Infinity is a concept that describes something without any limits or bounds. It refers to quantities that can grow indefinitely, like numbers that keep increasing or a space that extends endlessly. In mathematics, infinity is often used to represent values that go beyond any finite number. Itâs not just a large number, but rather an idea that challenges our understanding of size and extent.
Infinity can also apply in various contexts, such as in philosophy, where it raises questions about the universe, time, and existence, suggesting that some things may be beyond human comprehension. Essentially, infinity invites us to think about possibilities that stretch far beyond our everyday experiences.
The concept of infinity can be explored in various fields, such as mathematics and philosophy. In terms of mathematics, infinity is a boundless concept, which is larger than any and every number we can think of. In philosophy, it raises questions about the nature of existence and the universe. It was discussed philosophy as early as the ancient Greeks and in Mathematics during the 17th century.
Penrose Stairs
I can’t remember who or when exactly in my life that I was introduced to the concept of infinity. Though itâs present in so much pop culture like movies, TV shows, and games. An example of it is in the movie Inception. The idea generally makes me feel uneasy.
Infinity is often thought of as something vast and unending, existing beyond our reach. We are used to finding infinity in something abstract, but it also surrounds us in the natural process, especially the water cycle. This photograph, taken during the winter, caught a moment of that infinite cycle. The frozen lake, the snow-covered landscape, reminds us of the continuing state of transition that water is always undergoing: from vapor to liquid, from liquid to ice, and back again. This is a cycle without end, a natural depiction of infinity.
The water cycle is the infinity in math, because it works in a circle constantly. Just as an endless series of numbers without terminus, so too the perpetual motion of nature’s water: change of form, flow, and return onto itself. This has been going on for millennia and shall continue-independently of seasons or climate change. Each constituent part of the cycle-precipitation, freezing, melting, evaporation-is a link in an endless chain which reinforces nature’s own version of infinity.
The cycle somehow reminds us that infinity exists in tangible ways, even which we are able to see. It connects the photograph to that endless concept-that infinity isn’t just numbers or equations, but a part of life woven into the natural world and repeating endlessly before one’s eyes. But in this picture I would like to capture, not only the beauty of winter, but even something more transcendent, something like infinite, eternal nature.
The term “infinity” refers to objects that never end, such the list of natural numbers or the endless universe. According to the ancient Greek mathematician Aristotle, potential infinity exists but cannot be encountered directly. He also put out the idea of an actual infinite, which could be quantified similarly to the temperature of an object at a given location and moment. Aristotle, however, held that there are no real infinities in the physical world, and no actual infinity has ever been seen. Physicists continue to argue over the validity of Aristotle’s theory. There is considerable controversy among physicists today regarding the concepts of actual and prospective infinity.
Most people have some conception of things that have no bound, no boundary, no limit, no end. The rigorous study of infinity began in mathematics and philosophy, but the engagement with infinity traverses the history of cosmology, astronomy, physics, and theology. In the natural and social sciences, the infinite sometimes appears as a consequence of our theories themselves (Barrow 2006, Luminet and LachiĂšze-Rey 2005) or in the modelling of the relevant phenomena (Fletcher et al. 2019). Mathematics itself has appealed to some form of infinity from its beginning (infinitely many numbers, shapes, iterated addition or division of segments) and its contemporary practice requires infinitary foundations. Any field that employs mathematics at least flirts with infinity indirectly, and in many cases courts it directly.Philosophy countenances infinity in myriad ways, either directly or indirectly, in most of its sub-fieldsâhere is a tiny sample taken from the contemporary discussion. Some metaphysicians contend that there are infinitely many possibilities/possible worlds and canvas how big this infinity is (e.g. Lewis 1986). Philosophers of religion debate whether the divine is infinite, whether the divine creation is infinite, and whether the value of the afterlife is infinite. Epistemologists debate whether there can be an infinite regress of justification, and if so, whether it is problematic (Klein 2000, Peijnenburg 2007, Atkinson and Peijnenburg 2017). Formal epistemologists traffic largely in an infinitary notion of âprobabilityâ (more in Section 6). Population ethics for infinite populations is a lively topic, and they are thought to pose distinctive problems for consequentialism (Nelson 1991). Social and political philosophy appeal to the notion of convention. Yes I think that infinity in a religious setting refers to the same idea as infinity in mathematics? It deals with how further it goes, and religion is when anything goes on forever. Eternity is specifically when time goes on forever.
