A Mathematical Rabbit Hole
Looking at Numbers Through a Poetic Lens
Recently, while daydreaming, I stumbled upon a rather harmless question.
So harmless that it almost feels silly:
What is a number?
Not in the textbook sense. Not “7 is greater than 6.”
But in a very practical way.
The way numbers actually show up in everyday life.
Doesn’t every number always come with a piece of matter attached to it?
I have seen a 7 on paper.
A 7 as pixels on a screen.
I have heard a 7 as sound waves.
I have thought a 7 as neuronal impulses.
I have encountered a 7 in the memory of a computer.
But the number itself?
Where is it, really?
And this is exactly where my small fall into a mathematical rabbit hole began.
The First Strange Observation
Every number we ever encounter always arrives with something material.
It has a voice.
Or ink.
Or pixels.
Or electric charge.
Or neural activity.
This led to a simple, but oddly unsettling idea:
Perhaps every number-in-use always consists of two parts that influence each other.
One part is what we mean — the abstract value.
Let us call it n.
The other part is what allows it to exist — its physical manifestation.
Let us call it x.
So not just “7,” but rather:
(n, x)
A number as a small dual being.
Suddenly, Everything Becomes Strangely Practical
Because now something unexpected happens.
If every number always has a physical side, then not all “sevens” are the same.
At least not in the real world.
A 7 carved into stone survives for millennia.
A whispered 7 may vanish instantly.
A 7 in working memory dies when the power goes out.
A 7 in a blockchain is copied thousands of times.
They all mean the same thing.
But they live very different lives.
And suddenly a question arises:
Is a number that still exists tomorrow somehow “more of a number,” or even “more valuable,” than one that disappears immediately?
At first, this feels wrong.
But the longer one thinks about it, the harder it becomes to shake the question off.
The Rabbit Hole Gets Deeper
Then came the next thought — and that one was genuinely strange.
When the “physical side” of a number is examined more closely, it keeps breaking down:
- ink → pigments
- pixels → electrical states
- neurons → chemical processes
- bits → charges
- charges → physical states
And every time it seems like the bottom has been reached, it goes on.
Like roots.
The deeper one digs, the more branches appear.
There is no final point at which one can say:
“This is now the ultimate physical reality of the number.”
At some point, digging simply stops — not because it is finished, but because it is practically sufficient.
A Curious Insight
At this point it became clear why all of this felt so fascinating.
Mathematics often appears timeless, pure, untouched.
But the moment it is used, it suddenly becomes bodily, fragile, finite.
Perhaps mathematics is not a weightless realm floating above the world.
Perhaps it lives in the world — in brains, machines, symbols, and media.
Perhaps every mathematical truth that is actually used is also a small physical event.
And What Does All of This Lead To?
This perspective does not change how calculations work.
But it changes how one thinks about calculating.
It connects mathematics with:
- physics
- information
- media
- perception
- technology
- time
- impermanence
And it explains things that otherwise seem strangely disconnected:
Why computation costs energy.
Why storage matters.
Why errors occur.
Why repetition counts.
Why stability plays a role.
If One Descends Further …
From this small idea, a larger model has emerged, in which numbers are understood as pairs:
(n, x) — meaning plus embodiment.
Within this model, one finds:
- a “root structure” of physical instantiations
- a notion of physical robustness of numbers
- interactions between abstraction and materiality
- and even the question of whether dividing by zero might be not only logically, but physically impossible
Here is the paper on the topic, presented in a more formal and official style: