The mental number line (MNL) is a popular metaphor for magnitude representation in numerical cognition. Its shape has frequently been reported as being nonlinear, based on nonlinear response functions in magnitude estimation. We investigated whether this shape reflects a phenomenon of the mapping from stimulus to internal magnitude representation or of the mapping from internal representation to response. In five experiments, participants (total N = 66) viewed stimuli that represented numerical magnitude either in a symbolic notation (i.e., Arabic digits) or in a nonsymbolic notation (i.e., clouds of dots). Participants estimated these magnitudes by either adjusting the position of a mark on a ruler-like response bar (nonsymbolic response) or by typing the corresponding number on a keyboard (symbolic response). Responses to symbolic stimuli were markedly different from responses to nonsymbolic stimuli, in that they were mostly powershaped. We investigated whether the nonlinearity could be explained by effects of previous trials, but such effects were (a) not strong enough to explain the nonlinear responses and (b) existed only between trials of the same input notation, suggesting that the nonlinearity is due to input mappings. Introducing veridical feedback improved the accuracy of responses, thereby showing a calibration based on the feedback. However, this calibration persisted only temporarily, and responses to nonsymbolic stimuli remained nonlinear. Overall, we conclude that the nonlinearity is a phenomenon of the mapping from nonsymbolic input format to internal magnitude representation and that the phenomenon is surprisingly robust to calibration.

中文翻译：

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比较符号和非符号数轴：符号对输出度量的一致影响

心理数轴 (MNL) 是数值认知中量级表示的流行隐喻。基于幅度估计中的非线性响应函数，它的形状经常被报告为非线性的。我们研究了这种形状是否反映了从刺激到内部幅度表示的映射或从内部表示到响应的映射现象。在五个实验中，参与者（总共 N = 66）查看了以符号表示法（即阿拉伯数字）或非符号表示法（即点云）表示数值大小的刺激。参与者通过调整标尺状响应栏上标记的位置（非符号响应）或通过在键盘上键入相应的数字（符号响应）来估计这些幅度。对象征性刺激的反应与对非象征性刺激的反应明显不同，因为它们大多是权力塑造的。我们研究了非线性是否可以通过先前试验的效应来解释，但这种效应 (a) 不足以解释非线性响应，并且 (b) 仅存在于相同输入符号的试验之间，这表明非线性是由于输入映射。引入真实反馈提高了响应的准确性，从而显示了基于反馈的校准。然而，这种校准只是暂时存在，对非符号刺激的反应仍然是非线性的。总的来说，我们得出结论，非线性是从非符号输入格式映射到内部幅度表示的一种现象，并且这种现象对校准具有惊人的鲁棒性。