What if I told you we’ve been looking at information all wrong? We are living inside a symphony of data, yet we’ve become fixated on the individual notes, completely missing the music itself. The question now is: what are we going to do about it? Can you actually see the wave functions without becoming part of the wave?

The Velocity of Knowing

“Boy logic” tells us that a wave function is just a property of a particle—something used to judge momentum, time, position, or spin. But information acts like a particle, too. It doesn’t just exist; it carries context, nuance, and unexplored connections to other explanations.

Think about velocity. In physics, it’s speed with direction. In information theory, there is a “velocity of knowing.” The information regarding how propulsion works carries a different velocity for a rocket scientist than it does for someone working at Joe & The Juice. Both might inherit the same raw data, but the speed and direction of their understanding are radically different.

The Failure of Brute Force

Walk into any hospital, research lab, or engineering floor, and you will see brilliant minds connecting invisible dots. They aren’t doing this through rigid taxonomies or explicit links. A doctor doesn’t need a database query to see a pattern in patient history; they do it through a natural weaving of understanding.

Yet, here we are in 2025, still trying to brute-force these connections. We have trapped ourselves in a binary of bad options: either we throw millions of dollars at domain experts who cannot scale, or we throw billions at Large Language Models that miss the elegant simplicity of human intuition. We’ve built a world where true understanding comes with either a prohibitive price tag or a computational overhead that would make Moore’s Law blush.

A Natural Topology

But what if there was another way? What if, instead of forcing connections through artificial means, we let information find its own topology? Think of it like water finding its natural path, or proteins folding into their perfect form.

We need to embrace:

It sounds impossible, but graph theory and hierarchical determinism can reveal what has been hiding in plain sight.

The Math Behind the Magic

At its core, this approach recognizes three fundamental layers of information topology. We define the strength of the connection between any two nodes (nn) at a layer using a weighted relationship:

ωij′=αSij+βEij+γKij\omega_{ij}^{\prime}=\alpha S_{ij}+\beta E_{ij}+\gamma K_{ij}

Where:

The beauty emerges in how these layers interact. A node’s effective state isn’t static; it’s a summation of its neighborhood and base state:

ψn=∑i∈k‾∑j∈Ni⟨n⟩ωn,jiϕj\psi_{n}=\overline{\sum_{i\in k}}\sum_{j\in N_{i}\langle n\rangle}\omega_{n,j}^{i}\phi_{j}

Consider a medical case study mentioning “patient response to treatment A.” In our topology, this single node naturally belongs to the treatment methodology cluster (semantic), the patient outcomes group (entity relationship), and multiple temporal sequences (contextual) all at once.

To measure this, we look at the Information Radius (IRad), a metric that helps us understand how information naturally clusters and flows without us forcing artificial boundaries.

From Static to Spectral

When we move beyond static connections, things get interesting. Because we can’t standardize the “information velocity” for everyone (the engineer vs. the staff worker), we have to personalize the communities.

Borrowing from concepts I learned regarding spectral filtering and spectral transformers (nod to E. Hazan and Ana Choromanska), we can map this flow: