The concept of infinity has grasped a lot of people, including me, because of its unimaginable greatness. The infinite is something that is beyond reach and comprehension. Some people associate the infinite with God while others wear the “∞” symbol mindlessly as their earrings or (semi mindlessly) as tattoos. The infinite is an intriguing concept but you don’t hear that many people really talking about it. This might be because some people argue that is useless to talk about because infinity is just a concept that doesn’t exist in real life; it’s not really there, so it hasn’t got that many practical applications. I believe in some ways that’s true but in many ways it isn’t. I think that the infinite does play a huge role in our lives but to get that we need to approach the infinite in a certain way. In this article, I will try to define the infinite and how it plays a role in our life on a very non-spiritual manner. First, we’ll talk about our understanding of infinity. Secondly, we’ll talk about the role it plays in our life, and why we enjoy it that much.

The definition of infinity
Wikipedia describes infinity as a concept describing something without any bound, or something larger than any  natural number. Wikipedia describes infinity as a “something” and many people approach infinity like it is a certain type of number. “From here to infinity” also implicitly defines infinity as a certain end, a static number. But I believe that is not really what infinity really is. I think that infinity is more of a process than an actual outcome. Something that moves will never (or ever) reach infinity, but it might get stuck in a process towards infinity. This process is happening with things that get stuck in a loop, useless machines for example are machines that get stuck in a loop, and if they don’t run out of their battery, they will go on forever (for an infinite amount of time). This also accounts for perfectly looped GIF’s( look at this Reddit page), or manipulated fractal zooms like these. But some infinite processes don’t really start over, they go on and on but never reach an end. Zeno’s Achilles and the Tortoise is a good example that is often used to explain infinity.  The example goes as follows, copied from: Slate.com

“Achilles, the fleet-footed hero of the Trojan War, is engaged in a race with a lowly tortoise, which has been granted a head start. Achilles’ task initially seems easy, but he has a problem. Before he can overtake the tortoise, he must first catch up with it. While Achilles is covering the gap between himself and the tortoise that existed at the start of the race, however, the tortoise creates a new gap. The new gap is smaller than the first, but it is still a finite distance that Achilles must cover to catch up with the animal. Achilles then races across the new gap. To Achilles’ frustration, while he was scampering across the second gap, the tortoise was establishing a third. The upshot is that Achilles can never overtake the tortoise. No matter how quickly Achilles closes each gap, the slow-but-steady tortoise will always open new, smaller ones and remain just ahead of the Greek hero.”

The reason why Achilles can’t overtake the tortoise is because the movement of both the tortoise and Achilles is depended on each other.  Achilles “only” comes closer as the tortoise moves further away, so when both factors influence each other with these limits, they end up in an infinite lasting chase. Within (almost) each infinite there is a thing that goes forward (like the process you follow), but this thing gets pulled back to the initial position, and the process starts all over again. So the infinite has at least two processes involved, one thing that seems to go forward, and another factor that puts that same thing backward to its relative starting point on that relative scale. The forward- and backward process need to be proportionate to each other to create the actual infinite loop. For example, if you take a piece of paper and cut that in half, then you cut that new paper in half again, and so forth, you could go on with cutting until infinity (in a theoretical world). So here, with each cut, you zoom into the new piece of paper, then you zoom into the new piece of paper, and so forth. With the cut, you are doing the forward process, but once you zoom in, you are brought back to the original starting position. The cutting and the zooming are depended on each other and sustain the process, making it ever lasting.

The infinite in religion
The fact that the infinite is ever lasting gives it something magical. In many religions the infinite and the loop are represented in some form. The God of infinite wisdom, Ying and Yang, Karma, Ouroboros (the snake that eats his own tail), and reincarnation are some examples of balanced entities/parts that hold an infinite/loopy relation with each other. Although religion is a huge aspect of many lives, I won’t go into the details but I just want to say that the infinite plays a role in some form for many different people across the world. I rather keep it more down to earth, very real and in front of our eyes. I see the infinite omnipresent in nature and in our own daily lives.

The infinite in society
In our lives, there is no real infinity present, but I believe there is a desire towards reaching infinity. People try to achieve infinity by “closing the loop”. Although this is a common saying, it holds quite some truth to it. Closing the loop is often used in circular economy to sustain the value of the products and services we use by reusing old material, and not wasting anything. The Lion King framed it different with naming it “the circle of life”, and focusing it on the balance in nature. In eco systems for example, predators (like humans), prey and plants sustain each other existence through interacting with each other. Imagine you have foxes and bunnies, the foxes eat the bunnies, but when there are too little bunnies, the foxes will die, resulting in more bunnies, more room for foxes, less bunnies, and so on. They put each other forward and backward over time. Many species have co-evolved for millions of years through similar roads. In biology, this is called the Lotka Volterra model if you want to read more about it.

