A reoccurring question in cognitive science concerns the way the world is represented. Cognitive scientists quantify the contribution of a physical attribute to a sensation and try to characterize the underlying mechanism. In numerical cognition, the contribution of physical properties to quantity perception in comparison tasks was widely demonstrated albeit leaving the underlying mechanism unclear. Furthermore, it is unclear whether this contribution is related solely to comparison tasks or to a core, general ability. Here we demonstrate that the shape of the convex hull, the smallest convex polygon containing all objects in an array, plays a role in the transfer function between quantity and its mental representation. We used geometric probability to demonstrate that the shape of the convex hull is correlated with quantity in a way that resembles the behavioral enumeration curve of subitizing and estimation. Then, in two behavioral experiments we manipulated the shape of the convex hull and demonstrated its effect on enumeration. Accordingly, we suggest that humans learn the correlation between convex hull shape and numerosity and use it to enumerate.

中文翻译：

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放眼世界：数量的心理表现形式。

认知科学中一个反复出现的问题与世界的表示方式有关。认知科学家量化了物理属性对感觉的贡献，并试图描述其潜在机制。在数值认知中，尽管比较不清楚其潜在机理，但在比较任务中物理性质对数量感知的贡献得到了广泛证明。此外，还不清楚这种贡献是仅与比较任务有关还是与核心的一般能力有关。在这里，我们证明了凸包的形状（包含数组中所有对象的最小凸多边形）在数量与其心理表示形式之间的传递函数中起作用。我们使用几何概率证明凸包的形状与数量相关，其方式类似于拟定和估计的行为枚举曲线。然后，在两个行为实验中，我们操纵了凸包的形状并演示了它对枚举的影响。因此，我们建议人类学习凸包形状与数量之间的相关性，并使用它来进行枚举。