Infinity is the state of something that has no bounds or end. It always outgrows any number that one can ever imagine and goes further. In math, it’s often used to describe things that have no end or processes that can be continued forever. But it isn’t a big number; it’s an entirely different kind of concept with no boundary or endpoint.
2. Who first introduced you to the idea of infinity? How old were you? How did this new idea make you feel?
I think the first time I ever thought of infinity was in elementary school, where we learned about the number system and how numbers could just keep getting larger. I was only seven or eight at that time, but it was something that really made me curious, though a little bit overwhelmed. Understanding that there is no “biggest number” made me realize that some concepts are really beyond what we are fully able to grasp.
3. Describe either a conversation you had about infinity or an argument you had about infinity. Give us the details!
I once had a debate with my friend as to whether or not there’s a “biggest” infinity. My friend said that infinity is only one thing, whereas I had heard about the different “sizes” or types of infinity, such as the infinity of real numbers being “bigger” than the infinity of whole numbers. We went back and forth trying to explain it, and I remember realizing that infinity was more complex than I originally thought.
4. Find a reference to infinity in popular culture (a song, a movie, a product, a book, etc.). What does infinity mean in this context? Does it mean the same thing that it means in mathematics? Explain.
One of the most famous pop references to infinity is when, in the movie Toy Story, it says, “To infinity and beyond!” There, infinity symbolizes an idea of limitless possibilities and courage. It doesn’t mean infinity in a severe mathematical sense; in math, there is no actual “beyond” of infinity. Instead, it’s rather an inspirational catchphrase to encourage people to go beyond their limits.
5. Is infinity an important idea in your religion? Do you think that infinity in a religious setting refers to the same idea as infinity in mathematics? Why or why not?
In most religions, infinity has to do more with the eternity of the universe, soul, or god. It is, in some ways, more of a philosophical or spiritual kind of infinity that generally speaks to time without end or unlimited existence. While the mathematical concept of infinity is exact and applied in formulae, religious infinity is more abstract and deals with ideas beyond human comprehension.
An infinity is a concept that represents the quantity of something that has no limit. It can be either the lifespan of a living thing, durability of a non-living thing or from the moment of existing to never seize to exist at all. An infinity is a concept that we apply to many spheres of our lives, including religion, science and even math. Throughout the history we tried to grasp the idea of infinity, but everything on Earth seems to be finite, as we know it.
I cannot pinpoint the exact location or the time that I was introduced to the idea of infinity; however, I would assume that around middle school I was visualizing the concepts outside the school programs. I used to sketch and draw fighting scenes on my free time during school hours, so entertainment elements such as comics and games characters seem very fun to me. Some of those comics characters have bigger lifespan than others due to the power they possess, therefore I probably started thinking about infinity when characters were immortal or there were some universal types of scale which makes you ponder upon the idea how small we are in an astronomical scale compared to outer planets, stars and even galaxies. Overall, I was probably around 12 years old when infinity came to my mind and this idea made me feel intrigued, because how can a person’s life be finite and yet, most of the religions have a concept of a God that is immortal, who created us and yet, there were never a mention of the ultimate end except for a human life. In my opinion, it really starts to deal with an abstract mind in a philosophical and even psychological way, since there is no definite answer to whether infinity really exists.