The infinite in our life
If you question yourself; why do you eat, work, sleep, and play? It is hard to answer those because they are so automatic, but all these activities are a form of self-sustainment. Most of us just want to be on this world. There are many loops in our life that contribute to our self-sustainment. When we close our eyes, we want to open them again, when we consume energy, we want to burn it again, when we invest energy, we want it to be returned to us again, when we hug someone, we want a hug back. Of course, some people perform activities which are above self-sustainment, and others are below it, but each activity comes down to a relative closed loop. When we look at development, we see ever changing and repeating loops. Every action we take in our environment provides us with feedback that we can use to learn. When we touch a fire, we get feedback of pain, and we won’t do it again (ending the loop). But when we grab fruit that’s delicious and nutritious, we’ll do that again. Through iteration (trial and error), we learn about our world and that helps us in sustaining ourselves. Failing actions will die of, while successful actions will iterate and loop. Successful actions that gain positive feedback are often actions we (are willing to) repeat, like wearing clothes, washing ourselves, and celebrating birthdays. These loops of behavior are so ingrained in our lives, that we hardly think about them while doing them. But you could wonder however, where do we loop/iterate towards?

Where do we loop towards?
Then, we get to difficult questions. How old do you want to become? What is your goal of life? For these questions, there are no concrete answers. I believe is that we don’t really have answers for this because life is an infinite journey. There is no age where most people really would like to die. After finishing your goals, new goals always emerge. When you try to solve something, new problems always emerge, the more you learn, the less you know, and so on and so on. Life is a process of zooming and zooming and never really finding the end where you are done with everything. There is always something new to discover and to find out. The universe is infinitely large, there is no way to read all the books there are, or learn everything about the basic things around you. I like to see our cognitive growth as a growing tree where the branches represent the paths we’ve discovered (iterated across), our largest branches have many small branches attached to it, which represent the “specialist details” that are only known for the ones who really dive into these details. A visual presentation is shown in the picture below. Of course, there are some states where people are done with living, being fragile and old or deeply depressed. But these are states where the imbalance between the self and the environment is too much, where there might be no return of all your investments or a complete detachment from the environment, limiting your growth.

Fractals
If you visualize looping processes over time that reach on until the infinite, we come directly to fractal structures. Fractals are iterative formulas that loop until infinity (or a certain scale) and thus continue with growing. If the increment of the growth is not too much, you will see aesthetic structures emerge. Although not many people know it, fractal structures are all around us in nature, trees grow fractal, mountains have fractal structures, many plants show fractal properties, and even own body is full with fractals. Our lungs, veins, limbic system, and brain grow fractally. There is a certain end to it because of natural limitations, but in its essence, fractals grow and grow on each level. You can argue that fractals are aesthetic to our eyes because they represent the actual infinite that we are all longing for, but you can also argue that we like to watch them because our eyes are evolved to process light in a fractal manner, making them smoothing to our brain. Anyway, in daily life we don’t see that many fractals anymore because we tried to distinguish ourselves from nature by isolating ourselves and making straight geometric lines and corners in our houses and the objects we own. But there is a trend backward to nature. We now get inspired by nature in making our buildings, ergonomic “natural” shapes, and use nature to come to rest. There is also a lot of science showing that sights of nature in offices reduces stress and in hospitals fasten recovery ( source). Therefore, it is no surprise that biophilic design, biomimicry, generative algorithms, is an emerging area in our society, we need to get back to nature a little bit.

Conclusions
Perceiving the infinite as a process makes a lot of sense for understanding why it’s such a fascinating concept that spread across all religions. If you see the infinite as an ever-repeating looping moving forward, like a fractal, you can see it emerge all around you, in your own behavior and in nature. The question still remains where this infinite process heads towards. As many intelligent people have mentioned before me; life is a music piece that is not really heading somewhere, it is the process of life itself that makes it beautiful. When you start to perceive every act as an (Kantian) “end” instead of a mean to getting somewhere, you don’t actually get somewhere, you are already there. The infinity is than the certainty that it will go on, the loop is every action you take in relation to the environment. The loop needs to be balanced to go on, so one could always take different paths if desired, making different trees. The relation between you and your environment will never be a perfect loop, as you learn from the interactions and have memory that supports your development, making each loop slightly different but similar. Your “tree” will be slightly chaotic, like a strange attractor, but I hope ever growing!