Abstract：
The ratio of two magnitudes can take one of two values depending on the order they are operated on: a \'big\' ratio of the larger to smaller magnitude, or a \'small\' ratio of the smaller to larger. Although big and small ratio scales have different metric properties and carry divergent predictions for perceptual comparison tasks, no psychophysical studies have directly compared them. Two experiments are reported in which subjects implicitly learned to compare pairs of brightnesses and line lengths by non-symbolic feedback based on the scaled big ratio, small ratio or difference of the magnitudes presented. Results of Experiment 1 showed all three operations were learned quickly and estimated with a high degree of accuracy that did not significantly differ across groups or between intensive and extensive modalities, though regressions on individual data suggested an overall predisposition towards differences. Experiment 2 tested whether subjects learned to estimate the operation trained or to associate stimulus pairs with correct responses. For each operation, Gaussian noise was added to the feedback that was constant for repetitions of each pair. For all subjects, coefficients for the added noise component were negative when entered in a regression model alongside the trained differences or ratios, and were statistically significant in 80% of individual cases. Thus, subjects learned to estimate the comparative operations and effectively ignored or suppressed the added noise. These results suggest the perceptual system is highly flexible in its capacity for non-symbolic computation, which may reflect a deeper connection between perceptual structure and mathematics.
摘要：
两个量值的比率可以取两个值中的一个，这取决于它们被操作的顺序：一个大的大的比率，或“小”与“大”的比值。尽管大小比例尺度具有不同的度量属性，并且对感知比较任务具有不同的预测，没有心理物理学研究直接比较它们。报告了两个实验，其中受试者隐含地学会了通过基于缩放的大比率的非符号反馈来比较亮度和线长对。所呈现的量值的小比率或差异。实验1的结果表明，所有三个操作都是快速学习的，并且具有很高的准确性，各组之间或密集和广泛模式之间没有显着差异。尽管对个体数据的回归表明存在差异的总体倾向。实验2测试了受试者是否学会了评估操作的训练或将刺激对与正确的反应相关联。对于每个操作，高斯噪声被添加到对于每对的重复是恒定的反馈。对于所有科目，当与训练的差异或比率一起输入回归模型时，添加的噪声分量的系数为负，并且在80％的个别病例中具有统计学意义。因此，受试者学会了估计比较操作，并有效地忽略或抑制了增加的噪声。这些结果表明，感知系统在非符号计算的能力方面具有高度的灵活性，这可能反映了感知结构和数学之间更深层次的联系。
