Is there an innate geometric module? Effects of experience with angular geometric cues on spatial re-orientation based on the shape of the environment

Non-human animals and human children can make use of the geometric shape of an environment for spatial reorientation and in some circumstances reliance on purely geometric information (metric properties of surfaces and sense) can overcome the use of local featural cues. Little is known as to whether the use of geometric information is in some way reliant on past experience or, as would likely be argued by advocates of the notion of a geometric module, it is innate. We tested the navigational abilities of newborn domestic chicks reared in either rectangular or circular cages. Chicks were trained in a rectangular-shaped enclosure with panels placed at the corners to provide salient featural cues. Rectangular-reared and circular-reared chicks proved equally able to learn the task. When tested after removal of the featural cues, both rectangular- and circular-reared chicks showed evidence that they had spontaneously encoded geometric information. Moreover, when trained in a rectangular-shaped enclosure without any featural cues, chicks reared in rectangular-, circular-, or c-shaped cages proved to be equally able to learn and perform the task using geometric information. These results suggest that effective use of geometric information for spatial reorientation does not require experience in environments with right angles and metrically distinct surfaces, thus supporting the hypothesis of a predisposed geometric module in the animal brain.     

Toddlers' use of metric information and landmarks to reorient

Mobile organisms can keep track of spatial location (both their own location and that of objects in the environment) using either an external referent system or one centered on the self and updated by information about movement through space. When the latter system is disabled (e.g., by rapid turning), aspects of the external world must be used to reestablish orientation. Recently, it has been claimed that, both for rats and for human toddlers, reorientation is achieved using a geometric module that accepts only information about the metric properties of the environment (C. R. Gallistel, 1990; L. Hermer & E. S. Spelke, 1994, 1996). In a series of experiments, this paper confirms that geometric information is used for reorientation by young children, but gives reason to doubt that the use of this information is achieved using a module impenetrable to nongeometric information.     

Use of geometry for spatial reorientation in children applies only to symmetric spaces

Proponents of the geometric module hypothesis argue that following disorientation, many species reorient by use of macro‐environment geometry. It is suggested that attention to the surface layout geometry of natural terrain features may have been selected for over evolutionary time due to the enduring and unambiguous location information it provides. Paradoxically, however, tests of the hypothesis have been exclusively conducted in symmetric (hence ‘unnatural’ and geometrically ambiguous) environments. The present series of studies examines reorientation by 18‐month–3‐year‐old children in a rectangular versus irregular quadrilateral enclosure (Study 1), a rectangular versus irregular quadrilateral array (Study 2) and an isosceles versus irregular triangular array (Study 3). Children were successful in symmetric but not asymmetric environments, casting doubt on the functional argument for an empirical basis of the geometric module hypothesis.     

The Manifestation Range of Innately Good Knowledge and Ability,and the Danger of Separation: On Zhuzi’s Question about Understanding Words

Zhuzi (Zhu Xi), Zhang Nanxuan and Lü Donglai continued a discussion begun by Hu Wufeng and his disciples on the subject of “knowing the form of benevolence,” and “seeking for a true mind in an absent one.” One result of their discussion was to make people realize that innately good knowledge and ability are not only manifested in loving one’s parents and respecting one’s elders, but also in the simple acts of drinking when thirsty and eating when hungry. This generated the idea of “manifestation range of innately good knowledge and ability.” However, another conclusion of this discussion claimed that if the desire to drink and eat or the king of Qi’s grudging an ox are included in this range, there would be a danger of viewing innately good knowledge and ability merely as inborn human nature or instinct. This discussion reveals an unsteady relationship between innately good knowledge and ability and the feeling of commiseration, which are sometimes united and sometimes separate.     

Is language necessary for human spatial reorientation? Reconsidering evidence from dual task paradigms

