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Geometric Encoding

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Global geometry; Local geometry; Spatial reorientation

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Bradley R. Sturz Georgia Southern University, Statesboro, GA, USA

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Main Text Successful movement between locations first requires the determination of a direction of travel, and understanding the process of determining a direction is the central focus of orientation research. As shown in the top panel of Fig. 1, the general approach to understanding orientation involves training disoriented participants to respond to a particular location within a rectangular enclosure (left). Importantly, this location is often uniquely specified by a distinctive feature. Interestingly, tests in the absence of the distinctive features reveal that participants not only respond to the originally trained location but also to its 180 rotationally equivalent location (right). Responses to this 180 rotationally equivalent location are termed a rotational error. The occurrence of the rotational error is particularly interesting because it suggests that

participants learn something about the geometric shape of the enclosure itself during training, and such learning about the geometric shape of the enclosure during training is unneeded because it is neither necessary nor sufficient to determine the correct location. Specifically, the correct location is uniquely and sufficiently specified by the distinctive feature; yet in its absence, participants respond as if they learned the correct location with respect to the environmental shape, and the rotational error is suggested to occur because, in the absence of the distinctive feature, environmental geometry alone cannot disambiguate the correct from the rotationally equivalent location. The occurrence of the rotational error has been observed in ants, chicks, pigeons, fish, and primates – including human children and human adults. In human adults, the rotational error also occurs in a sensory modality other than vision. Specifically, blindfolded adults trained to respond to a particular corner of a rectangle designated by a unique texture respond to the trained and rotationally equivalent locations when the unique texture is absent. This occurrence across species and sensory modalities suggests that orientation via geometric cues may be ubiquitous and fundamental process in the animal kingdom. As a result, determining the nature of this geometric encoding – environmental points, lines, angles, and overall shape to determine a direction – has received considerable research attention, and manipulations of shape from training to testing have revealed two basic categories of geometric

# Springer International Publishing AG 2017 J. Vonk, T.K. Shackelford (eds.), Encyclopedia of Animal Cognition and Behavior, DOI 10.1007/978-3-319-47829-6_857-1

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Geometric Encoding

Geometric Encoding, Fig. 1

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cues used during reorientation: local geometric cues and global geometric cues. Both types of cues explain the presence of the rotational error but differ with respect to what is encoded about environmental geometry. As shown in Fig. 1 (bottom left), local geometric cues are independent cues such as wall lengths and corner angles that constitute the environmental shape. Thus, local geometric encoding would involve encoding the correct location during training as a location specified by short wall right, long wall left, and 90 corner angle. Such local geometric encoding during training explains the occurrence of the rotational error during testing because both the correct and rotationally equivalent locations are located at the right side of a short

wall, the left side of a long wall, and at a 90 corner angle. In contrast, global geometric cues (often derived from computational geometry) are dependent on the overall shape of the environment because they must be encoded from the overall shape of the environment. For example, the principal axis of space, which runs through the centroid and approximate length of the space is a summary parameter derived from the boundaries. Thus, global geometric coding with respect to the principal axis would involve encoding the correct location during training as the location specified by the left side of the principal axis. Such global geometric encoding during training explains the occurrence of the rotational error during testing because both the correct and rotationally

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equivalent locations are located at the left side of the principal axis. Similarly, the medial axis of space which is a trunk and branch system that captures overall shape information is also derived from the boundaries. Thus, global geometric encoding with respect to the medial axis of space would involve encoding the correct location during training as the location specified by the terminal end of the trunk’s left branch. Such global geometric encoding during training explains the occurrence of the rotational error during testing because both the correct and rotationally equivalent locations are located at the terminal end of the trunk’s left branch. Despite recent debate about which global geometric cue may be encoded, it is clear that both local and global geometric cues are encoded and used for orientation. As importantly, it is also clear that a sense component (i.e., left or right) is part of this encoding process. Current research is continuing to manipulate aspects of the environment from training to testing to further illuminate the geometric cues used to reorient with respect to the environment.

Cross-References ▶ Cognitive Map ▶ Encoding ▶ Geometric Module ▶ Landmark ▶ Navigation ▶ Orientation ▶ Orienting ▶ Place Versus Response Learning ▶ Spatial Memory ▶ Spatial Relations

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Bodily, K. D., Eastman, C. K., & Sturz, B. R. (2011). Neither by global nor local cues alone: Evidence for a unified orientation process. Animal Cognition, 14, 665–674. Cheng, K., Huttenlocher, J., & Newcombe, N. S. (2013). 25 years of research on the use of geometry in spatial reorientation: A current theoretical perspective. Psychonomic Bulletin & Review, 20, 1033–1054. Kelly, D. M., Chiandetti, C., & Vallortigara, G. (2011). Re-orienting in space: Do animals use global or local geometry strategies? Biology Letters, 7, 372–375. Lubyk, D. M., Dupuis, B., Gutiérrez, L., & Spetch, M. L. (2012). Geometric orientation by humans: Angles weigh in. Psychonomic Bulletin & Review, 19, 436–442. Miller, N. Y., & Shettleworth, S. J. (2007). Learning about environmental geometry: An associative model. Journal of Experimental Psychology: Animal Behavior Processes, 33, 191–212. Sovrano, V. A., & Vallortigara, G. (2006). Dissecting the geometric module: The association of metric and landmark information with sense in animals’ spatial reorientation. Psychological Science, 17, 616–621. Sturz, B. R., & Bodily, K. D. (2012). On discriminating between geometric strategies of surface-based orientation. Frontiers in Psychology, 3, 112. doi:10.3389/ fpsyg.2012.00112. Sturz, B. R., Gurley, T., & Bodily, K. D. (2011). Orientation in trapezoid-shaped enclosures: Implications for theoretical accounts of geometry learning. Journal of Experimental Psychology: Animal Behavior Processes, 37, 246–253. Sturz, B. R., Forloines, M. R., & Bodily, K. D. (2012). Enclosure size and the use of local and global geometric cues for reorientation. Psychonomic Bulletin & Review, 19, 270–276. Sturz, B. R., Gaskin, K. A., & Roberts, J. E. (2014). Incidental encoding of enclosure geometry does not require visual input: Evidence from blind-folded adults. Memory & Cognition, 42, 935–942. Sutton, J. E. (2009). What is geometric information and how do animals use it? Behavioural Processes, 80, 339–343. Tommasi, L., Chiandetti, C., Pecchia, T., Sovrano, V. A., & Vallortigara, G. (2012). From natural geometry to spatial cognition. Neuroscience and Biobehavioral Reviews, 36, 799–824.

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Geometric Encoding

troid and approximate length of the space is a. 85 summary parameter derived from the boundaries. 86. Thus, global geometric coding with respect to the. 87 principal axis would involve encoding the correct. 88 location during training as the location specified. 89 by the left side of the principal axis. Such global. 90.

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