What is the format of spatial representation? In mathematics, we often conceive of two primary ways of representing 2D space, Cartesian coordinates, which capture horizontal and vertical relations, and polar coordinates, which capture angle and distance relations. Do either of these two coordinate systems play a representational role in the human mind? Six experiments, using a simple visual-matching paradigm, show that (a) representational format is recoverable from the errors that observers make in simple spatial tasks, (b) human-made errors spontaneously favor a polar coordinate system of representation, and (c) observers are capable of using other coordinate systems when acting in highly structured spaces (e.g., grids). We discuss these findings in relation to classic work on dimension independence as well as work on spatial representation at other spatial scales.

空间表示的格式是什么？在数学中，我们经常想到两种表示二维空间的主要方式，笛卡尔坐标，捕捉水平和垂直关系，以及极坐标，捕捉角度和距离关系。这两个坐标系中的任何一个在人类思维中都扮演着代表性的角色吗？六个实验，使用简单的视觉匹配范式，表明 (a) 表示格式可以从观察者在简单空间任务中所犯的错误中恢复，(b) 人为错误自发地倾向于极坐标表示系统，以及 (c) ) 观察者在高度结构化的空间（例如网格）中工作时能够使用其他坐标系。我们讨论与维度独立性的经典工作以及其他空间尺度的空间表示工作相关的这些发现。