Being able to reorient to the spatial environment after disorientation is a basic adaptive challenge. There is clear evidence that reorientation uses geometric information about the shape of the surrounding space. However, there has been controversy concerning whether use of geometry is a modular function, and whether use of features is dependent on human language. A key argument for the role of language comes from shadowing findings where adults engaged in a linguistic task during reorientation ignored a colored wall feature and only used geometric information to reorient [Hermer-Vazquez, L., Spelke, E., & Katsnelson, A. (1999). Sources of flexibility in human cognition: Dual task studies of space and language. Cognitive Psychology, 39, 3-36]. We report three studies showing: (a) that the results of Hermer-Vazques et al. [Hermer-Vazquez, L., Spelke, E., & Katsnelson, A. (1999). Sources of flexibility in human cognition: Dual task studies of space and language. Cognitive Psychology, 39, 3-36] are obtained in incidental learning but not with explicit instructions, (b) that a spatial task impedes use of features at least as much as a verbal shadowing task, and (c) that neither secondary task impedes use of features in a room larger than that used by Hermer-Vazquez et al. These results suggest that language is not necessary for successful use of features in reorientation. In fact, whether or not there is an encapsulated geometric module is currently unsettled. The current findings support an alternative to modularity; the adaptive combination view hypothesizes that geometric and featural information are utilized in varying degrees, dependent upon the certainty and variance with which the two kinds of information are encoded, along with their salience and perceived usefulness.     

Learning about environmental geometry: a flaw in Miller and Shettleworth's (2007) operant model

Many studies have examined how humans and other animals reestablish a sense of direction following disorientation in enclosed environments. Results showing that geometric shape of an enclosure is typically encoded, sometimes to the exclusion of featural cues, have led to suggestions that geometry might be encoded in a dedicated geometric module. Recently, Miller and Shettleworth (2007) proposed that the reorientation task be viewed as an operant task and they presented an associative operant model that appears to account for many empirical findings from reorientation studies. In this paper we show that, although Miller and Shettleworth's insights into the operant nature of the reorientation task may be sound, their mathematical model has a serious flaw. We present simulations to illustrate the implications of the flaw. We also propose that the output of a simple neural network, the perceptron, can be used to conduct operant learning within the reorientation task and can solve the problem in Miller and Shettleworth's model.     

Uncovering the structure of a memorist's superior "basic" memory capacity

After extensive laboratory testing of the famous memorist Rajan, Thompson, Cowan, and Frieman (1993) proposed that he was innately endowed with a superior memory capacity for digits and letters and thus violated the hypothesis that exceptional memory fully reflects acquired "skilled memory." We successfully replicated the empirical phenomena that led them to their conclusions. From additional analyses and new experiments, we found support for an alternative hypothesis, namely that Rajan's superior memory for digits was mediated by learned encoding techniques that he acquired during nearly a thousand hours of practice memorizing the mathematical constant pi. Our paper describes a general experimental approach for studying the structure of exceptional memory and how Rajan's unique structure is consistent with the general theoretical framework of long-term working memory (Ericsson and Kintsch, 1995).     

Theory of mind, language and the temporoparietal junction mystery

Brain imaging of adults during false-belief story tasks consistently shows activation of the temporoparietal junction in English-speaking Americans and German-speaking Europeans. Kobayashi et al. find this observation in adult English speakers but not in English-speaking children or in English-Japanese bilingual persons. This finding suggests a cultural or linguistic influence on location of brain function and argues against maturation of innately specified neural substrates. It is reminiscent of effects of linguistic development, bilingualism and cultural differences on theory of mind development.     

Young children's use of features to reorient is more than just associative: further evidence against a modular view of spatial processing

Proponents of a geometric module have argued that instances of young children's use of features as well as geometry to reorient can be explained by a two-stage process. In this model, only the first stage is a true reorientation, accomplished by using geometric information alone; features are considered in a second stage using association ( Lee, Shusterman & Spelke, 2006 ). This account is contradicted by the data from two experiments. Experiment 1a sets the stage for Experiment 1b by showing that young children use geometric information to reorient in a complex geometric figure without a single principal axis of symmetry (an octagon). In such a figure, there are two sets of geometrically congruent corners, with four corners in each set. The addition of a colored wall leads to the existence of three geometrically congruent but, crucially, all unmarked corners; using the colored wall to distinguish among them could not be done associatively. In Experiment 1b, both 3- and 5-year-old children showed true non-associative reorientation using features by performing at above-chance levels on all-white trials. Experiment 2 used a paradigm without distinctive geometry, modeled on Lee et al. (2006) , involving an equilateral triangle of hiding places located within a circular enclosure, but with a large stable feature rather than a small moveable one. Four-year-olds (the age group studied by Lee et al.) used features at above-chance levels. Thus, features can be used to reorient, in a way not dependent on association, in contradiction to the two-stage version of the modular view.     