I cannot recall any conversations I had about an infinity; however, I have an argument that I have been thinking about recently, is that how can our universe expand without any limits into an infinity if anything we ever know on the Earth and even within our galaxy, such as planets and stars have a certain lifespan they can co-exist relatively to their creation. For example, my main theory on that, is that even if the universe is expanding, it needs a certain outside space to do it, it cannot just bend the fabric of reality and form new stars, planets and even galaxies as it wishes out of nothing. As one of the principles that governs our physics is the “Law of conservation of energy”, which states that matter cannot be created or destroyed, which implies that even the universe itself, in theory, cannot just create new matter out of nowhere and disperse the energy as it wishes, there has to be a limit at some point, and I believe that the concept of physics that we have discovered throughout the history should be applicable anywhere else outside of our scope of astronomical scale. And based on science, the idea of infinity is arbitrary/abstract, instead of something that has a value. Therefore, my conclusion on this argument, is that either there is a being like God that governs over the universe and the way it behaves, or the universe does have a limit even if it expands beyond our human understanding as of right now.
One of the references to the infinity found in pop-culture that I can relate to is the endless, internal battle between good and evil within the Star Wars franchise. Even since I was a kid, I really enjoyed playing Lego Star Wars, where I build my own minifigures, battles and scenarios as an entertainment. What really intrigued me about Star Wars, is that there is an always ongoing rivalry between the good and evil forces that somehow need to stay in balance, or the entire civilizations will collapse if the either side would go out of hands. It really makes you think philosophically about how even in real life, we have positive/negative emotions, law-abiding and criminal activities, as well as good and evil intentions from our overall surroundings. This made me wonder, how we as humans cannot be fully good or fully bad either, we are a combination of both. This brings my topic to an idea of Yin and Yang, a Chinese philosophy on how the light and dark sides of the circle are in balance with each other, which shows two opposite flowing substances which collide into one shape. However, this philosophical notion about good and evil concept isn’t the same as in mathematics. Because as a referenced before, the Star Wars franchise is portraying light and darks sides of the force as individuals who have the ability to wield the force and even lightsaber as a way to fight their opponents, but it is up to a person to decide which sides he is on, based on his experience in life. But in mathematics, we use infinity to represent points on the graph within the curve that has no limits, either towards the negative or positive directions. (Star Wars pop-culture link: https://toxigon.com/the-philosophy-of-the-force ); (Yin and Yang link: What Is the Meaning of Yin and Yang? ).
A drawing that illustrates the concept of infinity:
I’ve always found the topic about infinity interesting as it explores mostly the unknown, whether that be the vastness of space, math, etc. The way I would describe infinity would be something that we have no or little control over, and something that has no limit, or at least a limit that we cannot fathom or understand. We experience some type of infinity in out every day lives, pretty commonly, from infinite refills, to seemingly infinite red lights, to the earth travelling in the infinity of space, orbiting around a sun which is also travelling into the infinity, which is also orbiting around a galaxy heading towards infinity, and so on, you get the point.
An object that I would represent infinity as is a Möbius strip, which is a sort of paradoxical object that could be made even from a piece of paper. The reason I chose this object, is due to its oddly weird properties, which somewhat tie into infinity. It is an object that only has one side to itself, continuing on for infinity, as well as looking like the infinity symbol from a certain perspective. If you were to cut a Möbius strip in half at a certain angle, it would double in size and be twice as long, if you were to do it again, it would double again, and as you cut it, it would become infinitely long, and infinitely thin.
My understanding of infinity is that it is a concept that represents the idea that things can be boundless. It is used in mathematics to symbolize endless processes or sizes, such as the notion that a line can extend indefinitely in both the positive and negative directions or that there is an infinite set of numbers that can fit on a number line. We use the concept of infinity to comprehend big, complicated concepts in math, physics, and other fields, even though it can be difficult to fully understand them in the real world.
A great example of infinity in popular culture is in the movie Avengers: Infinity War. In the film, the concept of the âInfinity Stonesâ is central. These stones are said to control different aspects of the universeâtime, space, reality, power, mind, and soulâand when brought together, they grant their possessor unlimited power. The idea here reflects a different take on infinity, not in terms of endless quantity but in terms of boundless potential and control. While infinity in this context doesnât follow mathematical rules, it symbolizes the essence of infinity, which is the idea that there are things in this world that are all-encompassing and limitless in their own way. The possessor of the stones in the MCU (Marvel Cinematic Universe) is Thanos, and as he collects more and more infinity stones throughout the movie, he makes his potential power and control over time, space, reality, etc. more boundless.
