A recent study published in the experimental psychology journal Learning, Memory, and Cognition found that people don’t seem to recognize the infinity symbol (∞) as representing the concept of endlessness. Rather, people often mistake it for a concrete number like other numerical values. This finding suggests that our minds may process infinity as simply a point on a numerical scale, rather than as an abstract concept distinct from numbers.
The concept of infinity has long intrigued mathematicians and philosophers, but it remains difficult for most people to understand. Infinity represents something that is beyond the limits of numbers. Infinity is unending, immeasurable, and unlike any number on the numerical scale. Previous research has shown that people struggle to fully understand the nature of infinity and do not perceive it as a truly limitless entity.
However, few studies have directly examined how the infinity symbol is mentally processed when it appears alongside concrete numbers. The researchers aimed to fill this gap by examining whether people intuitively treat the infinity symbol as a “maximum” or misinterpret it as just another number in a sequence of finite values.
“Traditional cognitive science has focused on phenomena based on sensory experience, but infinity is completely different. Understanding infinity requires abstract thinking that goes beyond concrete representations and everyday experience, which to me is puzzling and difficult,” said Michal Pinas, lead researcher in Ariel University’s Quantitative Thinking and Cognition Lab and author of the study.
“In my lab, we study how people understand and process abstract or non-intuitive mathematical concepts beyond infinity, such as zero and exponential growth. The goal is to gain deeper insight into how the human mind processes concepts that have no direct, concrete connection to everyday experience, and how this affects reasoning and decision-making. I believe that by studying these unique and challenging concepts, we can expand the way we think about numerical representations and processes.”
Piñas conducted four main experiments with a total of 120 participants to investigate how people process the infinity symbol in comparison to numbers. The methods used in each experiment were designed to test whether the infinity symbol is perceived as “maximum” or just another number. There were two main types of tasks used: a numerical comparison task and a physical comparison task.
In the numerical comparison task, participants were presented with pairs of numbers or infinity symbols and asked to choose which was bigger or smaller. The task required participants to actively evaluate the magnitude of each symbol and attend to its numerical meaning. Symbols included single-digit numbers (e.g., 1, 5, 9), multi-digit numbers (e.g., 44, 666), and the infinity symbol. The goal of the task was to determine whether participants intuitively understood infinity as an infinite concept or whether they processed it as a large but finite number.
In the physical comparison task, participants were shown pairs of symbols, but they were instructed to ignore the symbols themselves and focus on the size of the frame surrounding the symbols. For example, participants were asked to choose the larger or smaller frame, regardless of the symbol inside. The symbols (whether numbers or infinity signs) differed in physical size within the frame, with some symbols appearing smaller than others.
This task was designed to assess how participants automatically processed the numerical and physical properties of the symbol, despite being explicitly instructed to focus only on the frame. By manipulating the physical size of the symbol, the researchers aimed to examine whether the physical appearance of the infinity symbol unconsciously influenced participants’ judgments and whether participants treated it as something separate from a number.
The results from these tasks were consistent across all experiments. In the numerical comparison tasks, participants did not consistently treat the infinity symbol as a “largest” concept, even though it is theoretically larger than any number. For example, when comparing infinity to small numbers (such as 1 or 5), participants responded faster when asked to choose the larger option.
However, when comparing infinity to larger numbers (e.g., 999), reaction times were slower, suggesting that participants did not automatically perceive infinity as much larger than these multi-digit numbers. This pattern suggests that participants may have processed the infinity symbol as representing a large but finite number, rather than an abstract, infinite concept.
The physical comparison task provided further insight: when the infinity symbol was physically smaller than the number it was paired with, participants took longer to respond, indicating that the physical size of the symbol influenced their decision. This suggests that people rely on visual cues such as size to judge how large symbols are, including abstract concepts like infinity.
Interestingly, participants responded more quickly when the infinity symbol was physically larger than the number it was paired with, reinforcing the idea that the physical size of the symbol plays an important role in processing it.Despite these size manipulations, participants did not consistently treat it as an ultimate final value or “maximum,” as would be expected if they fully understood the abstract meaning of the infinity symbol.
“We were surprised to find that in certain circumstances, people process the infinity symbol as smaller than multi-digit numbers,” Piñas told PsyPost, “This suggests that our automatic, intuitive processing of number symbols can sometimes override our conceptual understanding of abstract concepts like infinity.”
Another important finding was the “distance-like effect” observed in the numerical comparison task. Typically, when comparing two numbers, the further apart the numbers are, the faster people react. A similar effect was observed when participants compared the infinity symbol with a number: reaction times increased as the number being compared to infinity increased. This indicates that participants were incorrectly aligning the infinity symbol with a concrete number on a numerical scale and treating the infinity symbol as having a measurable value, rather than recognizing it as a concept that represents something beyond all numerical values.
“The key point is that although we often think of infinity as the ‘greatest’ or ‘beyond all numbers,’ our minds don’t necessarily process it that way,” Piñas explained. “People appear to mistake the infinity symbol (∞) as representing a concrete number, rather than an abstract concept distinct from numbers. This is evident in participants’ perception of larger numbers as closer to infinity than smaller numbers.”
Although this study offers valuable insights, it also has limitations. First, participants were primarily undergraduate students from psychology and engineering faculties, so the findings may not generalize to other populations. Future studies could explore how people with more extensive training in mathematics, such as mathematicians, process the infinity symbol. Additionally, researchers could investigate whether other representations of infinity, such as the written word “infinity,” lead to similar patterns of misunderstanding.
“This study focused only on the infinity symbol, and it’s possible that other symbolic representations of infinity are processed differently,” Piñas said. “In fact, new research from my lab suggests that this may indeed be the case.”
This research opens the door to investigating other abstract mathematical concepts. Infinity is unique in that it has no concrete counterpart in the physical world, but many other mathematical concepts (such as zero and negative numbers) also challenge our intuitive understanding. Investigating how people process these concepts could deepen our understanding of how the human mind grasps abstract numerical information.
“This study highlights how our understanding of numerical concepts is deeply rooted in physical experience,” Piñas says, “and it also raises broader questions about how our minds perceive abstract concepts in general.”
The study was titled “The Perception of Infinity: The Interplay of Numerical Values and Physical Size.”
