Psychology Department, Yale University, New Haven, USA.
Sci Rep. 2020 Aug 7;10(1):13407. doi: 10.1038/s41598-020-68593-z.
The study of numerical estimation collectively spans hundreds of papers and hundreds of thousands of citations. Interest in this topic hinges on one assumption: that we can approximate number independently of continuous spatial dimensions (e.g., area). Accordingly, many studies have specifically tried to demonstrate sensitivity specific to number while controlling other dimensions. However, recent work demonstrates that perceived area (based on psychophysical judgments) differs from true area (i.e., a precise pixel count). This difference raises concerns about most past studies of approximate number, by asking if they have systematically controlled for the wrong dimension(s). Building on recent findings that the percept of area may be systematically illusory, the current study examines the relation between perceived area and number. Four experiments reveal that (1) perceived area, but not mathematical area, strongly influences numerosity judgments, (2) perceived area influences perceived number but not the reverse, (3) number acuity is greatly reduced in stimuli controlled for perceived area, and (4) the ability to make area discriminations on the basis of 'additive area' but not mathematical area predicts number discrimination ability. Together, these findings highlight a potentially serious confound in prior work, raising new theoretical and methodological challenges for the field.
该研究对数值估计进行了综合研究，涵盖了数百篇论文和数十万条引文。人们对这个话题的兴趣基于一个假设：我们可以独立于连续的空间维度（例如面积）来近似数字。因此，许多研究专门试图在控制其他维度的同时，证明对数字的敏感性。然而，最近的研究表明，感知到的面积（基于心理物理判断）与真实面积（即精确的像素计数）不同。这种差异引发了对过去大多数近似数量研究的关注，这些研究是否系统地控制了错误的维度。基于最近的研究发现，面积感知可能是系统性的错觉，当前的研究考察了感知面积和数量之间的关系。四项实验表明：（1）感知面积，而不是数学面积，强烈影响数量判断；（2）感知面积影响感知数量，但反之则不然；（3）在受感知面积控制的刺激中，数量锐度大大降低；（4）基于“附加面积”而非数学面积进行面积辨别能力，预测数量辨别能力。这些发现共同强调了先前工作中潜在的严重混淆，为该领域提出了新的理论和方法学挑战。
