Data_Sheet_1_A Mental Odd-Even Continuum Account: Some Numbers May Be “More Odd” Than Others and Some Numbers May Be “More Even” Than Others.pdf

Numerical categories such as parity, i.e., being odd or even, have frequently been shown to influence how particular numbers are processed. Mathematically, number parity is defined categorically. So far, cognitive, and psychological accounts have followed the mathematical definition and defined parity as a categorical psychological representation as well. In this manuscript, we wish to test the alternative account that cognitively, parity is represented in a more gradual manner such that some numbers are represented as “more odd” or “more even” than other odd or even numbers, respectively. Specifically, parity processing might be influenced by more specific properties such as whether a number is a prime, a square number, a power of 2, part of a multiplication table, divisible by 4 or by 5, and many others. We suggest that these properties can influence the psychologically represented parity of a number, making it more or less prototypical for odd- or evenness. In the present study, we tested the influence of these numerical properties in a bimanual parity judgment task with auditorily presented two-digit numbers. Additionally, we further investigated the interaction of these numerical properties with linguistic factors in three language groups (English, German, and Polish). Results show significant effects on reaction times of the congruity of parity status between decade and unit digits, even if numerical magnitude and word frequency are controlled. We also observed other effects of the above specific numerical properties, such as multiplication attributes, which facilitated or interfered with the speed of parity judgment. Based on these effects of specific numerical properties we proposed and elaborated a parity continuum account. However, our cross-lingual study also suggests that parity representation and/or access seem to depend on the linguistic properties of the respective language or education and culture. Overall, the results suggest that the “perceived” parity is not the same as objective parity, and some numbers are more prototypical exemplars of their categories.

数值类别，如奇偶性，即奇数或偶数，已被证明经常会影响特定数字的处理方式。在数学上，数字奇偶性被定义为一种类别。迄今为止，认知和心理学解释都遵循数学定义，将奇偶性定义为一种类别的心理表征。在本研究中，我们旨在检验一种替代性解释，即认知上，奇偶性以更为渐进的方式被表征，某些数字相对于其他奇数或偶数而言，被表征为“更奇”或“更偶”。具体而言，奇偶处理可能受到更具体属性的影响，例如一个数字是否为素数、平方数、2的幂、乘法表的一部分、能否被4或5整除等。我们提出，这些属性可以影响数字的心理表征奇偶性，使其在奇数或偶数类别中更加或更加典型。在本研究中，我们通过一项涉及听觉呈现两位数的双手动奇偶判断任务，测试了这些数值属性的影响。此外，我们还进一步研究了这些数值属性与三种语言群体（英语、德语和波兰语）中的语言因素之间的相互作用。结果显示，即使在控制数字大小和词汇频率的情况下，十年位和个位数字奇偶状态一致性对反应时间也存在显著影响。我们还观察到了上述特定数值属性（如乘法属性）的其他效应，这些效应有助于或干扰奇偶判断的速度。基于这些特定数值属性的影响，我们提出了一个奇偶连续体解释，并对其进行了详细阐述。然而，我们的跨语言研究也表明，奇偶表征和/或访问似乎取决于各自语言的属性或教育与文化。总体而言，结果表明，“感知”的奇偶性与客观奇偶性并不相同，某些数字是它们类别中更加典型的例子。