Operational momentum was originally defined as a bias towards underestimating outcomes of subtraction and overestimating outcomes of addition. It was suggested that these estimation biases are due to leftward attentional shift along the mental number-line (spatially organized internal representation of number) in subtraction and rightward shift in addition. This assumes the use of “recycled” mechanisms of spatial attention, including “representational momentum” – a tendency to overestimate future position of a moving object, which compensates for the moving object's shift during preparation of a reaction. We tested a strong version of this assumption directly, priming two-digit addition and subtraction problems with leftward and rightward motion of varied velocity, as velocity of the tracked object was found to be a factor in determining representational momentum effect size. Operands were subsequently moving across the computer screen, and the participants' task was to validate an outcome proposed at the end of the event, which was either too low, correct, or too high. We found improved accuracy in detecting too-high outcomes of addition, as well as complex patterns of interactions involving arithmetic operation, outcome option, speed, and direction of motion, in the analysis of reaction times. These results significantly extend previous evidence for the involvement of spatial attention in mental arithmetic, showing movement of the external attention focus as a factor directing internal attention in processing numerical information. As a whole, however, the results are incompatible with expectations derived from the strong analogy between operational and representational momenta. We suggest that the full model may be more complex than simply “moving attention along the mental number-line” as a direct counterpart of attention directed at a moving object.

中文翻译：

---

感知运动和操作动量：速度、距离和时间如何影响两位数算术

操作动量最初被定义为偏向于低估减法结果和高估加法结果。有人提出，这些估计偏差是由于在减法和加法中沿着心理数轴（数字的空间组织内部表示）向左转移。这假设使用空间注意力的“循环”机制，包括“表征动量”——一种高估移动物体未来位置的趋势，它补偿了移动物体在准备反应过程中的移动。我们直接测试了这个假设的强版本，启动了向左和向右变速运动的两位数加减问题，因为发现被跟踪物体的速度是决定代表性动量效应大小的一个因素。操作数随后在计算机屏幕上移动，参与者的任务是验证事件结束时提出的结果，该结果要么太低，要么正确，要么太高。在反应时间分析中，我们发现在检测过高的加法结果以及涉及算术运算、结果选项、速度和运动方向的复杂交互模式方面的准确性有所提高。这些结果显着扩展了先前关于空间注意力参与心算的证据，表明外部注意力焦点的运动是在处理数字信息时引导内部注意力的一个因素。不过整体来看，结果与从操作动量和代表性动量之间的强类比得出的预期不符。我们建议完整模型可能比简单地“沿着心理数字线移动注意力”更复杂，因为它是针对移动对象的注意力的直接对应物。