Loop and Non-Infinity
Chapter 1: Is Infinity Really Infinite?
The word “infinity” has been with us since childhood.
In math class, we’re told numbers go on forever. In science shows, the universe keeps expanding. In philosophy, the soul is said to be eternal. Even when we speak of “eternal love,” we are emotionally projecting the idea of infinity.
Infinity seems natural and everywhere.
But have you ever seriously asked yourself: “Does infinity truly exist?”
Or is it just a concept we use when we face things too big, too far, or too hard to understand? When we can’t imagine what happened before the universe began, or what comes after it ends, we often just say, “It’s infinite.” As if that ends the question — and makes it no longer our concern.
In this chapter, we’ll look at “infinity” again from different angles — everyday life, math, science, and philosophy.
The doubt toward infinity isn’t new. Even in ancient Greece, Aristotle already said there’s a difference between potential infinity and actual infinity. He believed actual infinity doesn’t exist in the real world — it’s only a logical idea. In modern times, thinkers debated Cantor’s theory of infinite sets. Some “finitists” pushed back, saying infinity is only a math tool, not a real thing. Even in Eastern thought, Laozi said, “Reversal is the movement of the Dao,” which also points to cycles and limits.
Inspired by these ideas, I propose a new way of seeing reality — a theory I call Non-Infinity Theory — a fresh perspective on an ancient debate.
1.1 The Illusion of Infinity in Daily Life: Cycles Can Fool Us
Imagine standing by the ocean, watching wave after wave roll onto the shore.
You might say, “The waves are infinite.”
But let’s look deeper. Each wave has a beginning and end. Waves are caused by wind and the moon’s gravity. And one day, even the Earth will end — and the waves will stop.
We call it “infinite” because we’re only watching for a short time. We don’t see the full cycle. So we assume it never ends.
We do the same with the changing seasons, the ticking of a clock, and the spinning of the Earth. They seem to go on forever — but each cycle has a clear start and end. These endpoints reconnect to form loops. That looping creates an illusion of infinity.
This is what I call the illusion of infinity in limited cycles. Because our senses and time frames are limited, we easily mistake repeated or ongoing things as “infinite,” even though they are not.
1.2 Is the Universe Truly Infinite? Or Just Beyond Our Observation?
When we look up at the stars, we often ask: “Does the universe have an edge?”
Some scientists say the universe is finite but without boundaries — like the surface of a sphere, limited in size but with no edge to fall off. Some theories say the universe may expand, then shrink back, in a big cosmic loop. Even in the idea of an “ever-expanding universe,” scientists admit that what we can see is limited, because the speed of light limits how much information can reach us.
So we return to a deeper question: when we say “infinity,” are we just using a placeholder for “we don’t know where the edge is yet”?
That means “infinity” might just be a sign of our limits — not the universe’s. This will be one of the key ideas repeated throughout this book.
1.3 What Is Non-Infinity Theory? A Difference Between Concept and Reality
Based on all this, I propose a simple idea:
Non-Infinity Theory: Everything in the universe, whether it looks cyclic or not, is finite. “Infinity” is just a feeling or illusion caused by how limited our observation or thinking is.
This doesn’t mean the word “infinity” is useless. It just means we need to rethink its role. Infinity is a temporary guess we use when facing the unknown — when we can’t experience or measure the end of something, we fill the gap with “infinity.” It’s a projection, a way to describe areas we haven’t reached yet, not the areas themselves. And it is a concept in our mind, not a real thing in the physical world.
So Non-Infinity Theory isn’t a final answer. It’s an invitation — to question what we take for granted, and to rethink the difference between abstract ideas and actual reality.
1.4 What Games Can Teach Us: Complexity Isn’t Infinity
To help explain this better, let’s look at two common games.
Soccer — Looks Infinite, But Isn’t
Imagine a professional soccer match. 22 players, 90 minutes, high speed action. So many passes, goals, decisions. From the outside, it seems like infinite possibilities — no two games are ever the same.
