Recent research published in scientific report This provides evidence that the human brain processes the physical length of multi-digit numbers at the earliest stages of visual perception. The findings suggest that the physical length of a number acts as a fast automatic signal for overall size, before the brain fully evaluates the actual number.
The mathematical systems that people use every day rely on two primary pieces of information to convey quantities. The first part is the specific shape of the number, such as the 7 or 2 symbol. The second part is the total number of digits and is known as number syntax. When you look at a number like 300, you know it’s larger than 30 because it contains extra digits and appears visibly longer.
This physical length serves as a reliable visual hint of the magnitude of the number. Scientists are evaluating different models to explain how the mind interprets this information. Some models propose that people process numbers as single visual objects. Other models suggest that the brain reads numbers by breaking them down into their component parts.
Nadav Newman, a recent PhD graduate, and Michal Piñas, a researcher in the Quantitative Thinking and Cognition Laboratory in the Department of Psychology at Ariel University in Israel, designed a study to test how the brain disentangles these discrete pieces of information. This paper is based in part on Neumann’s doctoral thesis.
“Multi-digit numbers are the numbers we use most often in our daily lives, but surprisingly little is known about how the brain processes them compared to single-digit numbers,” Piñas says. “We were particularly interested in a seemingly simple question: When you see a number like 22222, does your brain record the number of digits before understanding its meaning?”
Pinhas explained that the Arabic numeral system has a built-in feature that makes it easier to answer this question: Longer numbers usually represent larger values, so the length of a number is the real clue to magnitude. “We wanted to know whether and how quickly the brain takes advantage of that cue while controlling the overall visual size of the numbers on the screen,” she said.
To measure this mental process, Neumann and Piñas looked at electrical activity in the brain. They used a technique that records electrical signals produced by the brain in response to specific sights or tasks. By examining the exact milliseconds after a participant views a number, researchers can plan the timeline of mental processing. They focused on three specific brainwave patterns that appear during early, middle, and late stages of visual and cognitive processing.
Past research has struggled to separate the actual length of a number from its overall visual size on the screen. Generally, 5-digit numbers tend to take up more physical space than 2-digit numbers. This makes it difficult to determine whether the brain is responding to a huge amount of black ink on a white background or to a specific concept of the length of a number.
To address this visual problem, researchers created images of special numbers. They used numbers made up of repeating numbers, such as 22 and 88888. I then added some random scribbles next to all the numbers. This allows a short number like 44 to occupy exactly the same total width on your computer monitor as a long number like 44444.
By equalizing the visual size of the images, scientists were able to isolate the specific mental effects of reading multiple numbers. 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 wearing a special hat that recorded their brain’s electrical activity. They observed a series of repeating numbers of varying lengths. They were instructed to decide whether a particular number repeated on the screen was mathematically smaller or larger than the number 5.
The instructions asked us to completely ignore the length of the numbers. For example, a participant might see the number 77 and compare it to a mental standard of 555. Since 7 is greater than 5, the correct answer is greater.
However, the number 77 only has two digits, while 555 has three. This creates a mismatched situation where the actual number is mathematically larger, but the physical length of the number is smaller. In matching situations, such as 88888, both digits and length are greater than the standard 555.
Behavioral results from the first experiment showed that participants responded faster when the value of the digits matched the length of the digits. When the traits were incongruent, participants took slightly longer to respond. This suggests that the brain automatically processes the length of numbers, even when people are actively trying to ignore them.
EEG recordings provided a detailed timeline of this interference. For 120 to 150 milliseconds after the digits appeared on the screen, early brain wave patterns showed a strong response to the length of the digits. This shows that the brain detects the length of numbers during the early stages of visual recognition.
“The most direct evidence comes from brain recordings, where we found robust and consistent neural sensitivity to digit length as early as 120 to 150 milliseconds after viewing the digits,” Piñas said. “This is surprising because it places size-related processing at the earliest stages of perceptual encoding earlier than most previous studies have demonstrated. Importantly, this early effect was found independent of the overall visual size of the digits, meaning that it reflects the syntactic structure of the digits themselves rather than general visual properties.”
“When you see a multi-digit number, your brain quickly reads the number and then forms an impression of its size,” Piñas told PsyPost. “Within approximately 120 to 150 milliseconds of seeing a number, in the first stages of perceptual processing, the brain is already using the physical length of the number to quickly estimate how big it is.”
“This is the brain taking a shortcut, and it usually works well because long numbers are actually big,” Piñas says. “This is a striking example of how deeply our intuitions about quantities are shaped by the visual structure of the symbols we use.”
Later in the timeline, between 150 and 190 ms, a second EEG pattern appeared in the recording. This intermediate stage reflects a more sophisticated processing of numerical distances and indicates that the brain is beginning to evaluate the actual value of the numbers. Finally, between 300 and 360 milliseconds, a third brainwave pattern associated with resolving mental conflicts emerged.
In the second experiment, another group of 27 students completed a physical comparison task. They viewed the exact same type of scribbled images while wearing brain recording devices. This time I was asked to decide whether the number on the screen was physically shorter or longer than the standard 555. They were told to ignore the actual mathematical value of the numbers.
Behavioral data from the second experiment showed no significant delays when participants saw incongruent digits. People were able to evaluate the length of a number without interference from the value of the number. The EEG data supported the idea of early automatic detection of number length, but with a unique twist based on task instructions.
“One of the striking findings was the discrepancy between the two experiments,” Piñas said. “Even when participants focused on digit identity and ignored length, digit length intruded and slowed behavior, but not during the early neural stages.”
“We focused on physical length instead, and the early ERP components showed a number, even though it was unrelated to the task,” Pinhas says. “This asymmetry suggests that the brain does not process these two dimensions in a simple and symmetrical way, and that even at very early perceptual stages, attention determines which dimension takes precedence.”
Although these findings provide detailed insights into mathematical processing, this study has several limitations. One potential misconception is that these early brainwave patterns apply to all types of mathematical reading.
“In our stimuli, we used ‘tie numbers,’ meaning numbers made up of repeating single digits, such as 4444 and 88888,” Piñas says. “This is a deliberate methodological choice to control for compatibility effects within the numbers, but it means we can’t yet say whether the same pattern holds for everyday numbers with mixed numbers.”
“We also tested only two levels of numerical length differences, so the full shape of the relationship between length distance and brain response is still unknown,” Piñas said. “Extending these findings to more natural numbers will be an important next step in future research.”
Another limitation is that the researchers tested only young people. The way the brain processes mathematical symbols tends to change over time due to education and experience. Future research could investigate how children develop these early detection systems as they learn the rules of numerical syntax. Furthermore, the exact reason for the initial left-hemisphere bias observed in this study is still unclear.
Understanding these early mental stages allows us to take a deeper look into how the human mind organizes everyday mathematical information. “This paper is part of a broader research program investigating how the physical and syntactic properties of numerical symbols shape mental representations of quantities,” Piñas said.
“We are particularly interested in numerical concepts that are not cognitively intuitive, such as very large multi-digit numbers, the empty set, and infinity. These are concepts that lack a direct perceptual basis or that interfere with intuitive understanding of numbers,” Piñas 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 real-world settings. “These findings have potential relevance beyond basic research,” Piñas said. “If the brain relies on number length as an early automatic cue for magnitude, this could have implications for how multi-digit numbers are taught and displayed, especially for children who are still developing place value fluency.”
“Understanding the shortcuts the brain takes with numbers may help us design better learning environments for mathematical thinking,” Piñas says.
The study, “Early neurophysiological signatures of multidigit numerical length encoding,” was authored by Nadav Neumann and Michal Pinhas.
