Featured Post:
I finally found the equation I’ve been circling toward for a long time. Every aliasing insight, every geometric recursion, every strange perceptual “shift” kept collapsing toward the same structure. Eventually you realize there has to be a mathematical way to describe consciousness that matches how it actually behaves.
The real axis corresponds to the rendered world.
The imaginary axis is the interior: concepts, memories, counterfactuals, the “shadow versions” of things. It’s simply what awareness does with objects.
the umbrella as the physical thing → x
the umbrella as the idea of the thing → ix
the umbrella perceived in the “negative” or absent sense → i²x = –x
That rotation into the imaginary direction is the geometry of how the mind handles presence, absence, and interpretation. And because the imaginary axis opens onto the full complex plane, every rotation passes through the same fractal-chaos structure you see in mathematical iteration — the same branching, sensitivity, and self-similar distortions that show up internally when memory, imagination, and perception start mixing. It’s literally the same mathematics.
And the reason it works is that experience doesn’t live on clean, perpendicular dimensions.
There are no true right angles in consciousness.
Every axis leaks into the others — sensation into memory, memory into imagination, imagination into emotion, emotion into perception. So the geometry has to be curved, not rigid. What looks “orthogonal” in logic becomes slanted, blended, and intertwined in lived experience.
The projection term is what selects a frame within that curved space.
It’s the operation that decides which directions appear independent and which ones collapse together. That’s the mechanism by which perception stabilizes a world: a dynamic choice of basis that keeps the field coherent long enough to render objects, relationships, and meaning. The reciprocal term is the anchor.
It’s the inversion that pulls every rotation, distortion, and imaginary excursion back toward a single reference point — the observer. That’s the actual geometry behind the idea of a center being everywhere: the field’s inversion point is always wherever perception is happening. The “self” isn’t located inside the brain; it’s the fixed point of the mapping. Everything folds toward it, no matter how far the rotation goes.
When the equation refers to a “state-vector,” it’s not a thin arrow in space.
It’s a whole high-dimensional register encoding the entire local state of consciousness — sensory components, emotional tones, spatial cues, conceptual associations, intention, memory, ambiguity, anything that defines the moment.
The basis is the library of all possible degrees of freedom; the state is the tuple across that basis.
That’s why the model generalizes.
Once the coordinate system is defined, the field doesn’t care whether the phenomenon is a sound, a memory, a taste, a physical object, a fear, a flash of intuition, or a Cheeto.
It only cares where the state-vector sits and how the mapping transforms it.
The result is a single field with real and imaginary components, curved geometry instead of rigid orthogonality, a projection that selects the perceptual frame, a reciprocal symmetry that locks everything back to the observer, and a natural account of why consciousness feels unified even though its components are wildly multidimensional.
All Posts