But is it really infinite? The field size is fixed. The number of players is fixed. Human bodies have limits. The rules forbid many actions. So actually, every second of play fits into a system with huge but countable combinations. It’s very complex, but not truly infinite. We feel it’s infinite only because it’s too big for us to track.
PAC-MAN — Simple Map, Countable Paths
In the old game PAC-MAN, the map is fixed, you can only move up, down, left, or right, and the enemies move by preset rules. You may feel there are many ways to play — eat pellets, run from ghosts, gain points. But in truth, if we had enough time and computing power, we could list every possible path and outcome. That’s not infinity — it’s limited paths in a complex system.
Even a game like tic-tac-toe has only 19,683 total board combinations, and just 5,478 valid endgames if following the rules. Players may feel free, but the system is still closed and countable.
Now let’s return to soccer. Doesn’t it look like a giant version of PAC-MAN? The “map” is the field, the “characters” are players, and movement is limited by physics and rules. It’s more complex than PAC-MAN — but it’s still inside a framework.
We only think it’s infinite because it’s too much to calculate in real-time. In the 1700s, people thought the universe had no end. Now, science tells us it might be finite but very large — and that’s different.
This is exactly what Non-Infinity Theory says: most things we call “infinite” are just complex finites that we can’t fully count. In math, this is called a combinatorial explosion — when a small number of variables creates a huge number of combinations. The system blows up in complexity, but is still finite.
1.5 The Truth About the Infinite Hotel: Potential Infinity vs. Actual Finiteness
The Classic Story: Hilbert’s Infinite Hotel
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In math and philosophy, there’s a famous thought experiment called “Hilbert’s Infinite Hotel.” Imagine a hotel with infinite rooms — Room 1, Room 2, Room 3, forever — and every room is full. A new guest arrives. The manager doesn’t turn them away. Instead, he asks every guest to move to the next room: Room 1 moves to Room 2, Room 2 to Room 3, and so on. Room 1 is now free.
Even if an infinite number of new guests arrive, the manager can still fit them all — by moving each guest in Room n to Room 2n, leaving all odd-numbered rooms free.
It sounds impossible, but mathematically it works. This is the strange nature of what we call “countable infinity.” It doesn’t match our everyday thinking, but it’s logically consistent.
The Challenge from Non-Infinity Theory: Is the Hotel Really Infinite?
From a math view, Hilbert’s Hotel is a perfect logical game. But from a non-infinity view, it’s more like a mental illusion.
Imagine the hotel opens just three days before Earth is destroyed. Even if it has “infinite rooms,” its actual time to function is limited. No one can ever use all those rooms. When the hotel closes, its “infinity” ends with it. What we really mean is “potential infinity” — not something that can ever be fully experienced in reality.
This type of infinity has no physical existence. It’s a structure created by language and math. In reality, everything still depends on beginnings, endings, and limited time.
The Power of Language
When we say “infinite rooms,” are we describing something that actually exists? Or are we simply talking about what’s possible in language?
We can say “Room 1, Room 2, Room 3…” forever in words, but we can’t actually walk to all those rooms. Just like we can say π goes on forever, but we’ll never write out all its digits. We know it’s infinite in concept, but we can never complete that infinity in real life.
Galaxies may be countless, but they are still part of a limited, observable space. Time may feel endless, but we only live moment by moment. Hilbert’s Hotel is like a kaleidoscope — endless on paper, endless in the mind, but not endless in the physical world.
If Earth Ends Tomorrow, Does the Hotel Still Exist?
This question isn’t just about the hotel. It’s about infinity itself. If the hotel never gets to host an infinite number of guests because Earth ends too soon, then “infinite rooms” is just a potential idea, not a real thing.
From the non-infinity view: infinity is not something that exists — it’s a concept that might go on and on, but never gets completed.
1.6 Infinity in Mathematics: A Tool, Not a Thing
Mathematics is one of the first places where humans explored infinity. Take this simple example:
1 ÷ 3 = 0.333…
That repeating 3 goes on forever. But does it really “exist”? Mathematicians will tell you: the infinite 3s are not a physical thing, but a way to express a concept. It’s not that there are “really” infinite 3s — it’s just the clearest way to show this number.
