Abstract: The SNARC Effect (Dehaene, Bossini, & Giraux, 1993; Dehaene, Dupoux, & Mehler,1990) and Spatial Shifts of Attention (Fischer, Castel, Dodd, & Pratt, 2003; Casarotti, Michielin, Zorzi, & Umiltà, 2007) indicate that there are tight connections between number processing and representation and space. These discoveries, however, are only regarded with positive numbers presently, there are few effective experimental studies or evidence on the mechanism of the processing and representation of negative numbers with 0, or on the connections between negative numbers and space.
For a lack of effective experimental methodology (Fischer, & Rottmann, 2005; Nuerk, Iversen, & Willmes, 2005; Fischer, 2003), it is less than possible to set up research to investigate the secrets behind the processing and representation of negative numbers with 0. As a result, there’s no persuasive answer to the questions about whether there are connections between negative numbers and space; or whether the low level processing of negative numbers with 0 can induce Spatial Shifts of Attention. The present study, including 3 effective experiments by using stimuli detection task with number cues, was to investigate the connections between negative numbers with 0 and space, and the mechanism of the processing and representation of negative numbers and 0, through observing if the low level processing of negative numbers can induce spatial shifts of attention, and whether it depends upon their magnitude or absolute value.
Experiment 1 was a within-subject design of 2 (target side: left and right) × 2 (magnitude of cueing number: small and large) × 6 (variable delays: 50 ms, 100 ms, 200 ms, 300 ms, 400ms and 500 ms). Results from Experiment 1, in which only negative numbers were included, showed that left (right) targets were detected significantly faster than right (left) ones when numbers with small (large) absolute value were preceded, revealing spatial shifts of attention depending upon absolute value of negative numbers. Experiment 2 was a 2 (target side: left, right) × 5 (number magnitude: quite small, small, medium, large, quite large) × 6 (variable delays: 50 ms, 100 ms, 200 ms, 300 ms, 400 ms, or 500 ms) within-subject design, in which both positive and negative numbers, and zero were mixed as cues, showed that left (right) targets were detected significantly faster than right (left) ones when numbers with small (large) magnitude were preceded, revealing spatial shifts of attention depending upon their magnitude, therefore, there is a mental number line extending to the left side of zero, and representing numbers depending upon number magnitude. Experiment 3 was a 2 (target side: left, right) × 3 (number magnitude: small, large, 0) × 6 (variable delays: 50ms, 100ms, 200ms, 300ms, 400ms, or 500ms) within-subject design, in which only negative numbers with 0 were designed as effective cues, although still cued by the whole mix of all negative, 0 and positive numbers as numbers preceding the targets, subjects were only requested to respond to targets preceded by effective cues (negative numbers and 0), while not respond to targets preceded by non-effective cues (positive numbers). Consistently, spatial shifts of attention depending upon number magnitude were successfully induced by processing effective cueing numbers (-8, -9, -1, -2,0). By ensuring that the minus signs were processed with the numbers holistically, it can be put that there can be a low-level processing of negative number magnitude to some extent of automation.
As a whole, the present study suggested that low level processing of negative numbers as cues can induce spatial shifts of attention, whether it depends upon their magnitude or absolute value, however, seems to depend upon the task requirement and the inter-influence from other involved numbers in the task; there are connections between negative numbers, 0 and space; there can be a low-level processing of negative number magnitude to some extent of automation; the forming and representing of mental number line is dynamic and flexible to fit the task requirements, mental number line, therefore, can extend to the left side of zero, while representing number magnitude.

Key words: negative numbers, spatial shifts of attention, numerical cognition, number processing and representation, mental number line