Related Experiment Video
Updated: Jun 14, 2026
05:39
Generating Strictly Controlled Stimuli for Figure Recognition Experiments
Published on: March 18, 2019
Number line compression and the illusory perception of random numbers
Arnaud Viarouge1, Edward M Hubbard, Stanislas Dehaene
1INSERM-CEA Cognitive Neuroimaging Unit, Gif/Yvette, France. arnaud.viarouge@vanderbilt.edu
Experimental Psychology
|April 13, 2010
Summary
Adults show a "compression illusion" where large numbers are perceived as closer together than they are. This numerical bias persists even after training, indicating a robust, context-dependent cognitive effect.
Area of Science:
- Cognitive psychology
- Developmental psychology
- Numerical cognition
Background:
- Children initially have a compressed intuition of numerical distances, with larger numbers being less discriminable.
- Education linearizes numerical intuition by age eight, enabling symbolic numeral mapping onto a spatial scale.
- A dormant form of numerical compression may persist in adults.
Purpose of the Study:
- To investigate the persistence of numerical distance compression in adult cognition.
- To determine if this illusion is observable in adult participants under specific experimental conditions.
Main Methods:
- Adult participants rated sequences of numbers for randomness, specifically assessing oversampling of small or large numbers.
- A geometric series oversampling small numbers was judged as random, indicating a compression bias for large numbers.
- Training involved a number-space mapping task, and participants were exposed to linear sequences.
Main Results:
- Participants showed a significant bias, misjudging a geometric series as random due to compressed perception of large numbers.
- The illusion persisted despite training on a number-space mapping task, even with linear performance on that task.
- Explicit exposure to linear sequences moderately reduced the illusion, but responding remained significantly compressed.
Conclusions:
- The numerical compression illusion is robust in adults within this task context.
- Adults can exhibit both linear and compressed numerical responding depending on the experimental setup.
- Cognitive context plays a crucial role in revealing dormant numerical biases.
Related Concept Videos
01:27Real Number Operations
The concept of real numbers includes all the values that can be represented on a continuous number line. The system began with basic counting values used for enumeration. It later expanded to include values that represent the absence of quantity and opposites of the counting values. When situations required expressing parts of a whole or dividing quantities evenly, values capable of representing such proportions were developed. When written using decimal notation, these values can end or repeat...
01:04Random Error
Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
01:21Gestalt Principles of Perception
Gestalt principles provide a framework for understanding how humans perceive objects as unified wholes within their context. These principles are essential in explaining the cognitive processes that make sense of complex visual stimuli by organizing them into coherent groups. One fundamental principle is proximity, which posits that objects located close to each other are perceived as a collective group. For instance, when dots are positioned near one another, the visual system interprets them...
01:26Introduction to Sequences
The ancient Greek philosopher Zeno of Elea proposed a series of paradoxes to challenge prevailing notions of motion and continuity. One such paradox imagines a man walking toward a door but only ever covering half the remaining distance with each step. This sequence of movements—first one-half, then one-quarter, then one-eighth of the total distance, and so on—forms a mathematical concept known as a geometric sequence. Each term is half of the previous one and can be written...
01:37Reason and Intuition
The human brain processes information for decision-making using one of two routes: an intuitive system and a rational system (Epstein, 1994; popularized by Kahneman, 2011 as System 1 and System 2, respectively). The intuitive system is quick, impulsive, and operates with minimal effort, relying on emotions or habits to provide cues for what to do next, while the rational system is logical, analytical, deliberate, and methodical. Research in neuropsychology suggests that the brain can only use...
01:17Wald-Wolfowitz Runs Test II
The Wald-Wolfowitz runs test, commonly referred to as the runs test, is a nonparametric test used to assess the randomness of ordered data. The test evaluates the number of runs, which are consecutive sequences of similar elements within the data. If the number of runs is significantly higher or lower than expected, the data is considered non-random, indicating a detectable pattern or structure.
For binary data, runs are identified using symbols such as + and −, or equivalently, 1s and 0s. In...
For binary data, runs are identified using symbols such as + and −, or equivalently, 1s and 0s. In...