Comparing black-capped (Poecile atricapillus) and mountain chickadees (Poecile gambeli): use of geometric and featural information in a spatial orientation task

Since Cheng (Cognition 23:149–178, 1986) first proposed the “geometric module” in rats, a great deal of research has focused on how other species use geometric information and how geometric encoding may differ across species. Here, hand-reared and wild-caught black-capped chickadees and wild-caught mountain chickadees searched for food hidden in one corner in a rectangular environment. Previous research has shown that mountain chickadees do not spontaneously encode geometric information when a salient feature is present near the goal location. Using a slightly different training and testing procedure, we found that both hand-reared and wild-caught black-capped chickadees encoded geometric information, even in the presence of a salient landmark. Some, but not all, mountain chickadees also encoded geometric information. Overall, our results suggest that use of geometric information may be a less preferred strategy for mountain chickadees than for either wild-caught or hand-reared black-capped chickadees. To our knowledge, this is the first direct interspecies comparison of use of geometric information in a spatial orientation task.     

Enclosure shape influences cue competition effects and goal location learning

In virtual-environment spatial-learning procedures, Experiment 1 investigated blocking of learning about distal landmarks beyond the walls of an enclosure following preliminary training to find a goal using local landmarks within the enclosure. Separate sets of blocking and control groups searched within enclosures that, in plan view, formed either a square or a circle. Blocking was apparent when training and testing occurred in the circular but not the square enclosure. In Experiment 2, preliminary training to find a goal using local landmarks blocked spatial learning based on a circular enclosure divided into four differently coloured sections. The results are discussed in relation to theories of incidental versus error-correcting learning linked to different types of spatial cue.     

Use of landmark features and geometry by children and adults during a two-dimensional search task

Three- to six-year-old children (n = 28) and adults (n = 46) participated in a two-dimensional search task that included geometry and feature conditions. During each of 24 trials, participants watched as a cartoon character hid behind one of three landmarks arranged in a triangle on a computer screen. The landmarks and character then disappeared and reappeared in the same or a new position on the screen. During feature condition trials participants could use unique features of the landmarks to locate the hidden character, while during geometry trials participants could only use the geometry of the triangle. In both conditions, adults’ performance was near ceiling while children’s performance was significantly worse. Children’s performance was worse in the geometry condition than in the feature condition but search accuracy improved with age for both types of information. Findings are considered in the context of the broader literature on spatial cognition and development.     

Intrinsic frames of reference in haptic spatial learning

It has been proposed that spatial reference frames with which object locations are specified in memory are intrinsic to a to-be-remembered spatial layout (intrinsic reference theory). Although this theory has been supported by accumulating evidence, it has only been collected from paradigms in which the entire spatial layout was simultaneously visible to observers. The present study was designed to examine the generality of the theory by investigating whether the geometric structure of a spatial layout (bilateral symmetry) influences selection of spatial reference frames when object locations are sequentially learned through haptic exploration. In two experiments, participants learned the spatial layout solely by touch and performed judgments of relative direction among objects using their spatial memories. Results indicated that the geometric structure can provide a spatial cue for establishing reference frames as long as it is accentuated by explicit instructions (Experiment 1) or alignment with an egocentric orientation (Experiment 2). These results are entirely consistent with those from previous studies in which spatial information was encoded through simultaneous viewing of all object locations, suggesting that the intrinsic reference theory is not specific to a type of spatial memory acquired by the particular learning method but instead generalizes to spatial memories learned through a variety of encoding conditions. In particular, the present findings suggest that spatial memories that follow the intrinsic reference theory function equivalently regardless of the modality in which spatial information is encoded.     

In any way,shape, or form? Toddlers’ understanding of shapes

Using the intermodal preferential looking paradigm, two-year-old children’s ability to discriminate valid (typical and atypical) squares, rectangles, triangles, and circles from invalid distractors was examined. The cognitive and environmental factors that might predict this ability were also investigated. Two-year-old children (N = 33) were able to discriminate squares, triangles, and circles, but not rectangles. No significant cognitive or environmental predictors of this ability were found. The results suggest that the ability to shape discriminate at age two is under considerable development and that other factors may be responsible for children’s ability to discriminate shapes.     

