Can conceptual congruency effects between number,time, and space be accounted for by polarity correspondence?

Conceptual congruency effects have been interpreted as evidence for the idea that the representations of abstract conceptual dimensions (e.g., power, affective valence, time, number, importance) rest on more concrete dimensions (e.g., space, brightness, weight). However, an alternative theoretical explanation based on the notion of polarity correspondence has recently received empirical support in the domains of valence and morality, which are related to vertical space (e.g., good things are up). In the present study we provide empirical arguments against the applicability of the polarity correspondence account to congruency effects in two conceptual domains related to lateral space: number and time. Following earlier research, we varied the polarity of the response dimension (left-right) by manipulating keyboard eccentricity. In a first experiment we successfully replicated the congruency effect between vertical and lateral space and its interaction with response eccentricity. We then examined whether this modulation of a concrete-concrete congruency effect can be extended to two types of concrete-abstract effects, those between left-right space and number (in both parity and magnitude judgment tasks), and temporal reference. In all three tasks response eccentricity failed to modulate the congruency effects. We conclude that polarity correspondence does not provide an adequate explanation of conceptual congruency effects in the domains of number and time.     

The revelation of the negative side of a mental number line depends on list context: Evidence from a sign priming paradigm

Two parity judgement experiments examined how the activation of spatial-numerical associations of a single, centrally presented digit, reflected by the Spatial-Numerical Association Response Codes (SNARC) effect, is modulated by a preceding + (plus) or ? (minus) prime. The centrally presented prime prior to a digit presentation presumably triggers its positive or negative attributes. When the plus- and minus-primed trials were blocked, the left-small/right-large SNARC effects occurred regardless of prime type. When the plus- and minus-primed trials were randomly intermixed, this left-small/right-large SNARC effect occurred for plus-primed digits, but was reversed for minus-primed digits. The implications of this finding for context-dependent SNARC effects are discussed.     

Manipulating number generation: Loud + long = large?

Humans make numerous choices every day and tend to perceive these choices as free. The present study shows how simple free choices are biased by experiencing unrelated auditory information. In two experiments, participants categorized tones according to their intensity on the dimensions volume and duration on the majority of trials. On some trials, however, they were to randomly generate a number, and we found these choices to be influenced by tone intensity. Particularly, if participants were cued toward volume, loud tones clearly biased participants to generate larger numbers. For tone duration, a similar effect only emerged if spatial information was reinforced by the motor context of the task. The findings extend previous findings relating to the ATOM framework (A Theory of Magnitude) by an explicit focus on auditory magnitude processing. As such, they also constrain ATOM by showing that the connections between different magnitude dimensions vary to a considerable degree.     

Malleable conjoint partworths: How the breadth of response scales alters price sensitivity

In one laboratory study and one field study conducted with a large, representative sample of respondents, we show that seemingly innocuous questions that precede a conjoint task, such as demographic and usage-related screening questions can alter the price sensitivities recovered from the main conjoint task. The findings demonstrate that whether these prior questions use broad response categories (i.e., few scale points) or narrow response categories (i.e., many scale points) systematically influences consumers' price sensitivity in a CBC (Choice Based Conjoint) study. We suggest that this may occur because the narrow (vs. broad) response categories in the prior questions lead to consideration of a greater (vs. fewer) number of attributes during the key conjoint task. Since both groups of consumers readily consider the naturally salient price attribute, responding to previous questions with narrow (vs. broad) response categories leads to a greater (vs. fewer) number of non-price attributes being considered, and consequently, decrease the weight afforded to price and reduce price sensitivity.     

