The Effect Of Number On The Perception Of An Empty Interval

Psychological representation of time, space, and number represent the basic content ofcognitive system of the people. There is a close relationship between time processing andnumber processing. Walsh (2003) outlined A Theory Of Magnitude (ATOM) that proposedtime, space and quantity could be part of a generalized magnitude system in cognitive systemand that cognitive components influenced each other, the generalized magnitude systemapplied to those dimensions that were described as ‘prothetic’, meaning dimensions thatcould be experienced as ‘more than’ or ‘less than’.Time interval have two presenting forms:full interval and empty interval. Empty intervalstudies showed that empty interval was affected by a number of factors, such as, presentingform of objects, presenting position, presenting order, the length of empty interval. Recentfindings have shown that some magnitude, such as Arabic numbers, luminance and size,modulated time estimates, magnitude biased duration judgment to produce under estimationfor smaller magnitude and overestimation for larger magnitude. Based on A Theory ofMagnitude (ATOM), the current study combined number with empty interval to assesswhether empty interval perception could be influenced by number information, as well ashow they affect.Three experiments adopted a time bisection task, with standard short and long durationsbeing presented as visual stimuli (a gray square,70×70pixels) lasting500ms and900ms. Inthe first experiment, a group of healthy subjects was submitted to a time-bisection task inwhich numerical cues were blocked (blocked design). In the small digits block (1and2) andlarge digits block (8and9), a short, empty interval was demarcated by two same number,subjects were required to judge whether the empty interval was closer to previous standardshort or long duration. the results showed that the numerical size itself can not affect emptyinterval. In experiment2, all numbers (low-1and2; high-8and9) were randomly presentedin a single block. The results showed that numbers biased duration judgment to produceunder estimation for smaller empty interval and overestimation for larger empty interval. Wedemonstrated that the implicit comparison of magnitude differences across the displayednumbers biased duration judgment. In experiment3, we used a new presentation form, empty interval was demarcated by two different number (1-8,1-9,2-8,2-9,8-1,8-2,9-1,9-2), theresult showed that the intensity of the second marker altered perceptions in anempty-interval-specific manner, empty intervals were perceived to be longer in small-largecondition than those occurring in large-small condition.Through three studies, we deserve the results as follows:(1) There is a close relationship between time processing and number processing. Themagnitude differences of numbers, rather than the number itself, seems to be the key factorunderlying the present temporal bias, numbers biased duration judgment to produce underestimation for smaller empty interval and overestimation for larger empty interval. Theintensity of the second number altered perceptions in an specific manner, empty intervalswere perceived to be longer in small-large condition than in large-small condition. Consistentwith the prediction of A Theory of Magnitude (ATOM), duration judgments were affected bythe numerical magnitude of the presented stimulus. These findings argue for a functionalinteraction between time and numbers in the human brain within the framework of ATOM,and provide new evidence for the theoretical implication of a common generalized magnitudesystem. Together with other empirical findings, the current study indicates that the commongeneralized system can be extended to include empty interval.(2) In the process of number presentation, the second number appears in the mind of theperson, subjects refer to number in sensory memory to estimate empty interval.(3) In the experiments, subjects were required to judge whether the duration of a teststimulus was closer to previous standard short or long duration, rather than number. Theinfluence of number on empty interval estimation implies that subjects keep track of numbermagnitude when cued to empty interval. These results concur with ours in suggesting anautomatic activation of number magnitude during empty interval perception, even in acontext where numerosity did not have to be processed to carry out the task.