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

Lozin, Mariya; Pinhas, Michal

doi:10.1037/xlm0001126

Cited by 10 publications

(45 citation statements)

References 88 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The visual analyzer also has several other syntax-related subprocesses. One sub-process detects how many digits a number has (Cohen & Dehaene, 1991;Dotan & Dehaene, 2020;Dotan & Friedmann, 2018;García-Orza et al, 2022;Lozin & Pinhas, 2022). Another sub-processes handles the digits 0 and 1, which have special syntactic importance (Cohen & Dehaene, 1991;Dotan et al, 2021;Dotan & Friedmann, 2018).…”

Section: How Does the Visual Analyzer Represent Number Syntax?mentioning

confidence: 99%

Syntax-driven number reading: The identification of digits is dominated by the number’s syntactic structure

Dotan¹

2022

Preprint

View full text Add to dashboard Cite

Humans have a remarkable ability to process complex syntactic structures using hierarchical representations. Within the domain of numbers, syntactic-hierarchical processing appears to exist in linguistic tasks involving verbal numbers. Here, I asked whether syntactic-hierarchical processing exists even within the nonverbal mechanism that parses visually-presented digit strings. I asked literate adults to read aloud multi-digit strings that were presented serially, digit after digit. The inter-digit SOA was identical in all positions except one SOA, which was longer – either between the thousand and hundred digits, congruent with the syntactic principles of the decimal system and how it divides numbers to triplets, or between the hundred and decade digits (incongruent grouping). The participants were sensitive to this visual manipulation: their accuracy was higher in the congruent condition than in the incongruent one, indicating that the visual analyzer divides the digit string into triplets in accord with the decimal system standards. This congruency effect was found when the participants read the numbers as syntactically-structured number names (“twelve”), and critically, also when they read each number as a syntax-less series of digit names (“one, two”). Namely, the triplet-grouping is not a top-down effect from syntactic verbal-production processes, it is a property of the visual analyzer itself. These results indicate that the visual analyzer intrinsically handles digit strings with at least 2 levels of hierarchy – the triplets, and the digits within each triplet.

show abstract

Section: How Does the Visual Analyzer Represent Number Syntax?mentioning

confidence: 99%

Syntax-driven number reading: The identification of digits is dominated by the number’s syntactic structure

Dotan¹

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Despite the salient perceptual cue for number value provided by number length, two recent studies show that number length does not serve as the sole indicator of magnitude. In our previous study (Lozin & Pinhas, 2022) investigating comparisons of multi-digit numbers that varied in their left digits and scales (ranging from tens to trillions), we found a left-digit-scale compatibility effect. That is, responses were faster when comparing compatible pairs (i.e., the larger/longer number contained the larger left digit; e.g., 4,000,000,000 vs. 2,000,000) than for incompatible pairs (i.e., the larger/longer number contained the smaller left digit; e.g., 2,000,000,000 vs. 4,000,000).…”

Section: Perception Of Multi-digit Number Magnitude Is Dominated By N...mentioning

confidence: 64%

“…In line with the notion of a syntactic end effect is our recent theoretical postulation according to which (at least) two independent processes running in parallel and racing against each other underlie number comparisons (Lozin & Pinhas, 2022). One process, termed magnitude comparison, evaluates which number is smaller/larger based on a crude evaluation of magnitudes.…”

Section: The Present Studymentioning

confidence: 97%

“…This place-value structure links number values with certain positions in a string of digits and associates the overall number length with its magnitude; the more digits there are, the larger the value of the number. Thus, the number's length serves as a primary cue for a crude evaluation of its value (e.g., Dixon, 1978;García-Orza et al, 2022;Hinrichs et al, 1982;Huber, et al, 2014;Lozin & Pinhas, 2022;Varma & Karl, 2013). Some models postulate that a number's length and other syntactic and lexical aspects are encoded during early visual analysis of multi-digit number stimuli.…”

