A recent study published in Scientific Reports provides evidence that the human brain processes the physical length of a multi-digit number at the very earliest stages of visual perception. The findings suggest that the physical length of a number acts as a fast automatic signal for its overall size, before the brain fully evaluates the actual numerical value.
The mathematical system people use every day relies on two main pieces of information to communicate quantity. The first piece is the specific shape of the digit, such as the symbol for a seven or a two. The second piece is the total number of digits, which is known as the numerical syntax. When looking at a number like 300, a person knows it is larger than 30 because it contains an extra digit and looks visibly longer.
This physical length acts as a reliable visual hint for the magnitude of the number. Scientists evaluate different models to explain how the mind interprets this information. Some models propose that people process a number as a single visual object. Other models suggest that the brain breaks the number down into its component parts to read it.
Nadav Neumann, who recently completed his doctorate, and Michal Pinhas, a researcher in the Quantitative Thinking and Cognition Lab in the Department of Psychology at Ariel University in Israel, designed a study to test how the brain untangles these distinct pieces of information. The paper is based on part of Neumann’s doctoral dissertation.
“Multi-digit numbers are the numbers we use most in everyday life, yet surprisingly little is known about how the brain processes them compared to single digits,” Pinhas said. “We were particularly interested in a seemingly simple question: when you see a number like ‘22222,’ does your brain register how many digits it has before it even knows what the digits mean?”
Pinhas explained that the Arabic number system has a built-in feature that makes this question tractable, namely that longer numbers typically represent larger values, which means number length is a genuine cue to magnitude. “We wanted to find out whether, and how early, the brain exploits that cue, while controlling for the overall visual size of the numbers on screen,” she said.
To measure this mental process, Neumann and Pinhas looked at electrical brain activity. They used a technique that records the electrical signals produced by the brain in response to specific sights or tasks. By looking at the exact milliseconds after a participant views a number, researchers can map out a timeline of mental processing. They focused on three specific brainwave patterns that appear at early, middle, and late stages of visual and cognitive processing.
Past studies have struggled to separate the true length of a number from its overall visual size on a screen. Typically, a five-digit number tends to take up more physical space than a two-digit number. This makes it difficult to tell if the brain is responding to the sheer amount of black ink on a white background or to the specific concept of numerical length.
To address this visual issue, the researchers created specialized images of numbers. They used numbers made of repeating digits, such as 22 or 88888. Then, they added randomized scribbled lines to the sides of every number. This ensured that a short number like 44 took up the exact same total width on the computer monitor as a long number like 44444.
By equalizing the visual size of the images, the scientists could isolate the specific mental impact of reading multiple digits. The researchers conducted two separate experiments to test different aspects of mathematical reading. Each experiment involved 27 undergraduate psychology students.
In the first experiment, participants sat in front of a computer screen while wearing specialized caps that recorded their brain’s electrical activity. They viewed a series of repeating numbers of varying lengths. They were instructed to decide whether the specific repeating digit on the screen was mathematically smaller or larger than the digit five.
The instructions asked them to completely ignore how long the number was. For example, a participant might see the number 77 and compare it to a mental standard of 555. Since seven is larger than five, the correct answer is larger.
However, the number 77 only has two digits, while 555 has three. This creates an incongruent situation, where the actual digit is mathematically larger but the physical length of the number is shorter. In a congruent situation, like seeing 88888, both the digit and the length are larger than the standard 555.
The behavioral results of the first experiment showed that participants responded faster when the digit value and the number length matched. When the properties were incongruent, participants took slightly longer to respond. This suggests that the brain automatically processes the length of a number, even when a person is actively trying to ignore it.
The brainwave recordings provided a detailed timeline of this interference. Between 120 and 150 milliseconds after the number appeared on the screen, an early brainwave pattern showed a strong response to the length of the number. This indicates that the brain detects numerical length during the earliest stages of visual perception.