儿童空间再定向的几何模块论及其局限

儿童的空间再定向指的是迷失方向的儿童在空间中重新确定自己方位并找回被藏物体的能力。儿童的这一能力与某些低等哺乳动物（如大鼠）相似,都只能利用空间环境所构成的几何信息,不能利用非几何信息来再定向。几何模块论认为造成这一现象的原因是儿童与低等哺乳动物的认知系统里存在几何模块。然而,众多研究对这种简单化的观点提出了异议。针对这些异议,几何模块论又进行了新的修订     

Using perceptrons to explore the reorientation task

The reorientation task is a paradigm that has been used extensively to study the types of information used by humans and animals to navigate in their environment. In this task, subjects are reinforced for going to a particular location in an arena that is typically rectangular in shape. The subject then has to find that location again after being disoriented, and possibly after changes have been made to the arena. This task is used to determine the geometric and featural cues that can be used to reorient the agent in the arena. The purpose of the present paper is to present several simulation results that show that a simple neural network, a perceptron, can be used to generate many of the traditional findings that have been obtained using the reorientation task. These results suggest that reorientation task regularities can be explained without appealing to a geometric module that is a component of spatial processing.     

Inexperienced newborn chicks use geometry to spontaneously reorient to an artificial social partner

A fundamental process underlying navigation behaviour, shown to occur in every species tested, uses geometric properties of the environment for location memory and orientation. Here we employ a new method to ask whether this basic geometric orientation ability is innately predisposed in the brain or depends on specific experiences navigating in a geometrically rich environment. Using the newborn domestic chick as a model system, we present a working memory task testing reorientation towards a filial imprinting object under rigorous controlled rearing conditions. In the absence of any previous exposure to a geometrically rich environment, newly hatched chicks spontaneously recovered their bearings by making use of distances and directional relations to reorient themselves to an artificial social partner. These findings provide evidence for an innate capacity to navigate by the geometric structure of the environment.     

Children's use of landmarks: implications for modularity theory

Previous studies have shown that disoriented children use the geometric features of the environment to reorient, but the results have not consistently demonstrated whether children can combine such information with landmark information. Results indicating that they cannot suggest the existence of a geometric module for reorientation. However, results indicating that children can use geometric information in combination with landmark information challenge the modularity interpretation. An uncontrolled variable in the studies yielding conflicting results has been the size of the experimental space. In the present studies, which tested young children in spaces of two different sizes, the size of the space affected their ability to use available landmark information. In the small space, the children did not use the landmark to reorient, but in the large space they did. The ability of children to use landmarks in combination with geometric information raises important questions about the existence of an encapsulated geometric module.     

有关进化心理学局限性的理论思考

进化心理学是现代西方心理学的新取向之一。这一新取向吸引了众多的追随者,但是它自身的核心假设、方法论和认识论方面却存在着局限性。文章从三个方面分析了这种局限性：第一,进化心理学的核心假设是心理的模块性观点。依据这种观点,心灵由大量功能各异的心理模块组成,但是来自于心理学和生物学的研究都表明这种观点是缺乏科学依据的。第二,进化心理学从过去的角度理解现在,所依据的事实大多是推测性的,更多的是一种历史叙事,从方法论的角度来说,这种研究不具备可证伪性,不符合科学方法论的基本原则。第三,在认识论方面,进化心理学继承了社会生物学的传统,有意或无意地夸大了基因的作用,贬低了个体发展过程中其它因素,现代生命科学的研究已经证明了基因决定论的虚假性     

Assessing human reorientation ability inside virtual reality environments: the effects of retention interval and landmark characteristics

The purpose of the present study was to assess the navigational behaviour of adult humans following a disorientation procedure that perturbed their egocentric frame of reference. The assessment was carried out in a virtual reality (VR) environment by manipulating the disorientation procedure, the retention interval, the relative positions of target and landmark. The results of experiment I demonstrated that adding a physical rotation to a virtual disorientation procedure did not yield an additional decrease in searching performance. The results of experiment II showed that shortening the delay between study and test phase decreased the errors more markedly for geometric than landmark ones. An orientation specificity effect due to the manipulation of the relative position between target and landmark was discussed across the experiments. In conclusion, VR seemed to be a valuable method for studying human reorientation. Moreover, the virtual experimental setting involved here promoted knowledge of the relationship between working memory and spatial reorientation paradigm.     