We can measure the behavior of functions over an infinite domain by using integrals from any number to infinity. Sequences are another example in math that represent the idea of a list of numbers following a certain pattern that grows infinitely unless otherwise specified. Although one infinity focuses on mathematical accuracy and concepts, the other focuses relatively on power; both infinity concepts highlight the underlying them being limitless. These concepts are closely related to the film’s illustration of unbounded power. The video below illustrates how Thanos grows stronger with each stone he gathers, creating new uses for each stone. This embodies the idea that some processes or quantities are infinite. While the infinity in the movie doesnât follow mathematical rules, it symbolizes something all-encompassing and limitless in its own way. It’s a more creative take on infinity than the precise, organized concept we see in mathematics.
This is just a 6-minute video showing all the times Thanos used the infinity stone against The Avengers, progressively getting stronger.
At first glance of the picture, it may be difficult to see the correlation between the rows of strangely phrased words and infinity, but the connection is there. It’s in the colors! Infinity, per the dictionary, is endless and with no bounds, and that, to me, is also a good way to describe colors. It is known that in the visible spectrum, we can see about seven colors (red, orange, yellow, green, blue, indigo, violet). Those same colors appear in the image; however, the spectrum is home to an endless range of colors, all identified by a different combination of letters and numbers. The color spectrum is so infinite that even the subtlest change in a letter or number in the color code will result in a different color or even shade. (#66FF66 vs. #66CC66 results in a different shade.) (#CCCCFF vs. #CCCCCC results in different colors.)
Imagine a line that stretches out in both directions so far out that there is no sign of a beginning nor an end. No matter how far back or how far forward you travel along it, there is always more line in both directions. This is the concept referred to as “infinity”, the idea of something that can be so large it extends beyond any limits, thus, no beginning and no end.
I believe we all once met a hero, one draped in white and green. He has a suit which boasts of flashy buttons, and from his back springs a pair of wings ready to carry him beyond the bounds of the playground. Most know him as Buzz Lightyear, to Andy, he is the coolest space ranger, but to him, he is Andy’s friend. As he stretches his plastic arms towards his plastic head, he boldly declares, “To infinity…and beyond!”
To Buzz, infinity is a representation of an endless journey full of possibilities and new adventures to explore the beyond, pushing him past his limits. Buzz’s infinity is the same as the infinity presented in mathematics, as long as we are referring to it as a concept of no beginning nor end.
This picture might not quite be infinity; however, it can still be a representation of the basic concept. The picture showcases a view of mountains that stretches far beyond our view. At simple sight, one would not have the ability to identify an end, and much less a start, to this stretch of land, which might be represented as a kind of infinity.
Infinity is a concept that stretches beyond ordinary understanding, representing something that has no end or limit. In mathematics, itâs often symbolized as ââ,â a number larger than any finite quantity we could ever reach. But the concept of infinity is much more than numbers; it also appears in everyday life and nature, suggesting the boundlessness of time, space, and even ideas. When we try to understand infinity, weâre stepping into a realm that our minds struggle to fully grasp, where the limitations of what we know dissolve, and weâre left with only the wonder of endless possibilities.
Beyond the mathematical, infinity represents endlessness in many areas of life. The sky, the ocean, or even the passage of time all hint at this idea of an unending flow, with each moment leading into another, each wave rolling in just to be replaced by the next. This broader concept of infinity shapes how we think about the universe and our place within it, offering a perspective that is both humbling and intriguing.
One of my first experiences with the idea of infinity happened on a plane as I looked out at the endless stretch of clouds. The clouds seemed to blend into the horizon without any clear boundary, making me think about the vastness of the world and my place in it. As I later learned about infinity in math and philosophy, I kept returning to that view from the plane. Infinity wasnât just an abstract concept anymoreâit was something I could see and feel in that boundless sky.
For this post, I chose a photo I took from the plane window, capturing clouds extending to the horizon. This image, to me, shows infinity as a limitless view, where the clouds and sky seem to go on forever, evoking that same sense of wonder and mystery that defines infinity.
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