No power: exponential expressions are not processed automatically as such

Feder, Ami; Lozin, Mariya; Pinhas, Michal

doi:10.1007/s00426-020-01381-6

Cited by 6 publications

(23 citation statements)

References 51 publications

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“…Comparisons based on contrasting numbers’ left digits produced smaller effects than contrasting scales (instantiated by differences in the numbers’ lengths). This result contradicts the idea of left-to-right sequential processing (e.g., Korvorst & Damian, 2008; Meyerhoff et al, 2012; Poltrock & Schwartz, 1984) and confirms the notion of an early visual analysis of the physical parameters of the number’s length (e.g., Cohen & Dehaene, 1991; Dotan & Friedmann, 2018, 2019), as a readily available cue for determining its relative value (e.g., Dixon, 1978; Feder et al, 2021; Hinrichs et al, 1982; Huber, Klein, et al, 2014). Notwithstanding, the presented evidence of compatibility effects and redundancy gains in all experiments indicates that the processing of less relevant components, like the left and right digits, was also involved in participants’ comparative decisions beyond the processing of the physical size or length of the numbers.…”

Section: Discussioncontrasting

confidence: 55%

“…Also, the apparent physical length differences between two numbers from different scales, which do not exist in within-scale comparisons, presumably contributed to the shortening of RTs in between-scale comparisons (e.g., Dixon, 1978; Hinrichs et al, 1982). Previous research has consistently shown that the physical size of a number is processed automatically, even when not required by the task, and this can contribute to, or interrupt, task performance (e.g., Feder et al, 2021; Fitousi, 2014; Henik & Tzelgov, 1982). In addition, as expected, a redundancy gain was obtained for between-scale comparisons with two compatible components (left digit and scale) in contrast to those that varied in scale.…”

Section: Discussionmentioning

confidence: 99%

“…Moreover, as predicted, scale distance effects were apparent for between-scale comparisons of both small and large numbers, and emerged as the most substantial contributors in the analyses, reflecting the prominence of the scale component (Moeller et al, 2009; Nuerk et al, 2011). The dominance of this component seem to relate to the fact that it is easily detected by noticing the differences in the physical sizes of the numbers (e.g., Dixon, 1978; Feder et al, 2021; Fitousi, 2014; Henik & Tzelgov, 1982; Hinrichs et al, 1982; Huber, Klein, et al, 2014), and its processing demonstrated greater attention to the ordinal (and not cardinal) properties of the compared numbers (Brass & Harkness, 2017; Kabasakalian, 2007).…”

Section: Discussionmentioning

confidence: 99%

See 2 more Smart Citations

Differential processing of “small” and “large” multidigit numbers.

Lozin¹,

Pinhas²

2022

Journal of Experimental Psychology: Learning, Memory, and Cogni

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Section: Discussioncontrasting

confidence: 55%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Differential processing of “small” and “large” multidigit numbers.

Lozin¹,

Pinhas²

2022

Journal of Experimental Psychology: Learning, Memory, and Cogni

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“…Previous findings have also demonstrated interaction between numerical and physical magnitude in symbolic numbers, as instantiated by the SCE in single-and multi-digit numbers (e.g., Feder et al, 2021;Fitousi & Algom, 2006;Ganor-Stern et al, 2007;García-Orza et al, 2017;Henik & Tzelgov, 1982;Kallai & Tzelgov, 2012;Pansky & Algom, 1999;Pinhas et al, 2010;Schwarz & Ischebeck, 2003;Tzelgov et al, 1992), a string length congruity effect in decimal fractions (Huber et al, 2014) and (natural) multi-digit numbers (García-Orza et al, 2022;Lozin & Pinhas, 2022), and the interference of the number of digits with the processing of the numerical value of a digit in circular or matrix presentations (Naparstek & Henik, 2010Pansky & Algom, 2002;Pavese & Umiltà, 1998.…”

Section: Infinity Symbol?mentioning

confidence: 88%

Perceiving infinity: An interplay between numerical and physical magnitude.

Pinhas

2024

Journal of Experimental Psychology: Learning, Memory, and Cogni

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Our mental representation of the infinite has received little research attention in cognitive psychology. In countably infinite sets, the infinity symbol (∞) is presumed to be perceived as larger than any finite natural number. The present study sought to explore if the infinity symbol is processed as "larger than" natural numbers, and, if so, whether it is associated with the special status of "the largest." In a series of four experiments (N = 40, 20, 20, and 40, respectively), participants performed numerical and physical comparisons of the infinity symbol against single-and multidigit numbers. Overall, numerical comparisons yielded slower responses for comparisons between infinity and a number than for comparisons between two numbers. Furthermore, distance-like effects were obtained for comparisons to infinity, suggesting the infinity symbol was treated as larger than all numbers presented. Importantly, however, physical comparisons revealed a normal size congruity effect for comparisons of infinity and single digits, but a reversed effect for comparisons of infinity and multidigit numbers, suggesting that the infinity symbol was automatically processed as smaller than multidigit numbers. These novel findings reveal limitations in abstracting the meanings of infinity from its symbol, indicating that the infinity symbol is not perceived as "the largest" and can be misconceived as a "number" mapped onto the numerical magnitude system. More generally, the results seem to reflect a crude, automatic evaluation of numerical magnitude based on the physical magnitude of the stimuli, namely, their overall length and the number of symbols of which they are comprised.

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“…Recently, we adapted the unit-decade compatibility effect to exponential expressions and documented a base-power compatibility effect (Feder et al, 2021), producing faster reactions for base-power compatible pairs, where the base and power of one exponential expression were larger than those of the other (e.g., for the pair 3 2 _2 1 , both 3 > 2 and 2 > 1), compared to basepower incompatible pairs, where the base and the power led to different decisions (e.g., for the pair 4 1 _3 2 , 4 > 3, but 1 < 2). In this earlier study, we examined automatic processing (i.e., processing that runs without monitoring; Bargh, 1992) of exponential expressions, which is obtained if it occurs although it was not part of the task requirements (Tzelgov, 1997).…”

mentioning

confidence: 99%

Numerical comparisons of exponential expressions: The saliency of the base component

Feder,

Lozin,

Neumann

et al. 2024

Preprint

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Exponential expressions represent series that grow at an unfixed pace such as carbon pollution and the spread of disease. Despite their importance, people tend to struggle with these expressions. In two experiments, participants chose the larger of two exponential expressions as quickly and accurately as possible. We manipulated the distance between the base/power components and their compatibility. In base-power compatible pairs, both the base and power of one expression were larger than the other (e.g., 23 vs. 34), while in base-power incompatible pairs, the base of one expression was larger than the base in the other expression but the relation between the power components of the two expressions was reversed (e.g., 32 vs. 24). Moreover, while in the first experiment, the larger power always led to the larger result, in the second experiment we introduced base-result congruent pairs as well. Namely, the larger base led to the larger result. Our results showed a base-power compatibility effect, which was also larger for larger power distances (Experiments 1–2). Furthermore, participants processed the base-result congruent pairs faster and more accurately than the power-result congruent pairs (Experiment 2). These findings suggest that while both the base and power components are processed when comparing exponential expressions, the base is more salient during processing. This exemplifies a lack of understanding of the syntax of exponential expressions, where the power, even though physically smaller, typically has a larger mathematical contribution to the result of the expression.

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No power: exponential expressions are not processed automatically as such

Cited by 6 publications

References 51 publications

Differential processing of “small” and “large” multidigit numbers.

Differential processing of “small” and “large” multidigit numbers.

Perceiving infinity: An interplay between numerical and physical magnitude.

Numerical comparisons of exponential expressions: The saliency of the base component

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