“The most direct evidence comes from the brain recordings, where we found robust and consistent neural sensitivity to number length as early as 120-150 ms after seeing a number,” Pinhas said. “This is striking because it places magnitude-relevant processing at the very first stage of perceptual encoding, earlier than most previous research had demonstrated. Crucially, this early effect was found independently of the overall visual size of the numbers, meaning it reflects the syntactic structure of the number itself rather than general visual properties.”
“When you see a multi-digit number, your brain doesn’t wait to read the digits before forming an impression of its size,” Pinhas told PsyPost. “Within roughly 120-150 milliseconds of seeing the number, at the very first stage of perceptual processing, the brain has already used the number’s physical length as a quick, rough estimate of how large it is.”
“This is the brain taking a shortcut that usually works well, because longer numbers really are larger,” Pinhas said. “It’s a striking example of how deeply our intuitions about quantity are shaped by the visual structure of the symbols we use.”
Later in the timeline, between 150 and 190 milliseconds, a second brainwave pattern appeared in the recordings. This middle stage reflected a more refined processing of numerical distance, showing that the brain was beginning to evaluate the actual values of the digits. Finally, between 300 and 360 milliseconds, a third brainwave pattern emerged, which is associated with resolving mental conflict.
In the second experiment, a different group of 27 students completed a physical comparison task. They viewed the exact same types of scribbled images while wearing the brain recording equipment. This time, they were asked to decide if the number on the screen was physically shorter or longer than the standard 555. They were instructed to ignore the actual mathematical value of the digits.
The behavioral data from the second experiment showed no significant delays when participants viewed incongruent numbers. People were able to evaluate the length of the number without experiencing interference from the digit values. The brainwave data supported the idea of an early, automatic detection of number length, but with a unique twist based on the task instructions.
“One finding that stood out was the dissociation between our two experiments,” Pinhas said. “When participants focused on digit identity and ignored length, number length still intruded and slowed them down behaviorally, but not at the earliest neural stage.”
“When they focused on physical length instead, digit value showed up in the earliest ERP component even though it was task-irrelevant,” Pinhas said. “This asymmetry suggests the brain doesn’t process these two dimensions in a simple, symmetric way, and that attention shapes which dimension gets priority even at very early perceptual stages.”
While these findings provide detailed insights into mathematical processing, the study does have some limitations. One potential misinterpretation is that these early brainwave patterns apply to all types of mathematical reading.
“Our stimuli used ‘tie numbers,’ meaning numbers composed of a single repeated digit, like 4444 or 88888,” Pinhas said. “This was a deliberate methodological choice to control for compatibility effects within numbers, but it means we cannot yet say whether the same pattern holds for everyday numbers with mixed digits.”
“We also tested only two levels of number length difference, so the full shape of the relationship between length distance and brain response remains to be mapped out,” Pinhas said. “Future work extending these findings to more naturalistic numbers would be an important next step.”
Another limitation is that the researchers only tested young adults. The way the brain processes mathematical symbols tends to change over time with education and experience. Future studies could explore how children develop these early detection systems as they learn the rules of numerical syntax. Additionally, the exact reason for an early left-sided brain bias observed in the study remains unknown.
Understanding these early mental stages provides a deeper look into how the human mind organizes everyday mathematical information. “This paper is part of a broader research program examining how the physical and syntactic properties of numerical symbols shape the mental representation of quantity,” Pinhas said.
“We are especially interested in numerical concepts that are cognitively non-intuitive, such as very large multi-digit numbers, empty sets, and infinity, concepts that lack direct perceptual grounding or challenge our intuitive understanding of number,” Pinhas said. “Together, these lines of research aim to understand how the brain bridges the gap between visual symbols and abstract numerical meaning.”
The researchers hope to apply this knowledge to practical settings. “These findings have potential relevance beyond basic research,” Pinhas said. “If the brain relies on number length as an early, automatic cue to magnitude, this could have implications for how multi-digit numbers are taught and displayed, particularly for children who are still developing fluency with place-value notation.”
“Understanding the perceptual shortcuts the brain takes with numbers may help us design better learning environments for mathematical thinking,” Pinhas said.
The study, “Early neurophysiological signatures of multi-digit number length encoding,” was authored by Nadav Neumann and Michal Pinhas.
