Modelling the Mental Representation of Numerosity Perception based on a Logarithmic Function

By using numerosity perception tasks, in which nonsymbolic stimuli like a group of dots are presented to the participants and they are required to respond by using symbolic stimuli like Arabic numerals, we are investigating how numbers are represented mentally. In our study, we have used a two-choice numerosity decision task and manipulated whether feedback was provided or not. The participants were presented dots with a range of 10-90 and they were required to respond whether the number of dots were greater than 50. They were required to respond when a signal was presented at 60ms to 3,000 ms (seven lags) after the number of dots were presented. For this study, to model numerosity perception without a time constraint, we only used the responses of the 500 and 700 ms, which corresponds to free response time in the literature and our pilot studies. Results of numerosity perception research suggest that the mental representation of numbers which is refered to as the mental number line or the Approximate Number System is logarithmically scaled. Accordingly there is a consensus of an underestimation bias in numerosity perception tasks. For our data, we model the mental number line based on a logarithmic function by minimizing the underestimation bias, in other words number of errors for the numbers greater than our criterion, which is 50. We supported the general findings that support the logarithmically compressed mental number line by showing that the perceived “50” corresponds to a larger number mentally and this logarithmic compression is even more when no feedback is provided.