Buzz
Albert Einstein once remarked: “Two things are infinite: the universe and human stupidity. And I'm not sure about the universe.”
The idea of infinity has intrigued brilliant minds throughout history, from Aristotle to the renowned German mathematician Georg Cantor. To many people today, it’s something boundless or without end. But when you truly start to consider what that implies, it can be mind-boggling. Is infinity merely a theoretical concept? Or is it something that could potentially exist in the physical world?
INFINITY COMES IN MANY FORMS
Infinity is deeply ingrained in mathematics. However, as Justin Moore, a mathematics researcher at Cornell University in Ithaca, New York, explains, even within this field, the term has slightly different meanings. “It’s often viewed as a virtual number placed at the end of the real number line,” he tells Mytour. “Or, it could refer to something so large it can't be counted by any whole number.”
Infinity comes in more than one form. For instance, counting represents a type of infinity that is limitless—known as potential infinity. In theory, you could continue counting forever without ever arriving at the largest number. However, infinity can also be finite, such as the infinity symbol. You can trace its shape endlessly, but you must stay within its defined boundary.
Not all infinities are equal. At the close of the 19th century, Cantor controversially demonstrated that some sets of counting numbers are actually larger than the counting numbers themselves. Since counting numbers are already infinite, this means that some infinities exceed others. He also showed that some forms of infinity are uncountable, unlike collections such as the counting numbers.
"At the time, it was a real revelation—a complete surprise," Oystein Linnebo, a researcher of the philosophy of logic and mathematics at the University of Oslo, tells Mytour. "But over the following decades, it became an accepted part of mathematics."
Without the concept of infinity, many mathematical principles would fall apart. A prime example is the famous mathematical constant pi, which is fundamental to formulas involving the geometry of circles, spheres, and ellipses. As an irrational number—a number that cannot be expressed as a simple fraction—pi consists of an endless sequence of decimals.
If infinity didn't exist, it would imply there is a largest number. "That would be utterly impossible," says Linnebo. Every number can be used to generate an even larger one, so such a scenario wouldn't work, he explains.
IS IT POSSIBLE TO MEASURE THE IMMEASURABLE?
In reality, infinity remains an elusive concept. Perhaps you've observed the effect of infinite reflections between two parallel mirrors positioned across from each other in a room. However, this is merely an optical illusion—the objects themselves aren't infinite. "It's extremely debatable and doubtful that infinities exist in the real world," states Linnebo. "Infinity has never been measured."
Attempting to measure infinity in order to prove its existence might be a fruitless endeavor. Measurement inherently involves a finite quantity, meaning the result would be the absence of a specific amount. "The reading would be off the scale, and that's all you'd be able to determine," explains Linnebo.
The search for infinity in the real world has often pointed to the universe—the largest known entity. Yet, there's no concrete evidence as to whether the universe is infinite or merely extraordinarily vast. Einstein suggested that the universe is finite but unbounded—a sort of hybrid between the two. He envisioned it as a variant of a sphere, which is beyond comprehension.
While we often think of infinity as something vast, some mathematicians have explored the idea of the infinitely small. In theory, if you take a segment between two points on a line, you could divide it repeatedly, endlessly. (This concept is part of Zeno's paradox known as dichotomy.) But when you try to apply the same logic to matter, you encounter a limitation. You can continue breaking down real-world objects into smaller and smaller parts until you reach atoms and their elementary particles, like electrons and the components of protons and neutrons. According to current understanding, subatomic particles cannot be divided further.
THE INFINITIES OF THE SINGULARITY
Black holes might be the closest we’ve come to detecting infinity in the physical world. At the center of a black hole lies a point known as a singularity—a one-dimensional point believed to contain an immense amount of mass. Physicists speculate that at this peculiar point, certain properties of the singularity, such as its density and curvature, may be infinite.
Within the singularity, many of the laws of physics no longer apply because these infinite quantities "break" numerous equations. For example, space and time are no longer distinct entities and appear to merge into one.
However, according to Linnebo, black holes are far from representing a true, tangible infinity. "My impression is that most physicists would argue that this is where our theory ceases to be applicable," he states. "When you encounter infinite curvature or density, you are beyond the realm where the theory holds true."
New theories might be required to explain this point, which seems to go beyond what’s conceivable in the physical world.
For the time being, infinity exists only in the abstract. It appears to be a concept created by the human mind, but can we ever truly grasp what it looks like? Perhaps to fully comprehend it, our minds would need to be infinite as well.
