A recent study published in the Journal of Experimental Psychology: Learning, Memory, and Cognition suggests that people do not perceive the infinity symbol (ā) as representing an endless and boundless concept. Instead, individuals often misconstrue it as a concrete number similar to other numerical values. This finding indicates that our minds might process infinity not as an abstract idea distinct from numbers but as just another point on the numerical scale.
The concept of infinity has long intrigued mathematicians and philosophers, yet it remains challenging for most people to grasp. Infinity represents something beyond the limits of numbersāit is endless, unmeasurable, and distinct from any number on a numerical scale. Previous studies have shown that people struggle to fully understand the nature of infinity, often not recognizing it as a truly limitless entity.
However, few studies have directly examined how the infinity symbol is mentally processed when presented alongside concrete numbers. The researchers aimed to fill this gap by investigating whether people intuitively treat the infinity symbol as “the largest” or if they misconceive it as just another number in the sequence of finite values.
“Traditional cognitive science has focused on phenomena grounded in sensory experience, but infinity is entirely different. Understanding infinity requires abstract thinking that goes beyond concrete representations and everyday experiences, which I find both puzzling and challenging,” said study author Michal Pinhas, the principal investigator of the Quantitative Thinking and Cognition Lab at Ariel University.
“In my lab, we explore how people understand and process abstract or nonintuitive mathematical concepts beyond infinity, such as zero and exponential growth. The goal is to gain deeper insights into how the human mind handles concepts that lack direct, concrete connections to everyday experience, and how this influences reasoning and decision-making. I believe that studying these unique and challenging concepts can expand the way we think about numerical representations and processes.”
Pinhas conducted four main experiments, with 120 participants in total, to investigate how people process the infinity symbol compared to numbers. The methodologies used in each experiment were designed to test whether the infinity symbol is perceived as āthe largestā or simply as another number. Two main types of tasks were used: numerical comparison tasks and physical comparison tasks.
In the numerical comparison task, participants were presented with pairs of symbolsāeither numbers or the infinity symbolāand asked to choose which one was larger or smaller. This task required participants to actively evaluate the magnitude of each symbol, focusing on its numerical meaning. The symbols included single digits (like 1, 5, or 9), multidigit numbers (like 44 or 666), and the infinity symbol. This task aimed to determine whether participants intuitively understood infinity as a boundless concept or if 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 frames surrounding them. For example, participants were asked to select the larger or smaller frame, regardless of the symbols inside. The symbolsāwhether numbers or the infinity symbolāvaried in physical size within the frames, with some symbols appearing smaller than others.
This task was designed to assess how participants automatically processed the numerical and physical properties of the symbols, even though they were explicitly told to focus only on the frames. By manipulating the physical size of the symbols, the researchers aimed to determine whether the physical appearance of the infinity symbol subconsciously influenced participants’ judgments, and whether they treated it differently from numbers.
The findings from these tasks were consistent across all the experiments. In the numerical comparison task, participants did not consistently treat the infinity symbol as āthe largestā concept, even though it is theoretically larger than any number. For example, when comparing infinity to a small number (like 1 or 5), participants responded quickly when asked to select the larger option.
However, when infinity was compared to a large number (like 999), response times slowed down, suggesting that participants did not automatically perceive infinity as vastly larger than these multidigit numbers. This pattern suggests that participants may have processed the infinity symbol as though it represented a large but finite number rather than an abstract, boundless concept.
The physical comparison task provided further insights. When the infinity symbol was physically smaller than a number it was paired with, participants took longer to respond, suggesting that the physical size of the symbol affected their decision-making. This implies that people rely on visual cues like size to make judgments about the magnitude of symbols, including abstract concepts like infinity.
Interestingly, when the infinity symbol was physically larger than the number it was paired with, participants responded more quickly, reinforcing the idea that the physical size of the symbol played a significant role in how they processed it. Despite these size manipulations, participants did not consistently treat the infinity symbol as an ultimate end-value or “the largest,” as might be expected if they fully grasped its abstract meaning.
“I was surprised to find that, in certain conditions, people processed the infinity symbol as smaller than multidigit numbers,” Pinhas told PsyPost. “This suggests that our automatic, intuitive processing of numerical symbols can sometimes override our conceptual understanding of abstract notions like infinity.”
Another important finding was the “distance-like effect” observed in the numerical comparison task. Normally, when comparing two numbers, people respond faster when the numbers are farther apart in value. A similar effect was seen when participants compared the infinity symbol to numbers: response times increased as the numbers being compared to infinity grew larger. This suggests that participants were incorrectly placing the infinity symbol on a numerical scale alongside concrete numbers, treating it as if it had a measurable value, rather than recognizing it as a concept that represents something beyond all numbers.
“The key takeaway is that while we often think of infinity as ‘the largest’ or ‘something beyond all numbers,’ our minds donāt always process it that way,” Pinhas explained. “People seem to misconceive the infinity symbol (ā) as representing a concrete number, rather than an abstract concept distinct from numbers. This was evident in participants perceiving larger numbers as being closer to infinity than smaller ones.”
While the study provides valuable insights, it also has some limitations. First, the participants were primarily university students from psychology and engineering departments, which means the findings might not generalize to other populations. Future research 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 solely on the infinity symbol, and it’s possible that other symbolic representations of infinity might be processed differently,” Pinhas said. “In fact, new research in my lab suggests this may indeed be the case.”
The study opens the door to examining other abstract mathematical concepts. Infinity is unique in that it does not have a concrete counterpart in the physical world, but many other mathematical ideas (like zero or negative numbers) also challenge our intuitive understanding. Exploring how people process these concepts could deepen our understanding of how the human mind grasps abstract numerical information.
“This research highlights how deeply our understanding of numerical concepts is rooted in physical experience,” Pinhas said. “It also raises broader questions about how our minds perceive abstract concepts in general.”
The study was titled: “Perceiving Infinity: An Interplay Between Numerical and Physical Magnitude.”
