How Your Brain Organizes Numbers Depends on Direction

The ‘mental number line’ theory doesn’t appear to hold up vertically.

Smaller numbers should pull your attention downward. At least, that’s what many studies on mental number lines suggested. But when Japanese researchers tested this assumption, they discovered something that challenges our understanding of how brains organize numerical information: smaller numbers actually pushed attention upward.

Scientists at Tokyo Metropolitan University asked 37 healthy adults to find the center of lines filled with repeating numbers. When participants viewed vertical lines covered in 1s and 2s, they consistently marked the center higher than when viewing lines filled with 8s and 9s. The finding contradicts the expected “bottom-to-top” mental number line that scientists thought governed how we mentally arrange numbers in vertical space.

“Contrary to our hypothesis, the biases for smaller numbers were shown to be more upward than those for larger numbers in the vertical centering task,” wrote researchers Ryo Hishiya and Masami Ishihara in Scientific Reports.

How the Mental Number Line Usually Works

The discovery becomes even more puzzling when compared to horizontal results. For horizontal lines, everything worked as predicted. Participants placed their estimated center about half a millimeter farther left, a small but reliable shift, when viewing lines with 1s and 2s compared to lines with 8s and 9s. This matched the well-established left-to-right “mental number line” observed in cultures that read from left to right.

The mental number line theory suggests people automatically associate numbers with positions in space. When someone sees the number 1, their brain unconsciously links it to the left side; the number 9 pulls attention rightward. This happens so automatically that it affects reaction times, eye movements, and spatial judgments even when numbers are completely irrelevant to the task at hand.

In speeded response tasks, research with both Chinese and Japanese speakers seemed to confirm this pattern worked vertically too. Studies showed people making faster responses to smaller numbers when pressing lower buttons and faster responses to larger numbers when pressing upper buttons. The brain appeared to map small numbers to lower positions and large numbers to higher positions.

The Experiment That Reversed Expectations

But Hishiya and Ishihara’s centering task revealed something different. Rather than asking participants to make quick button presses, the researchers had them carefully identify the exact center of shapes displayed on a computer screen. Participants used a computer mouse to click where they believed the true midpoint was located.

The vertical lines measured 130 millimeters tall and just 4 millimeters wide. Each was filled with 33 identical numbers arranged in a string: either 1, 2, 8, or 9. Participants viewed the lines from 45 centimeters away while their heads remained fixed in a chin rest.

About 89 percent of participants showed an upward bias when judging vertical lines, regardless of which specific numbers were displayed. But the upward shift was noticeably stronger for lines containing smaller numbers, opposite to the predicted bottom-to-top mental number line.

“Participants positioned their subjective midpoint of the smaller number stimulus more upper side relative to that of the larger number stimulus,” the researchers explained.

Why Vertical Space Behaves Differently

The team explored several possible explanations for the unexpected reversal. One possibility involves how the brain processes order versus pure quantity. The numbers 1 and 2 might activate mental representations of “early” in a sequence, while 8 and 9 represent “later” positions. Some research suggests the brain maps “early” items in sequences to upper space and “later” items to lower space along a vertical axis.

This would create a conflict: the magnitude of numbers (small versus large) points one direction, but the sequential position (early versus late) points another. The sequential association might be overriding the magnitude association in vertical space.

Cultural factors seem unlikely to explain the reversal. Japanese speakers can write text vertically, moving from top to bottom down a column and then right to left across columns. However, the current study used Arabic numerals rather than Japanese characters, and previous research showed Japanese speakers still demonstrate Western-style left-to-right mental number lines with Arabic numerals.

The researchers also discovered differences when they tested two-dimensional squares instead of one-dimensional lines. Squares measured 130 millimeters on each side and contained either 33-by-33 grids of numbers or plain backgrounds.

Squares filled with number patterns produced stronger upward biases but weaker leftward biases compared to plain squares. The presence of number strings appeared to activate different brain processing pathways. In simple terms, the brain may have treated the squares more like objects to look at than spaces to measure.

“The upward biases for the square stimuli with number strings may reflect the activation of object-based processing rather than the cognitive function of numerical processing,” the study notes.

This suggests the brain can switch between different modes: processing objects and patterns versus processing pure spatial information. Object-based processing tends to be linked with brain pathways that favor upper visual space, while spatial processing connects with pathways that favor lateral attention.

Horizontal lines showed no such complications. The leftward bias for smaller numbers remained consistent across different shapes and conditions, suggesting horizontal and vertical dimensions operate through distinct brain mechanisms.

The team tested whether response speed affected the numerical biases, since some theories propose spatial coding of numbers requires time to develop. Surprisingly, response speed made almost no difference. Participants who took longer to respond showed similar numerical effects as those who responded quickly.

One exception emerged: when participants used their right hand to judge vertical lines, faster responders showed bigger differences between their reactions to small versus large numbers. This was opposite to the researchers’ expectations and remains difficult to explain.

What This Means for Understanding the Brain

The findings raise questions about how flexibly the brain maps numbers onto space. While horizontal associations appear relatively stable across cultures and contexts, vertical associations show surprising variability.

Scientists have documented bottom-to-top mental number lines in some tasks but not others. The type of judgment, the response method, and even which hand participants use can influence whether vertical number-space associations emerge and in which direction.

“The vertical axis has the potential to reflect either bottom-to-top or top-to-bottom spatial directions, depending on the nature of the activated representation,” Hishiya and Ishihara wrote.

The research suggests scientists may need to rethink assumptions about mental number lines. Rather than a single, universal mapping system, the brain might employ multiple strategies depending on context, task demands, and which brain pathways are most activated.

Although the attention shifts measured in this study were tiny—less than one millimeter in many cases—they reveal automatic processes happening beneath conscious awareness. These unconscious links between numbers and space influence how people navigate their environment, make decisions, and even how children learn mathematics.

Understanding why vertical number-space associations behave so differently from horizontal ones could shed light on how the brain organizes abstract information. The unexpected upward pull of small numbers suggests there’s still much to discover about the mental architecture underlying something as fundamental as counting.

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