Based on The Immeasurability of Non-Existence Hypothesis
I’ve been thinking about infinity.
Not because I’m trying to count to it. I have better things to do with whatever time I have left.
But because something about infinity has always bothered me.
We speak about it with extraordinary confidence.
Infinite space. Infinite time. Infinite possibilities. Infinite love.
We throw the word around as though we’ve visited infinity, taken a few measurements, and returned with photographs.
And apparently, everyone agreed that it exists.
But I have a question.
Who measured it?
I don’t mean who invented the symbol. I don’t mean who developed the mathematics. I mean who established that something actually exists without an end.
Because there’s something strange about claiming that something exists while simultaneously claiming that it cannot be completely measured.
And the more I think about it, the more I wonder whether infinity is something we’ve discovered or simply something we’ve invented to explain what we haven’t discovered.
Maybe infinity isn’t a property of existence.
Maybe it’s a confession about the limitations of our understanding.
And perhaps we’ve mistaken that confession for a discovery.
The problem with nothing
Before I can explain why I question infinity, I have to explain something else.
Nothing.
Which is already a ridiculous place to begin.
How do you explain nothing?
The moment I describe it, I’ve given you something to consider.
If I ask you to imagine nothing, you might picture an empty room.
But that’s not nothing.
There’s a room.
Remove the room.
Now perhaps you’re imagining darkness.
But darkness is something we can identify.
Remove the darkness.
Maybe you’re imagining an endless black space.
Well, congratulations. You’ve invented space.
We’re remarkably talented at filling nothing with something.
Even when we’re trying not to.
But here’s what interests me.
If something doesn’t exist, what exactly are we supposed to measure?
We can measure the absence of something within a defined context. We can say there’s no water in a glass or no furniture in a room.
But those are measurements of existing conditions.
The glass exists. The room exists. The reference exists.
We aren’t measuring absolute nothingness.
We’re identifying the absence of something relative to something else.
And that’s where my hypothesis begins.
Everything that exists must be measurable. Everything that can be measured exists.
Now, before someone runs off to find a ruler, I should explain what I mean by measurement.
Because I don’t think measurement begins with numbers.
Everything we know begins with a reference
Imagine I point toward the sky.
There’s something up there.
You ask me what.
I tell you it’s a star.
I’ve identified something.
I’ve established a reference.
I can describe it, compare it, observe it, or distinguish it from something else.
I may not know its exact distance.
I may not know its composition.
I may not even possess the technology necessary to examine it properly.
But my inability to perform a particular measurement doesn’t mean the star is inherently immeasurable.
And measurement doesn’t require me to be standing there with an instrument.
Something only needs to be measurable in principle.
This led me to a definition that became central to my research:
Measurement is the establishment of a reference that makes something distinguishable within existence, whether through identification, description, comparison, observation, or quantity.
I don’t consider measurement exclusively mathematical.
When I recognize someone’s face, I’ve distinguished that person.
When I describe an emotion, I’ve established characteristics that allow me to identify it.
When I compare two experiences, I’ve created a relationship between them.
Even when I imagine something that doesn’t physically exist, the concept itself becomes identifiable.
A unicorn exists as a concept.
That doesn’t establish the existence of a biological unicorn wandering through a forest somewhere.
The distinction matters.
A representation is not necessarily the thing it represents.
And naming something doesn’t establish that the thing we’ve named exists outside our imagination.
Which brings me back to infinity.
We have a name for it.
We have a symbol for it.
We have mathematical systems that define and work with it.
But does any of that establish that physical infinity exists?
Or have we established the existence of a concept and mistaken it for the existence of the thing?
The four statements that started bothering me
I eventually formulated my thinking into four connected statements.
I want to preserve them exactly as I originally expressed them:
To measure something, it must exist, and if it exists, you can measure it, and if something does not exist, you cannot measure it, and if you cannot measure it, then it doesn’t exist.
That’s the proposition.