Section: Perception Of Multi-digit Number Magnitude Is Dominated By N...mentioning

confidence: 99%

“…It should be considered that magnitude comparison in such a context, namely, comparing a "longer" number to a "shorter" one, could rely (at least in part) on the numbers' lengths (e.g., Dixon, 1978;García-Orza et al, 2022;Hinrichs et al, 1982;Huber, et al, 2014;Lozin & Pinhas, 2022;Varma & Karl, 2013). If end-values are detected based on numerical syntax alone (i.e., identified as such based on a rough visual analysis of the numbers' lengths) then end effects may occur without fully realizing the exact value each of the compared numbers represents.…”

Section: The Present Studymentioning

confidence: 99%

See 2 more Smart Citations

Perceiving the “smallest” or “largest” multi-digit number: A novel numeric-scale end effect

Lozin¹,

Pinhas²

2022

Preprint

Self Cite

View full text Add to dashboard Cite

Little is known about the perception of multi-digit number magnitude, and what causes us to categorize these numbers as “small/large” or “smallest/largest.” The present study examined end effects in multi-digit numbers and whether such effects are impacted by numerical syntax. Across four experiments, participants performed three types of numerical comparisons: same-scale comparisons between an end-value and a non-end-value (e.g., 100 vs. 200), different-scale comparisons between an end-value and a non-end-value (e.g., 1,000 vs. 200), and same-scale comparisons of non-end-values (e.g., 300 vs. 200). The type of the end-value (i.e., lower/upper) and overall numerical range used in each experiment varied. The results revealed: (1) a novel syntactic end effect, characterized by a relatively small end effect for comparisons between non-end-values and end-values from an adjacent scale, and a larger, consistently sized end effect for all comparisons between non-end-values and end-values from non-adjacent scales (a gap of 2 scales), (2) no end effect for same-scale comparisons of multi-digit numbers, and (3) a replication of the lower end effect for comparisons between the lower end-value of 1 and other single digits (i.e., non-end-values). These results reveal differential processing of numbers from adjacent versus non-adjacent scales. We rule out a psychophysical explanation for our findings and instead provide a syntactical explanation which is based on the perceptual dominance of the scale component and the way it is manifested in the counting process. We conclude that numerical syntax plays a crucial role in evaluating multi-digit number magnitude.

show abstract

Adults systematically underestimate decimals and whole number exposure induces further magnitude-based underestimation.

Schiller¹,

Abreu-Mendoza²,

Rosenberg‐Lee³

2024

Journal of Experimental Psychology: Learning, Memory, and Cogni

View full text Add to dashboard Cite

Decimal numbers are generally assumed to be a straightforward extension of the base-ten system for whole numbers given their shared place value structure. However, in decimal notation, unlike whole numbers, the same magnitude can be expressed in multiple ways (e.g., 0.8, 0.80, 0.800, etc.). Here, we used a number line task with carefully selected stimuli to investigate how equivalent decimals (e.g., 0.8 and 0.80 on a 0-1 number line) and proportionally equivalent whole numbers (e.g., 80 on a 0-100 number line) are estimated. We find that young adults (n = 88, M age = 20.22 years, SD = 1.65, 57 female) have a linear response pattern for both decimals and whole numbers, but those double-digit decimals (e.g., 0.08, 0.82, 0.80) are systematically underestimated relative to proportionally equivalent whole numbers (e.g., 8, 82, 80). Moreover, decimal string length worsens the underestimation, such that single-digit decimals (e.g., 0.8) are perceived as smaller than their equivalent double-digit decimals (e.g., 0.80). Finally, we find that exposing participants to whole number stimuli before decimal stimuli induces magnitude-based underestimation, that is, greater underestimation for larger decimals. Together, these results suggest a small but persistent underestimation bias for decimals less than one, and further that decimal magnitude estimation is fragile and subject to greater underestimation when exposed to whole numbers.

show abstract

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

Cited by 10 publications

References 88 publications

Syntax-driven number reading: The identification of digits is dominated by the number’s syntactic structure

Syntax-driven number reading: The identification of digits is dominated by the number’s syntactic structure

Perceiving the “smallest” or “largest” multi-digit number: A novel numeric-scale end effect

Adults systematically underestimate decimals and whole number exposure induces further magnitude-based underestimation.

Contact Info

Product

Resources

About