Holistic or compositional representation of two-digit numbers? Evidence from the distance, magnitude, and SNARC effects in a number-matching task

Whether two-digit numbers are represented holistically (each digit pair processed as one number) or compositionally (each digit pair processed separately as a decade digit and a unit digit) remains unresolved. Two experiments were conducted to examine the distance, magnitude, and SNARC effects in a number-matching task involving two-digit numbers. Forty undergraduates were asked to judge whether two two-digit numbers (presented serially in Experiment 1 and simultaneously in Experiment 2) were the same or not. Results showed that, when numbers were presented serially, unit digits did not make unique contributions to the magnitude and distance effects, supporting the holistic model. When numbers were presented simultaneously, unit digits made unique contributions, supporting the compositional model. The SNARC (Spatial-Numerical Association of Response Codes) effect was evident for the whole numbers and the decade digits, but not for the unit digits in both experiments, which indicates that two-digit numbers are represented on one mental number line. Taken together, these results suggested that the representation of two-digit numbers is on a single mental number line, but it depends on the stage of processing whether they are processed holistically or compositionally.     

A synesthetic walk on the mental number line: the size effect

Are small and large numbers represented similarly or differently on the mental number line? The size effect was used to argue that numbers are represented differently. However, recently it has been argued that the size effect is due to the comparison task and is not derived from the mental number line per se. Namely, it is due to the way that the mental number line is mapped onto the task-relevant output component. Here synesthesia was used to disentangle these two alternatives. In two naming experiments a digit-color synesthete showed that the congruity effect was modulated by number size. These results support the existence of a mental number line with a vaguer numerical representation as numbers increase in size. In addition, the results show that in digit-color synesthesia, colors can evoke numerical representation automatically.     

Numeric comparison in a visually-guided manual reaching task

Nearly all studies on perception and cognition have used discrete responses to infer internal cognitive processes. In the current study, we demonstrate that visually-guided manual reaching can provide new opportunities to access internal processes over time. In each trial, participants were required to compare a single digit Arabic number presented on the center square with the standard, 5. Participants were asked to reach and touch one of three squares on the screen with their index finger while their hand movement trajectories were recorded: the left square for 1-4, the center for 5, and the right for 6-9. Direct evidence for an analogue representation of numbers was found in early as well as in later portions of hand trajectories, showing systematic shifts in position for small differences in numerical magnitude.     

Number as a cognitive technology: evidence from Pirahã language and cognition

Does speaking a language without number words change the way speakers of that language perceive exact quantities? The Pirah? are an Amazonian tribe who have been previously studied for their limited numerical system [Gordon, P. (2004). Numerical cognition without words: Evidence from Amazonia. Science 306, 496-499]. We show that the Pirah? have no linguistic method whatsoever for expressing exact quantity, not even "one." Despite this lack, when retested on the matching tasks used by Gordon, Pirah? speakers were able to perform exact matches with large numbers of objects perfectly but, as previously reported, they were inaccurate on matching tasks involving memory. These results suggest that language for exact number is a cultural invention rather than a linguistic universal, and that number words do not change our underlying representations of number but instead are a cognitive technology for keeping track of the cardinality of large sets across time, space, and changes in modality.     

How counting represents number: what children must learn and when they learn it

This study compared 2- to 4-year-olds who understand how counting works (cardinal-principle-knowers) to those who do not (subset-knowers), in order to better characterize the knowledge itself. New results are that (1) Many children answer the question "how many" with the last word used in counting, despite not understanding how counting works; (2) Only children who have mastered the cardinal principle, or are just short of doing so, understand that adding objects to a set means moving forward in the numeral list whereas subtracting objects mean going backward; and finally (3) Only cardinal-principle-knowers understand that adding exactly 1 object to a set means moving forward exactly 1 word in the list, whereas subset-knowers do not understand the unit of change.     

Mental movements without magnitude? A study of spatial biases in symbolic arithmetic

McCrink (McCrink, Dehaene, & Dehaene-Lambertz (2007). Moving along the number line: Operational momentum in nonsymbolic arithmetic. Perception and Psychophysics, 69(8), 1324-1333) documented an “Operational Momentum” (OM) effect - overestimation of addition and underestimation of subtraction outcomes in non-symbolic (dot pattern) arithmetic. We investigated whether OM also occurs with Arabic number symbols. Participants pointed to number locations (1-9) on a visually given number line after computing them from addition or subtraction problems. Pointing was biased leftward after subtracting and rightward after adding, especially when the second operand was zero. The findings generalize OM to the spatial domain and to symbolic number processing. Alternative interpretations of our results are discussed.