# The Difficulty in Numerical Computation Impacts Motor Decisions in a Stop‐Signal Task

## TL;DR

This study shows that the difficulty of numerical comparisons affects how quickly and accurately people start or stop movements in a task.

## Contribution

The paper introduces a novel numerical comparison stop-signal task to investigate the link between cognitive demand and motor decisions.

## Key findings

- Larger numerical distances led to faster and more accurate movement initiation and better stopping performance.
- Drift rates in the drift-diffusion model increased with numerical distance and were influenced by stimulus location.
- Go process parameters, especially drift rate, predicted successful stopping and interacted with stop-signal delay.

## Abstract

The proper interpretation of environmental information is necessary for effective decision‐making. The resulting cognitive burden may affect the entire process if interpretation is not instantaneous. In this study, we investigated how numerical distance (ND), a measure of cognitive demand in numerical comparisons, influences movement initiation and inhibition. To this end, 32 participants completed a novel numerical comparison stop‐signal task (NC‐SST), in which the cognitive demand of each trial was manipulated by varying the ND between pairs of numbers presented in both Go and Stop signals. Participants were required to initiate or stop a movement if the number was higher or smaller than the one indicated as reference. Results showed that larger NDs (i.e., easier comparisons) facilitated faster and more accurate responses during movement initiation and enhanced stopping performance. Using a generalized drift‐diffusion model, we found that drift rates increased with Go ND and were modulated by the spatial location of numerical stimuli, consistent with a left‐to‐right space number association. A generalized linear mixed‐effects model further revealed that Go process parameters, particularly the drift rate, strongly predicted successful stopping and interacted with Stop ND and stop‐signal delay (SSD). These findings demonstrate that greater cognitive difficulty impairs both movement initiation and inhibition, and that motor decisions result from the integration of cognitive information onto perceptual features, extending the classical race model framework.

Cognitive difficulty arising from numerical comparison modulates motor control. In a stop‐signal task where the Go and Stop signal corresponded to the result of a numerical comparison, we show that the degree of difficulty in making this mental operation affects both movement initiation and inhibition, highlighting the interaction between cognitive demands and motor decisions.