用行为大研究数据集证明了它们对词汇加工的显著影响。表面形式特征预示了单音节词具体词性评分的很大一部分差异(25%),而随着多音节形式的增加,这一比例也随之增加(43%)。此外,在控制了一系列心理语言学变量和具体词性评分之后,具体词性形式的典型性对视觉和听觉词汇决策、命名和语义(具体/抽象)决策任务的成绩有显著的预测作用。总之,我们的研究结果首次证明了具体形式的典型性会影响词汇加工。我们讨论了对具体性效应的解释和语言加工模型的理论意义,这些模型尚未将形式和意义之间的非任意关系纳入其特征集。
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引用次数: 0
Domain-specific updating of metacognitive self-beliefs 元认知自我信念的特定领域更新。
IF 2.8 1区 心理学 Q1 PSYCHOLOGY, EXPERIMENTAL Pub Date : 2024-10-08 DOI: 10.1016/j.cognition.2024.105965
Kelly Hoogervorst , Leah Banellis , Micah G. Allen
Metacognitive self-monitoring is thought to be largely domain-general, with numerous prior studies providing evidence of a metacognitive g-factor. The observation of shared inter-individual variance across different measures of metacognition does not however preclude the possibility that some aspects may nevertheless be domain-specific. In particular, it is unknown the degree to which explicit metacognitive beliefs regarding one's own abilities may exhibit domain generality. Similarly, little is known about how such prior self-beliefs are maintained and updated in the face of new metacognitive experiences. In this study of 330 healthy individuals, we explored metacognitive belief updating across memory, visual, and general knowledge domains spanning nutritional and socioeconomic facts. We find that across all domains, participants strongly reduced their self-belief (i.e., expressed less confidence in their abilities) after completing a multi-domain metacognition test battery. Using psychological network and cross-correlation analyses, we further found that while metacognitive confidence exhibited strong domain generality, metacognitive belief updating was highly domain-specific, such that participants shifted their confidence specifically according to their performance on each domain. Overall, our findings suggest that metacognitive experiences prompt a shift in self-priors from a more general to a more specific focus.
元认知自我监控被认为在很大程度上具有领域通用性,之前的许多研究都提供了元认知 g 因子的证据。然而,在元认知的不同测量中观察到共同的个体间差异,并不排除某些方面可能是特定领域的。特别是,人们还不知道对自身能力的明确元认知信念在多大程度上会表现出领域普遍性。同样,人们对这种先前的自我信念在面对新的元认知经验时是如何保持和更新的也知之甚少。在这项对 330 名健康人进行的研究中,我们探讨了元认知信念在记忆、视觉和常识领域的更新情况,这些领域涵盖了营养和社会经济事实。我们发现,在所有领域中,参与者在完成多领域元认知测试后都会强烈地降低自我信念(即对自己的能力表示信心不足)。通过心理网络和交叉相关分析,我们进一步发现,虽然元认知信心表现出很强的领域普遍性,但元认知信念的更新却具有很强的领域特异性,因此,参与者会根据他们在每个领域的表现来改变他们的信心。总之,我们的研究结果表明,元认知经验会促使自我先验从更普遍的关注转向更具体的关注。
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引用次数: 0
Emotion in action: A study on the enactment effect on emotional action sentences 行动中的情感:关于情感动作句子颁布效应的研究。
IF 2.8 1区 心理学 Q1 PSYCHOLOGY, EXPERIMENTAL Pub Date : 2024-10-05 DOI: 10.1016/j.cognition.2024.105974
Silvia Serino, Rossana Actis-Grosso, Marta Maisto, Paola Ricciardelli, Patrizia Steca
While abundant literature suggests that both performing congruent actions and emotional stimuli can enhance memory, their combined impact on memory for action phrases remains underexplored. This study investigated the effects of enactment with emotionally charged stimuli on memory performance. Sixty participants encoded action sentences with negative, neutral, or positive emotional connotations using either enactment or verbal-reading methods. Memory performance was assessed through immediate free recall tasks and a delayed yes-no recognition task. Results demonstrated a significant memory advantage for action-enacted sentences compared to verbal reading in recall and recognition tasks. Moreover, recall accuracy was higher for negative action sentences, while recognition performance was enhanced for negative and positive sentences. No interaction was found between encoding type and emotional connotation in memory tasks. Our findings revealed that both enactment and valence independently enhance memory performance, extending the benefits of enactment to emotional stimuli. Furthermore, our results highlight the differential effects of valence on free recall and recognition tasks, suggesting task-specific processes related to memory for negative and positive stimuli.
