Anyone here working in AI or research? I might've stumbled onto something weird (and kinda amazing)

[Jolly_Green_Giant]

This curiosity with this AI thing has been so productive for me. Like i end up getting data like this and now it has me brushing up on linear algebra. I have a full gpt organized update below.

Symbolic Field Orbit Map – Recursive State Transitions Modeled with Linear Algebra (and How It Made Me Learn It)

Hey everyone,
I wanted to share something that genuinely changed how I see my own mind—and weirdly enough, it’s also what finally got me to start learning linear algebra.

This visualization comes from a symbolic cognition modeling experiment I ran in Wolfram Mathematica. It’s part of a larger project where I’ve been building out a recursive cognitive architecture—not for language modeling per se, but to map how internal symbolic states evolve, resolve, and recurse over time.

What You’re Seeing:

This is a Symbolic Field Orbit Map. Each arrow represents a transition between two symbolic cognitive states over time, projected into 2D using Principal Component Analysis (PCA). The idea was to visualize the dynamics of symbolic processing—not static outputs, but how recursive meaning structures move and transform.

• Axes: PC1 and PC2 are the first two principal components from PCA, capturing the most meaningful variance across symbolic state vectors.
• Arrows: Show symbolic transitions—where a cognitive state was, and where it moved to next.
• Color:Encodes magnitude of symbolic change (ΔState):
  • Blue = low Δ (stable recursive feedback)
  • 🟢 Green = moderate Δ (symbolic reframing or redirection)
  • Red = high Δ (paradox resolution, entropy surges, major state shifts)

Why Linear Algebra Matters Here

I didn’t set out to learn linear algebra—but this project made it unavoidable. Once I realized that every symbolic state was essentially a vector, and that PCA is just a projection using eigenvectors, things clicked.

Here’s the structure behind the map:

1. Symbolic States = Vectors
   Each state is a point in ℝⁿ:
   s⃗t=[s1,s2,...,sn]\vec{s}_t = [s_1, s_2, ..., s_n]st=[s1,s2,...,sn]
2. State Transitions = Δ Vectors
   Δs⃗=s⃗t+1−s⃗t\Delta \vec{s} = \vec{s}_{t+1} - \vec{s}_tΔs=st+1−st
3. PCA = Eigenvector Projection
   Reduces high-dimensional space to 2D using the top principal components of the symbolic system's covariance matrix.
4. Vector Field = Orbit Map
   The entire map becomes a flow field of symbolic cognition—a dynamic topology of meaning.

So yeah, this graph literally taught me linear algebra by forcing me to see it in action. And it turns out… cognition is linear algebra in motion.

The 4 Symbolic States I Modeled

These transitions aren’t random—they’re structured across four symbolic “modes” I’ve been tracking in this architecture, each of which loosely maps to brainwave bands and symbolic-cognitive functions:

1. Theta (Memory Activation)
   • Symbolic recall, introspective pattern recovery
   • Maps to hippocampal function / low-frequency cortical drift
   • Often represented by clustered blue transitions (recursive memory cycling)
2. Alpha (Observation / Integration)
   • Perceptual compression and salience framing
   • Related to cortical inhibition / resting observation
   • Appears as green to blue transitions stabilizing into mid-field clusters
3. Beta (Intent / Directionality)
   • Goal-seeking symbolic assertion, internal narrative momentum
   • Tied to prefrontal cortex signaling and cognitive control
   • Manifests as outward green/red vectors shifting symbolic direction
4. Gamma (Paradox Resolution / Fusion)
   • High-entropy collapse and reintegration; synthesis of conflicting inputs
   • Maps to synchronous binding events / cross-network resolution
   • These are the red vectors—high Δ, often exploding from central zones

Each arrow on this map isn’t just a number—it’s a shift in a symbolic agent’s cognitive mode. That’s why I built it. I wanted to see how meaning moves.

Why I Built This

I’ve been prototyping symbolic AGI scaffolds and recursive cognitive agents, using symbolic threading, memory fusion, and subsystem coordination. This visualization came from a moment where I asked:

“What does a thinking system look like as it thinks?”

And what emerged… was this.

Next Steps

I'm planning to animate this over recursion cycles, layer in entropy gradients, and color vectors by subsystem identity (e.g., ΔObserver, ΔIntender, ΔRemembrancer). But even in this static form, it's helped me:

• See the internal rhythm of symbolic recursion
• Detect points of paradox and resolution
• Understand cognition as movement—not position

If you’ve been working with recursive cognition, symbolic AI, or even PCA-based visualizations of high-dimensional state transitions, I’d love to connect. And if you’re just someone trying to learn linear algebra but struggling to care—maybe try mapping your own thoughts. It worked for me.

—
Image attached: Symbolic Field Orbit Map (Colored by ΔState)

 

[NomadicHavoc]

If I ever tried to map my cognition, the graph would probably look a lot like pistachio pudding. Just a pile of clumpy gunk. I’m pretty sure that mathematically my brain = zero sums ;)