I’m not presenting it as an established scientific law.
I’m presenting it as the foundation of a hypothesis I want to investigate.
Because if existence and measurability are inseparable, then something interesting happens when we introduce infinity.
Infinity is commonly understood as having no end or limit.
But how would we establish that something has no end?
We could begin measuring.
We could continue measuring.
We could measure for a thousand years.
And then another thousand.
But every measurement we’ve completed would establish only what we’ve measured.
We would know how far we’d gone.
We wouldn’t necessarily know whether something remained beyond our observations.
And we certainly wouldn’t have established that there was no end.
Not finding a boundary is not the same as establishing that no boundary exists.
That’s the distinction I keep returning to.
Because it seems to me that we have become comfortable confusing the absence of evidence for a boundary with evidence for the absence of a boundary.
And those are not the same thing.
A man walking around the world
Imagine a man who decides to walk until he reaches the end of the Earth.
He packs a bag.
He buys comfortable shoes.
He kisses his family goodbye.
And starts walking.
Years pass.
He crosses mountains, deserts, forests, and cities.
Eventually, after an extraordinary journey, he returns to the very place where he began.
He looks around.
Recognizes his house.
Recognizes his street.
And concludes that the Earth must be infinite because he never found its end.
Now, that would be a spectacular misunderstanding.
The Earth didn’t become infinite because he kept walking.
He was traveling around a finite object.
The possibility of continuing an action doesn’t necessarily establish that the object involved is infinite.
He could circle the planet repeatedly.
Ten times.
A hundred times.
A million times, assuming his knees were unusually cooperative.
But repeating the journey wouldn’t change the nature of the planet.
And that’s what interests me.
An action that can be repeated indefinitely is not necessarily evidence of an infinite physical object.
We sometimes confuse continuation with infinity.
We mistake the absence of an encountered ending for proof that no ending exists.
But what if we’re simply moving within boundaries we haven’t recognized?
What if the problem isn’t the size of existence?
What if it’s the way we’re measuring it?
What if infinity has always been an assumption?
Here’s where I know mathematicians might object.
And they would have legitimate reasons.
Mathematics contains rigorously defined infinite sets and processes. The natural numbers, for example, have no greatest member. That conclusion doesn’t depend on someone physically counting every number.
I understand the distinction.
My question isn’t whether infinity can be defined consistently within mathematics.
It can.
My question is whether mathematical definitions establish the physical existence of infinity.
If I define a mathematical structure that continues without a final element, I’ve established something about that structure.
But have I established that anything in physical reality possesses the same property?
I don’t think those are automatically equivalent claims.
And I wonder whether we sometimes move too casually between them.
We describe the universe as potentially infinite.
We discuss time extending indefinitely.
We imagine possibilities without limits.
But what exactly have we established?
Have we discovered infinity?
Or have we reached the boundaries of our observations and introduced infinity as an explanation for what lies beyond them?
My stronger hypothesis is that physical infinity does not exist.
That everything that exists is, in principle, measurable.
And that what we call infinity may represent an incomplete understanding rather than a property of reality.
I cannot claim to have demonstrated that conclusion.
But I also don’t think our inability to discover an ending should automatically be interpreted as evidence that no ending exists.
There’s a difference between an established fact and an assumption we have become comfortable making.
And comfort has never been particularly reliable evidence of truth.
The strange thing about time
This question eventually led me somewhere I hadn’t expected.
Time.
Because we talk about time as though it’s a substance moving around us.
Time passes.
Time flies.
Time heals.
Time runs out.
Apparently, time is extremely busy.
But what exactly are we measuring when we measure time?
Look at a clock.
Its hands move.
Or numbers change on a screen.
We observe a difference between one reference and another.
We call that duration.
But is duration the same thing as time itself?
I began wondering whether we have mistaken the measurement of duration for evidence of time as an independently existing entity.
A clock doesn’t contain time.
It undergoes physical processes that allow us to establish intervals.
