It’s taken me some time to understand this concept. How could one infinity be larger or smaller than another. And, for me, it comes down to how you think about the kind of infinity you are exploring.
A countable, organizable infinity, might look like…
1, 2, 3, 4, 5, 6, 7, 8, etc… ad infinum (badumtiss)
or
2, 4, 6, 8, 10, 12, 14, 16, etc.
The parts of this infinity can be categorized, organized, in order, it’s a clear, linear sort of infinity.
The second infinity, is uncountable, or unorganizable.
The example that finally got through to me, was think of all the numbers between zero and one.
0.1, 0.01, 0.001, 0.123456…, π-like decimals, etc.
There are:
numbers that go on forever
numbers with no repeating pattern
numbers you could never finish writing
No matter how you try to count, or organize these numbers between zero or one, there will always be some missing.
Like trying to catch mist with a butterfly net.
Another way to think about it, might be, like a library. If a smaller infinity is infinite books (Book One, Book Two, Book Three, etc), you still couldn’t capture infinite stories with infinite books.
You cannot capture a bigger infinity with a smaller one.
The countable vs the uncountable.
A bigger infinity, an uncountable infinity, allows you to take something from it, and I’ll make something just slightly different from everything you just did. And that “slightly different” thing will always escape what you thought was a captured infinity.
Art is an uncountable infinity. The possibilities are endless. That’s why I love it. That’s why I explore it.
Chasing infinity.
And maybe this is where it started to matter to me.
Not just as math, but as a way of understanding why things begin to feel the same.
Why a room full of paintings can blur together. Why ideas collapse into categories. Why systems—no matter how complex—start to repeat themselves.
Because we are always trying to take something uncountable and make it countable.
To list it.
To organize it.
To name it.
And in doing so, we compress it.
There’s a concept from information theory—Shannon entropy—that describes how many possible states something can have.
Low entropy: predictable, ordered, compressible.
High entropy: many possibilities, harder to pin down.
The uncountable feels like high entropy.
Not chaos, exactly, but possibility that refuses to be fully organized.
And this is where something else clicked for me.
What we often call “noise” might just be what escapes our list.
The part that doesn’t fit. The variation we didn’t account for. The thing that shows up and makes us pause.
Not error.
Not failure.
Just… uncounted.
In a network—whether it’s a brain, a community, or even a body of work—there’s always this tension:
Between what is known and stabilized, and what is still possible.
Too much structure, and everything starts to look the same.
Too much noise, and nothing holds together.
But somewhere in between—that’s where something new can actually happen.
Maybe consciousness itself sits there.
Holding patterns long enough to recognize them, but loose enough to let something else slip in.
A thought that doesn’t quite belong.
A connection you didn’t expect.
A shift in how you see something you thought you already understood.
And art—at least the kind I’m interested in—isn’t about capturing infinity.
It’s about staying close to the edge of it.
Letting just enough of it through that something feels alive again.
You cannot capture a bigger infinity with a smaller one.
But you can stand near it.
And sometimes, if you’re paying attention… you can feel when something escapes.
Not everything that escapes is lost.
Some of it is trying to show you what doesn’t fit yet.
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