From geometry to phenomenology

Richard Tieszen [Tieszen, R. (2005). Philosophy and Phenomenological Research, LXX(1), 153–173.] has argued that the group-theoretical approach to modern geometry can be seen as a realization of Edmund Husserl’s view of eidetic intuition. In support of Tieszen’s claim, the present article discusses Husserl’s approach to geometry in 1886–1902. Husserl’s first detailed discussion of the concept of group and invariants under transformations takes place in his notes on Hilbert’s Memoir Ueber die Grundlagen der Geometrie that Hilbert wrote during the winter 1901–1902. Husserl’s interest in the Memoir is a continuation of his long-standing concern about analytic geometry and in particular Riemann and Helmholtz’s approach to geometry. Husserl favored a non-metrical approach to geometry; thus the topological nature of Hilbert’s Memoir must have been intriguing to him. The task of phenomenology is to describe the givenness of this logos, hence Husserl needed to develop the notion of eidetic intuition. The author wishes to thank Academy of Finland for financial assistance that enabled her to work on this article.     

Philosophie und Geometrie. Zur jüngeren Protophysik-Kritik

The critique of my protophysical approaches to operational foundation of geometry by Lucas Amiras (Journal for General Philosophy of Science Vol. 34 (2003)) concerns my first publication from 1976 but not the further 30 years of work. It does not offer any argument leading from the (erroneous) judgement “lacking success” to the conclusion “impossible”. And it is, in general, based on a philosophical defect: it ignores the principle of methodical order as leading for constructivist protophysics.     

The use of geometric properties of 2D arrays across development

Four- to 10-year-old children (n = 50) participated in a 2D search task that included geometry (with- and without lines) and feature conditions. During each of 27 trials, participants watched as a cartoon character hid behind one of three landmarks arranged in a triangle on a computer screen. During feature condition trials, participants could use the unique features of landmarks to locate the hidden character. During geometry condition trials the landmarks were identical, and participants had to rely on the geometric properties of the triangle they formed to locate the hidden character. In the feature condition, search accuracy was high for children of all ages. In the geometry condition (both with- and without lines), there was a sharp developmental trend in which 4-year-olds showed poor search accuracy, but performance improved with age and was at ceiling by 9- to 10-years. The presence of lines connecting the landmarks boosted performance most dramatically for the youngest children. Findings are discussed in the context of the broader literature on spatial cognition in human and non-human animals.     

Spatial reorientation in large and small enclosures: comparative and developmental perspectives

Several vertebrate species, including humans, following passive spatial disorientation appear to be able to reorient themselves by making use of the geometric shape of the environment (i.e., metric properties of surfaces and directional sense). In some circumstances, reliance on such purely geometric information can overcome the use of local featural cues (landmarks). The relative use of geometric and non-geometric information seems to depend upon, among other factors, the size of the experimental space. Evidence in non-human animals and in human infants for primacy in encoding either geometric or landmark information depending on the size of the environment is reviewed, together with possible theoretical accounts of this phenomenon.     

Multiple landmarks, the encoding of environmental geometry and the spatial logics of a dual brain

A series of place learning experiments was carried out in young chicks (Gallus gallus) in order to investigate how the geometry of a landmark array and that of a walled enclosure compete when disoriented animals could rely on both of them to re-orient towards the centre of the enclosure. A square-shaped array (four wooden sticks) was placed in the middle of a square-shaped enclosure, the two structures being concentric. Chicks were trained to ground-scratch to search for food hidden in the centre of the enclosure (and the array). To check for effects of array degradation, one, two, three or all landmarks were removed during test trials. Chicks concentrated their searching activity in the central area of the enclosure, but their accuracy was inversely contingent on the number of landmarks removed; moreover, the landmarks still present within the enclosure appeared to influence the shape of the searching patterns. The reduction in the number of landmarks affected the searching strategy of chicks, suggesting that they had focussed mainly on local cues when landmarks were present within the enclosure. When all the landmarks were removed, chicks searched over a larger area, suggesting an absolute encoding of distances from the local cues and less reliance on the relationships provided by the geometry of the enclosure. Under conditions of monocular vision, chicks tended to rely on different strategies to localize the centre on the basis of the eye (and thus the hemisphere) in use, the left hemisphere attending to details of the environment and the right hemisphere attending to the global shape.This contribution is part of the special issue “Animal Logics” (Watanabe and Huber 2006).