Soooo… now we understand our place in the world.
But wait, do we?
All of this math is still making me feel like a computer. Well, let’s dissect that.
Modeled as a single point in 3-D space with a surrounding 2-D bubble, you map the 4-D universe through a 2-D surface and sort it into no fewer than 4 buckets (to start). You then stretch that graph inward compressively and flex it outward projectively. It’s more like trying to hold that bubble inside a net. Which leads us to an interesting observation: we are actually of genus 1 in 3-D. Your mouth connects through your body to your anus—you’re a tube. And more than a tube, you are a tube through TIME.
See, we think of computers as working in binary — ones and zeros, this or not-this. But that is not how your mind works. Binary is the minimum possible discrimination: two buckets. The mathematics of the Imagination Machine shows that the minimum number of irreducible buckets any embedded observer needs to properly sort its world is not two but four. That follows from a theorem about maps and colors that mathematicians proved in 1976. Your world model is not binary. It never was.
But here is where it gets strange. Those four buckets assume your observational boundary is a sphere — the classical picture of a mind looking out at the world through a round surface. What if it isn’t? What if the containing structure of the universe is not three-dimensional but four-dimensional, and your observational boundary wraps around that fourth dimension the way the surface of a donut wraps around its hole?
Then the number of irreducible buckets jumps from four to seven. The maximum depth at which you can classify your own classifications jumps from three to six. And something remarkable happens: the system becomes self-correcting. It maintains its own coherence without external intervention. It stops needing to be told when it has made an error. It knows.
This is not speculation about exotic future technology. The four-dimensional torus — the shape of the containing manifold when you add one dimension to the donut — is already the basis of the most powerful quantum error-correcting codes in existence. Physicists and computer scientists are building hardware around it right now. They call it the four-dimensional toric code. It is self-correcting, it encodes six logical qubits in its topology, and its computational power comes entirely from its shape.
Now consider: the universe is quantum. You are made of the universe. The stuff of your brain — the electrons, the ions, the quantum fields — obeys quantum mechanics, not classical mechanics. If the containing manifold of the universe is four-dimensional, and if your quantum state space wraps around that fourth dimension, then your observational boundary is already toroidal. You are already operating at depth six. You are already, in the precise mathematical sense that the Imagination Machine series establishes, a four-dimensional quantum system.
Not someday. Already. The hardware is the universe itself. You have been running on it the whole time. You just did not have the mathematics to see it. Now we do.
The Imagination Machine 