Here’s another example: π = 3.1415926535…
π never ends, and its digits never repeat. But those digits don’t exist somewhere in space. They are a result of logic and math we use to describe the ratio of a circle’s circumference to its diameter. Infinity here is not a thing — it’s a method.
It’s like dividing a ruler forever. In reality, no one actually cuts a line into infinite pieces. All math is done in finite steps. Infinity isn’t something we can reach — it’s the process of getting closer to a certain limit.
1.7 The Illusion of Infinity: The π Computer and the Cyclic Universe
We’ve talked about how “infinity” is often just a label for things that feel too big or too complex to grasp. But can mathematical infinity truly exist in the real universe? Let’s explore this with one final thought experiment.
Where Math Meets Reality
From school onward, we learn that math includes infinity. Numbers go on forever. Lines can stretch endlessly. π is infinite and non-repeating. In pure math, these ideas are elegant and consistent.
But when we try to apply them to the physical world, problems arise. Everything in the universe — time, space, energy, matter — seems to have boundaries. The universe had a beginning and may one day have an end. Every event happens in limited time and space. Matter is made of finite particles. Can mathematical infinity really be part of this kind of universe?
It’s like a video game with a “limitless” world. In theory, you can keep exploring. But in reality, the game engine and your computer’s memory set limits.
The π Computer: A Test of Infinity
Let’s imagine an ultimate test. Right after the Big Bang, a perfect machine is created somewhere in the early universe — a “π Computer.”
This machine is indestructible. It never runs out of energy. Its only task is to calculate the digits of π forever: 3.1415926535… It saves every digit it finds and never stops.
This seems like a perfect case of potential infinity — an endless process that never finishes. It represents any process in the universe that seems to go on forever. But can it actually become infinite?
The Universe’s Answer: End and Restart
Now let’s bring in the heart of Non-Infinity Theory: the universe is probably not a line that goes on forever. It’s more like a loop — a cycle with a beginning, middle, and end. After the cycle ends, the universe resets into a still, quiet state — nothingness. Later, this nothingness might explode again into a new universe.
So what happens to our π Computer? No matter how powerful it is, the computer still depends on the universe to exist. When the universe resets, the machine, its energy, and all its data vanish. The moment the universe loops back to nothingness, the machine is erased. All the π digits it found are gone. It has to start over in the next cycle — if it ever comes back.
The Real Lesson: Infinity Isn’t a Thing
This shows us some deep truths. Infinity can never be completed in real life — even if a machine calculates π forever, it can’t reach “all the digits,” because the universe itself is limited. Every cycle, it can only get to a large but still finite number of digits. Potential infinity is always stopped by actual finiteness — a process might go on and on, but it will always be ended by something bigger, like the universe restarting. And the universe defines all limits — no matter how powerful our tools or how grand our math ideas, everything in the physical world is bound by the rules and limits of this universe.
Even if we treat π as a purely mental idea — not a machine, but a thought — it still depends on the mind thinking it, and the universe holding that mind. Once the universe ends, so does the thought. The infinite idea gets reset with everything else.
So when we talk about infinity, we should stop treating it as a real, eternal thing. It’s a useful picture of our minds — a process we imagine but never finish. In a looping, finite universe, infinity is just a beautiful illusion we can never fully hold.
This doesn’t make math less powerful. In fact, it shows how amazing math is: it lets us imagine perfect things that the real world can’t contain. But like dreams aren’t reality, mathematical infinity might only be a tool of language — not a feature of nature.
Someone might ask: “Even if the universe resets, can’t the π Computer just keep going next time?” But in each reset, all data is lost — like waking from a dream and forgetting everything. No matter how many digits it calculated, they’re gone. This isn’t a rejection of infinity. It’s an honest recognition of the limits of our minds and the universe we live in.
Before we move on, take a moment to think: you have experienced things that seemed “infinite” — but were they truly endless, or just too vast for you to see the edge?