We compare those intervals with other processes.
And we construct systems that allow us to organize experience.
Those systems are extraordinarily useful.
But usefulness doesn’t necessarily answer the deeper question.
Does time exist independently, or are we identifying relationships between events and calling those relationships time?
My hypothesis goes further.
I question whether time exists as an independent thing at all.
That doesn’t mean I’m denying that clocks work or that physical events occur in measurable sequences.
I’m questioning what those measurements establish about the nature of time.
And once I began questioning time, another familiar idea became strangely uncertain.
Change.
Did the seed become a tree?
Imagine holding a seed in your hand.
Small.
Dry.
Almost insignificant.
You place it in the ground.
Water it.
Sunlight reaches the soil.
Days pass.
Then weeks.
Then years.
Eventually, there’s a tree.
Its roots extend beneath the earth.
Its branches reach toward the sky.
Birds settle among its leaves.
And someone points at it and says:
“Look how much that seed changed.”
Perfectly reasonable.
But I began wondering about something.
When did the seed stop being the seed?
At the first root?
The first leaf?
The first branch?
Or have we been observing the continuing existence of something through different states?
We identify one condition and call it a seed.
We identify another and call it a tree.
We compare them.
We establish differences.
And we describe those differences as change.
But what exactly has changed?
The underlying existence?
Its properties?
Its organization?
Our description?
Or some combination of these?
I don’t want to pretend those questions are interchangeable.
A thing can retain its identity while undergoing genuine physical transformation.
But I also wonder whether some of what we call change is actually the revelation of something that was already present.
Think about a Wi-Fi signal.
It may be present in a room even when I cannot detect it.
Then I introduce an instrument capable of identifying it.
Suddenly, I can observe something I couldn’t observe before.
Did the signal change?
Or did my ability to perceive it change?
Those are different events.
And that distinction interests me far beyond Wi-Fi.
How often do we mistake a change in what we know for a change in what exists?
Perhaps not every revelation is a transformation.
Perhaps not every difference represents the beginning of something new.
And perhaps understanding existence requires distinguishing what reality does from what our observations allow us to recognize.
The possibility that nothing becomes something else
This is where my hypothesis becomes particularly uncomfortable.
Because I started wondering whether change itself might be less fundamental than we assume.
What if existence persists while our measurements establish different states?
What if what we call beginnings and endings are sometimes reference points we’ve selected rather than intrinsic boundaries of the thing we’re observing?
A seed.
A tree.
A child.
An adult.
A beginning.
An ending.
We divide existence into recognizable categories.
Then we speak about those categories as though their boundaries necessarily exist independently of our observations.
But perhaps some of those boundaries belong to our descriptions.
Not to reality itself.
I don’t know how far that possibility extends.
I don’t know whether all change could be understood as revelation.
And I recognize that physical transformations are not disproved simply because an underlying identity persists.
But I want to ask the question anyway.
What would count as evidence that reality itself changed, rather than that we discovered something about it that we hadn’t previously understood?
That question has stayed with me.
Because it connects back to the very beginning.
Measurement.
References.
Boundaries.
Existence.
Perhaps the boundaries through which we understand reality are not always the boundaries of reality itself.
And perhaps that’s why infinity has become such an attractive idea.
Whenever we reach the edge of what we can establish, we imagine something beyond it.
Sometimes we’re right.
Sometimes we’re wrong.
But imagining beyond a boundary doesn’t tell us whether what we imagine actually exists.
The arrogance of infinity
I find something almost comical about the confidence with which we discuss infinity.
We’re creatures who struggle to remember where we left our keys.
We forget appointments.
We misjudge distances.
We misunderstand people we’ve known for decades.
We make confident predictions about tomorrow and spend the following week explaining why we were wrong.
Yet somehow, we’re comfortable declaring that something has no end.
Forever.
Never-ending.
Infinite.
Those are enormous claims.
And I wonder whether we’ve become so accustomed to the words that we’ve stopped considering what they require.
