The Representation Of Negative Numbers

Since negative numbers are composed of two components, a polarity sign and a digit, there are two opposite representations of negative numbers, componential representation and holistic representation. Different tasks were used to investigate the representation of negative numbers, such as parity judgment task, numerical comparison task and physical comparison task. It should be noted that, in these tasks the requirement of the tasks would influence the representation of negative numbers. In the parity judgment task, participants tended to ignore the polarity sign component, and only processed the digit component to complete the task; in the numerical comparison task, participants would use different response strategies based on the various experiment conditions; and in the physical comparison task, participants would pay more attention to the digit component, because the numbers’ sizes are mainly depended on the digit component. The present study aims to investigate the representation of negative numbers based on the relationship between time and number, and using the duration comparison task. In the duration comparison task, participants only need to compare the two numbers’ duration, the numerical value of the numbers is irrelevant to the task. Thus, the duration comparison task may avoid the response strategies used in the numerical comparison task, and avoid participants focusing their attention mainly on the digit component in the physical comparison task. So, we can have a more accurate understanding for negative numbers by using the duration comparison task.In experiment 1, positive numbers and negative numbers were presented in different blocks. The result showed that, when the numerical value of positive numbers was small, its duration was underestimated, and when the numerical value was big, its duration was overestimated; similarly, when the numerical value of negative numbers was small, its duration was underestimated, and when the numerical value was big, its duration was overestimated. The result of experiment 1 demonstrated that negative number was processed by its numerical value, and supported the holistic representation of negative numbers.In experiment 2, we investigated the influence of context effect. Positive numbers and negative numbers were presented in the same block. The result showed that, when the numerical value of positive numbers was small, its duration was underestimated, and when the numerical value was big, its duration was overestimated; on the contrary, when the numerical value of negative numbers was small, its duration was overestimated, and when the numerical value was big, its duration was underestimated. The result of experiment 2 demonstrated that negative number was processed by its absolute value, and supported the componential representation of negative numbers. The results of experiment 1 and 2 indicated that, there was a context effect existed in the duration comparison task.In experiment 3, we further investigated whether the context effect is due to the spatial distinction of the polarity and digit in negative numbers. To exclude the effect of the spatial distinction of the polarity sign and digit in negative numbers, polarity sign of negative numbers was marked by colour instead of a separate sign, then polarity and digit were both presented in one intergrated stimulus. Different colours(red and blue) were used to mark the positive and negative numbers. The result showed that, when the numerical value of positive numbers was small, its duration was underestimated, and when the numerical value was big, its duration was overestimated; similarly, when the numerical value of negative numbers was small, its duration was underestimated, and when the numerical value was big, its duration was overestimated. The result of experiment 3 demonstrated that negative number was processed by its numerical value, and supported the holistic representation of negative numbers.These results suggested that when influenced by the task conditions, negative numbers could be processed in terms of components, and when such influences disappeared, negative numbers were holistically processed. The context effect in duration comparison task was caused by the spatial distinction of the polarity and digit in negative numbers.