# Manual pointing bias reflects spatial organization of number knowledge

## TL;DR

The study shows that people's number knowledge is spatially organized, with numerical differences represented as physical distances in pointing movements.

## Contribution

The study introduces a novel two-step pointing task to investigate spatial-numerical associations without confounding factors.

## Key findings

- Numerical and Euclidean distances between pointing locations were positively associated.
- Positive magnitude changes led to leftward and upward shifts in pointing locations.
- Results support the emergence of vertical spatial-numerical associations in manual pointing.

## Abstract

Number concepts are thought to be spatially organized along a mental number line increasing left-to-right (in Westerners) and bottom-to-top. However, the evidence for the emergence of horizontal and/or vertical spatial-numerical associations (SNAs) in manual pointing is mixed, and tasks implying magnitude-dependent number arrangements in physical space prevent conclusions about the emergence and extent of SNAs. Addressing these issues, we investigated SNAs with a two-step pointing task where the movement’s first step (provided after listening to a spoken number) always ended on the same central target displayed on a touchscreen. We analyzed spatial bias of this space-invariant, magnitude-independent first step. In the second step, participants localized the spoken number’s position in a clock-face arrangement, decoupling physical and numerical distance. In Experiment 1 (N = 20, spoken numbers from 1 to 12), pairwise numerical and Euclidean distances between (space-invariant) pointing locations were positively associated. Changes in magnitude of spoken numbers across successive trials yielded trends suggesting systematic pointing-location shifts. Experiment 2 (N = 20) presented 24 spoken targets (1–12.5, e.g., “three point five”) to increase clock-face salience. Both clock-face distance and numerical difference predicted Euclidean distances between pointing locations. In successive trials, positive magnitude changes resulted in leftward (clock-face congruent) and upward (MNL-congruent) shifts of pointing locations. The results suggest that numerical differences may be represented as 2D physical distances and support the emergence of vertical SNAs in manual pointing while avoiding previous experimental confounds. The findings align with the view that conceptual knowledge is represented in low-dimensional models that are spatially organized.