If I tell you that a road continues forever, what have I actually established?
Perhaps I’ve traveled an extraordinary distance.
Perhaps I’ve never encountered its end.
Perhaps every available observation suggests that it continues.
But have I established that the road is infinite?
Or have I established that I haven’t found where it ends?
Those are two different conclusions.
And I think we owe ourselves the intellectual discipline to distinguish them.
Not because I want to destroy infinity.
But because I want to understand what we mean when we claim something exists.
I don’t want to confuse the limits of my observations with the limits of reality.
And I don’t want to confuse the limits of reality with the absence of limits.
Both mistakes are possible.
What if everything that exists can be measured?
I keep returning to the same proposition.
If something exists, it must be measurable.
Not necessarily by me.
Not necessarily today.
Not necessarily with any instrument humanity has invented.
But measurable in principle.
Because existence must provide some basis through which something can be distinguished.
Otherwise, what exactly am I claiming exists?
And if something is inherently incapable of being distinguished, identified, described, or established through any reference whatsoever, how would its existence differ from nonexistence?
That’s the question beneath my hypothesis.
It’s also where I recognize a serious philosophical challenge.
Perhaps something could exist independently of whether it is accessible to measurement.
Perhaps reality doesn’t owe us distinguishability.
And perhaps my definition of measurement is so broad that it needs further examination before it can establish the conclusions I’m proposing.
Those objections matter.
I don’t want to escape them by changing the meaning of my original proposition.
I want to confront them.
Because I’m not interested in protecting an idea merely because it’s mine.
I’m interested in discovering whether it survives examination.
And if it doesn’t, I want to know precisely where it fails.
But until then, I remain fascinated by the possibility that infinity is not a characteristic of existence.
That perhaps everything that exists has some measurable nature.
And that infinity is the word we invented when our understanding reached a place it could no longer distinguish.
The last number
Imagine that I spend my entire life counting.
One.
Two.
Three.
I count until my hair turns gray.
Until my hands begin trembling.
Until the people who once knew me have disappeared.
I count every day.
Every night.
I reach numbers so enormous that I can barely comprehend them.
And one afternoon, exhausted, I stop.
Someone asks me whether I’ve reached infinity.
I tell them no.
They ask how close I am.
And that’s when I realize something.
I have no way of knowing.
Not because the numbers I’ve counted are meaningless.
Every number represents something I can identify.
Every step establishes another reference.
But none of those steps tells me that I’ve measured a physically existing infinity.
I’ve measured a sequence.
I’ve established how far I’ve gone.
And perhaps I’ve demonstrated something about the mathematical rules governing that sequence.
But I haven’t discovered an infinite physical object simply by continuing to count.
I look at the enormous number I’ve reached.
Then I look at the world around me.
And I wonder how many other things I’ve called infinite simply because I couldn’t find their boundaries.
Space.
Time.
Possibility.
Existence itself.
Maybe some of them truly have no end.
Maybe they don’t.
But I no longer want to mistake my inability to find an ending for proof that an ending cannot exist.
And I certainly don’t want to confuse the existence of a word with the existence of whatever that word claims to describe.
Because perhaps the most extraordinary thing about infinity isn’t that it goes on forever.
Perhaps it’s that we’ve convinced ourselves we know what forever means.
I put down my pencil.
For the first time in years, I stop counting.
Not because I’ve reached the end.
But because I’ve realized that counting was never going to answer the question I was actually asking.
I wasn’t trying to discover the next number.
I was trying to discover what it means for something to exist.
And perhaps that’s where the real inquiry begins.
If everything that exists must be measurable, what exactly have we measured when we claim that something is infinite?
I don’t know whether my hypothesis will survive that question.
But I intend to find out.
The Question of Infinity is a first-person philosophical essay based on The Immeasurability of Non-Existence Hypothesis by Keu Reyes. Its propositions concerning infinity, existence, measurement, time, and change remain open to formal investigation.