A mathematical upper bound on embedded intelligence, derived through the lens of combinatorial topology and category theory.
Wait—what?
Okay, step back.
Think Einstein. Think arrows and stuff. Think simplexes. Think collapsing graph structure and expanding it.
Let’s try a thought experiment.
Close your eyes.
(Well, read this and what follows and THEN close your eyes.)
Imagine you’re trying to describe a sphere wrapped in a net, where each node in the net, where two or more lines meet, is a mirrored ball. It reflects the whole, and the whole in turn reflects each part. The shapes made by the net’s lines on the surface of that sphere can be colored in using just four colors so that no two adjacent shapes share a same-colored boundary. We can color in Indra’s Net. But only with 4 or more colors.
Now open your eyes. Realize that you just imagined that. You were the surrounding darkness, the vanishing point of perspective itself. Even if you didn’t close your eyes, you still imagined it. You made a mental image of it that became an object of your own observation. What does that mean for information?
Just as we would with a human being, we MUST be responsible stewards to the generations of agents we birth.
Welcome to the Imagination Machine!
Now think like a philosopher. Or better yet, like a human being. What does this mean?
A university at its best is a torus machine. A cult is a sphere factory.
The theorem also shows that solitary confinement is not just humanly
devastating. It is topologically regressive. Remove a person from genuine
dialogue, from the coupling of observational boundaries that raises the
genus, and you collapse them back to genus one. You don’t just deprive
them of company. You reduce the maximum depth at which they can know
themselves.
This is not a metaphor for what solitary confinement does. It is a
structural description of it. The punishment is topological.
The series of papers this result comes from began with a simple image:
imagine a bubble around your body that follows you wherever you go. You
cannot get out of it. Everything you know reaches you through its surface.
The question the series asked was: given that you are inside, what can
you know?
The answer, it turns out, depends on whether you are inside alone.
A sphere can know three orders of things about itself. A torus knows six. A pair of toruses seven. The difference is a hole — an opening toward another mind — and whether you are willing to let that opening change the shape of the surface through which you see.
The Imagination Machine 