The theory of braids and the analysis of impossible figures

Impossible figures were regarded neither as new perceptual phenomena, nor as examples of known phenomena such as illusions. They were seen as geometric anomalies, not psychological ones, which serve a heuristic function in the study of perception. With this in mind, a topological analysis was undertaken with the anticipation of the following goals: (a) A systematic way (algorithm) of generating these figures should be evident; (b) simple properties of impossible figures which may not have been previously understood should be discovered. Both of these conditions were met.     

Reorientation in a rhombic environment: No evidence for an encapsulated geometric module

Reorientation behavior of young children has been described as dependent upon a geometric module that is incapable of interacting with landmark information. Whereas previous studies typically used rectangular spaces that provided geometric information about distance, we used a rhombic space that allowed us to explore the way children use geometric information about angles. Reorientation was studied in manipulatory space (Experiment 1) and locomotor space (Experiment 2) in the presence and absence of a salient landmark. In the absence of salient landmarks, 4- to 6-year-olds used geometric features to reorient in both spaces. When a salient landmark was available in manipulatory space, 4-year-olds used the landmark and ignored the geometry. Five- and 6-year-olds used the geometry, but in combination with the landmark. In locomotor space, this combined use was already seen at age 4, and increased with age. Taken together, these results offer no support for the notion that reorientation behavior in young children depends on an informationally encapsulated geometric module.     

The learnability of abstract syntactic principles

Children acquiring language infer the correct form of syntactic constructions for which they appear to have little or no direct evidence, avoiding simple but incorrect generalizations that would be consistent with the data they receive. These generalizations must be guided by some inductive bias – some abstract knowledge – that leads them to prefer the correct hypotheses even in the absence of directly supporting evidence. What form do these inductive constraints take? It is often argued or assumed that they reflect innately specified knowledge of language. A classic example of such an argument moves from the phenomenon of auxiliary fronting in English interrogatives to the conclusion that children must innately know that syntactic rules are defined over hierarchical phrase structures rather than linear sequences of words (e.g., [Chomsky, 1965] , [Chomsky, 1971] , [Chomsky, 1980] and [Crain and Nakayama, 1987] ). Here we use a Bayesian framework for grammar induction to address a version of this argument and show that, given typical child-directed speech and certain innate domain-general capacities, an ideal learner could recognize the hierarchical phrase structure of language without having this knowledge innately specified as part of the language faculty. We discuss the implications of this analysis for accounts of human language acquisition.     

Core Knowledge and the Emergence of Symbols: The Case of Maps

Map reading is unique to humans but is present in people of diverse cultures, at ages as young as 4 years old. Here, we explore the nature and sources of this ability and ask both what geometric information young children use in maps and what nonsymbolic systems are associated with their map-reading performance. Four-year-old children were given two tests of map-based navigation (placing an object within a small three-dimensional [3D] surface layout at a position indicated on a two-dimensional [2D] map), one focused on distance relations and the other on angle relations. Children also were given two nonsymbolic tasks, testing their use of geometry for navigation (a reorientation task) and for visual form analysis (a deviant-detection task). Although children successfully performed both map tasks, their performance on the two map tasks was uncorrelated, providing evidence for distinct abilities to represent distance and angle on 2D maps of 3D surface layouts. In contrast, performance on each map task was associated with performance on one of the two nonsymbolic tasks: Map-based navigation by distance correlated with sensitivity to the shape of the environment in the reorientation task, whereas map-based navigation by angle correlated with sensitivity to the shapes of 2D forms and patterns in the deviant-detection task. These findings suggest links between one uniquely human, emerging symbolic ability, geometric map use, and two core systems of geometry.     

Perception of growth: a geometric analysis of how different styles of change are distinguished

Although there have been many demonstrations that human observers can accurately recognize a variety of styles of change, such as rolling, walking, or growing, there are no existing theories capable of explaining how one style of change is distinguished from another. The present article offers a hypothesis that any recognizable style of change is uniquely specified by geometric invariants- the abstract properties of a visual display that are preserved by the change. In an effort to provide an empirical test of this hypothesis, several experiments involving the perception of growth were performed. Observers were required to make perceptual judgments of consequences of facial profiles, each of which was constructed by using a different mathematical transformation. The same pattern of results was obtained on both a free response task and a growth rating task: All transformations that were consistently identified as growth preserved the same geometric invariants.