The Geometry Literature

When rats, or 18-24 month old children for that matter, have the task of relocating an unmarked goal in a rectangular space, they search as often at the correct location as at the geometrically equivalent location marked rotational error (A). The rotational error is located at 180 degrees rotation through the centre from the correct location. To do this, rats and young children must have used only the information contained in the shape of the space (geometric information) some of the time. What this information consists of is a matter of debate.

The topic of 'geometry' is currently much researched. Here are some publications that I am an author on.

Cheng (1986) was the paper that started the line of research. Since then, my role on the topic has been theoretical rather than empirical. Of course, I also get to review lots of submitted journal papers on the topic.

Cheng & Newcombe (2005) was a thorough review. Since the review, a lot has happened in this line of work.

Cheng (2005) was a theoretical opinion piece, published in a special issue of Connection Science on navigation, edited by Kate Jeffery.

 

Jochen Zeil suggested that ambiguities found in view-based matching might account for the rotational error. We decided to work on this together, and Jochen recruited Wolfgang Stürzl and Allen Cheung to do the hard work. Well, to cut a long story short, the unsophisticated matching process of pixel-by-pixel image matching can produce rotational errors, and account for some other findings in the rat 'geometry' literature.


In 2013, Janellen Huttenlocher, Nora Newcombe, and I published an account of approaches/theories dealing with the geometry literature. We concluded that no major account does a satisfactory job at the moment.


References

Cheng, K. (1986).  A purely geometric module in the rat’s spatial representation.  Cognition, 23, 149-178.

Cheng K. (2005).  Reflections on geometry and navigation.  Connection Science, 17, 5-21 (special issue on navigation edited by K.J. Jeffery).

Cheng, K., & Newcombe, N.S. (2005).  Is there a geometric module for spatial orientation? Squaring theory and evidence.  Psychonomic Bulletin & Review, 12, 1-23.

Cheng, K. (2008).  Whither geometry? Troubles of the geometric module.  TRENDS in Cognitive Sciences, 12, 355-361.

Cheung, A., Stürzl, W., Zeil, J., & Cheng, K. (2008).  Information content of panoramic images: II. View-based navigation in nonrectangular experimental arenas. Journal of Experimental Psychology: Animal Behavior Processes, 34, 15-30.

Stürzl, W., Cheung, A., Cheng, K., & Zeil, J. (2008).  Information content of panoramic images: I. Rotational errors and the similarity of views in rectangular arenas.  Journal of Experimental Psychology: Animal Behavior Processes, 34, 1-14.

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, 10333-1054 (DOI 10.3758/s13423-013-0416-1).

 


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