虽然大量文献表明,做出一致的动作和情绪刺激都能增强记忆,但它们对动作短语记忆的综合影响仍未得到充分探讨。本研究调查了带有情绪刺激的行为对记忆表现的影响。60 名受试者分别采用表演法或口头阅读法对带有消极、中性或积极情绪内涵的动作句子进行了编码。记忆表现通过即时自由回忆任务和延迟是非识别任务进行评估。结果表明,在回忆和识别任务中,与口头阅读相比,动作表演句子具有明显的记忆优势。此外,消极动作句子的回忆准确率更高,而消极和积极句子的识别能力都有所提高。在记忆任务中,编码类型和情感内涵之间没有发现交互作用。我们的研究结果表明,制定和情感内涵都能独立地提高记忆成绩,从而将制定的益处扩展到情感刺激。此外,我们的研究结果还强调了情绪对自由回忆和识别任务的不同影响,这表明了与消极和积极刺激记忆相关的特定任务过程。
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引用次数: 0
Mapping and modeling the semantic space of math concepts 数学概念语义空间的映射和建模。
IF 2.8 1区 心理学 Q1 PSYCHOLOGY, EXPERIMENTAL Pub Date : 2024-10-05 DOI: 10.1016/j.cognition.2024.105971
Samuel Debray , Stanislas Dehaene
Mathematics is an underexplored domain of human cognition. While many studies have focused on subsets of math concepts such as numbers, fractions, or geometric shapes, few have ventured beyond these elementary domains. Here, we attempted to map out the full space of math concepts and to answer two specific questions: can distributed semantic models, such a GloVe, provide a satisfactory fit to human semantic judgements in mathematics? And how does this fit vary with education? We first analyzed all of the French and English Wikipedia pages with math contents, and used a semi-automatic procedure to extract the 1000 most frequent math terms in both languages. In a second step, we collected extensive behavioral judgements of familiarity and semantic similarity between them. About half of the variance in human similarity judgements was explained by vector embeddings that attempt to capture latent semantic structures based on cooccurence statistics. Participants' self-reported level of education modulated familiarity and similarity, allowing us to create a partial hierarchy among high-level math concepts. Our results converge onto the proposal of a map of math space, organized as a database of math terms with information about their frequency, familiarity, grade of acquisition, and entanglement with other concepts.
数学是人类认知中一个探索不足的领域。虽然许多研究都集中在数学概念的子集上,如数字、分数或几何图形,但很少有人涉足这些基本领域之外的领域。在这里,我们试图描绘出数学概念的完整空间,并回答两个具体问题:分布式语义模型(如 GloVe)能否令人满意地与人类数学语义判断相匹配?这种契合度又是如何随教育程度而变化的?我们首先分析了所有包含数学内容的法语和英语维基百科页面,并使用半自动程序提取了这两种语言中出现频率最高的 1000 个数学术语。第二步,我们收集了大量关于它们之间熟悉程度和语义相似性的行为判断。人类相似性判断中约有一半的变异是由向量嵌入解释的,向量嵌入试图捕捉基于共生统计的潜在语义结构。参与者自我报告的教育水平调节了熟悉度和相似度,使我们能够在高级数学概念之间建立部分层次结构。我们的研究结果汇聚成一个数学空间地图的提议,该地图是一个数学术语数据库,其中包含有关数学术语的频率、熟悉程度、获得等级以及与其他概念的纠缠等信息。
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引用次数: 0
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Cognition
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