How numbers mean: Comparing random walk models of numerical cognition varying both encoding processes and underlying quantity representations

Abstract

How do people derive meaning from numbers? Here, we instantiate the primary theories of numerical representation in computational models and compare simulated performance to human data. Specifically, we fit simulated data to the distributions for correct and incorrect responses, as well as the pattern of errors made, in a traditional “relative quantity” task. The results reveal that no current theory of numerical representation can adequately account for the data without additional assumptions. However, when we introduce repeated, error-prone sampling of the stimulus (e.g., Cohen, 2009) superior fits are achieved when the underlying representation of integers reflects linear spacing with constant variance. These results provide new insights into (i) the detailed nature of mental numerical representation, and, (ii) general perceptual processes implemented by the human visual system.

Limited-capacity identity processing of multiple integers

“…For the SIM condition, physical similarity alone accounted best for the data, r 2 = .15, F(1, 195) = 35.48, p < .001, slope = 5 The physical structure of the numerical symbol must be encoded, at least in part, in order to provide meaningful information to the quantity process (see Cohen & Quinlan, 2016). conditions were tested in Experiment 2 only.…”

“…As such, this work is akin to that undertaken by researchers in their quest to understand how processes concerning visual featural and letter encoding inform more general theories concerning the mental architecture underpinning word recognition and reading (see, e.g., McClelland & Rumelhart, 1981;Rumelhart & Siple, 1974). Although, historically, these "low-level" processes have not featured heavily in traditional accounts, there is now a growing body of evidence that these need to be considered if adequate models of numerical cognition are to be developed (see Cohen, 2009Cohen, , 2010Cohen & Quinlan, 2016;Cohen, Warren, & Blanc-Goldhammer, 2013;Defever, Sasangie, Vandewaetere, & Reynvoet, 2012;García-Orza, Perea, Mallouh, & Carreiras, 2012;Wong & Szücs, 2013;Zhang, Xin, Feng, Chen, & Szücs, 2018).…”

“…That is, the physical structure of every digit may be confused with the physical structure of every other digit, and the probability of this confusion is a function of the physical similarity of each digit to every other digit (similar assumptions are central to the interactive activation and competition model of letter processing put forward by McClelland & Rumelhart, 1981). Cohen and Quinlan (2016) modeled this process in detail. Encoding is characterized as a continuously updating process whereby information is continuously fed to the other processing stages (see Cohen & Quinlan, 2016).…”

“…Cohen and Quinlan (2016) modeled this process in detail. Encoding is characterized as a continuously updating process whereby information is continuously fed to the other processing stages (see Cohen & Quinlan, 2016).…”

Psychological Value Theory: The Psychological Value of Human Lives and Economic Goods

“…SDT predicts response choices, but not response time (RT). Sequential sampling procedures, such as the random walk and drift diffusion procedures, formalize the relation between the overlap of underlying psychological distributions (e.g., f(Yv1∩Yv2)) and participants' responses (both RT and response choice) in a two-choice decision process (Cohen & Quinlan, 2016;Link & Heath, 1975;Ratcliff, 2001;Ratcliff, 2014;Ratcliff & Rouder, 1998).…”